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Ken G
2018-Dec-20, 03:21 PM
I think I see some pretty rudimentary errors in his reasoning. Like for example his notion that gas pressure requires a hard surface within the sun to act upon. And that gas pressure is only exerted due to gas in motion colliding with a surface. Its pretty obvious that each atom has a surface in its own right, and can act on its neighbor atom, adding up collectively to gas pressure.I agree with you that the one useful thing about hearing completely wrong physics claims is that it provides a useful device for learning something that might be hard to see in some more regular context. Here is a good example.

A lot of people (even some educated in science) think gas pressure requires collisions, either with a wall or with other particles. This is simply not correct, and it stems from a fundamental misunderstanding what gas pressure is. Particles do not need surfaces to exhibit gas pressure, and they do not need to collide with anything either. It should be noted, though this is not the key point, that most particles interact via forces such that the actual particles never strike against each other's "surfaces" anyway. But much more to the point, gas pressure does not even require interparticle forces. For example, dark matter is thought to involve particles that do not interact with each other at all, except via the gravity of the entire system, and yet dark matter still has gas pressure. In fact, even if dark matter did not experience gravity, it would still have gas pressure. Gas pressure is not reliant on collisions or interactions of any kind.

So what is gas pressure, and how does it push gas around, if it requires no forces between the particles and no surfaces? Gas pressure stems from exactly one thing: the motion of the particles. If you make the single assumption that the particle motions are randomly directed (called "isotropic"), then you have gas pressure, period. This is because gas pressure is simply about the way a collection of moving particles carries momentum around. When you have a "pressure gradient," which means the tendency to carry momentum around is a little greater in one area than a neighboring area, then what happens is momentum gets carried, by nothing but the motion of the particles, from the one area to another. Moving momentum from area A to area B will always look in every way just like a force between A and B, where here A and B are not individual particles but large collections of indistinguishable particles that are interchanging positions all the time. That's what gas pressure is, it is never anything else. When you have a wall, all it means is that the wall provides a force on the gas to balance the momentum that is being transported into it by the gas, because the wall is always assumed to be connected to something that keeps it from moving.

The situation is like when you step on a bathroom scale and say it is measuring your weight, but your weight does not come from the scale-- when weight is defined as the force of gravity on you, you realize that the bathroom scale is not measuring your weight, it is measuring the force the scale needs to provide to balance your weight. It registers your weight, but it is not producing your weight (even though when in freefall, we say you are "weightless"-- our language is often not precise and adds to the confusion of people like Robitaille). So it is with surfaces and gas pressure. Robitaille might as well be saying that if you are not standing on the ground, there cannot be a force of gravity on you-- the logic is precisely the same when he says there is not gas pressure without a surface under it.

So where do collisions come in when there is gas pressure? In one and only one place: they are often needed to keep the motions isotropic. That's it, that's all they do, and when there are other ways to do that (such as in the magnetic fields containing a plasma experiment), collisions aren't needed at all-- they simply have no role whatsoever in gas pressure when they are not needed to maintain the random directions of the particle motions.

Thus it should be clear that Dr. Robitaille does not know the first thing about gas pressure. It is easy to conclude that he also does not know the first thing about almost any other aspect of what a gas is. In particular, he never calculates the single most important quantity in determining if a bunch of particles will act like a gas-- the ratio of their average kinetic energy to their average interparticle (nearest neighbor) potential energy. Whenever that number is very large, you have a gas-- that's what a gas means. (It is very large for the Sun.) So when someone tells you something isn't a gas, and doesn't even know what the definition of a gas is, you should not spend any more time with them-- unless you want to use their foolishness as a vehicle to learn these things yourself.

And atoms dont need to be in kinetic motion to impose gas pressure when gravity is imposing a constant weight pressure.
Actually, as you can see from the above, kinetic motion is the one, and only, thing you need to have what we call "gas pressure". Any system of particles exhibiting random kinetic motions in all directions has an easily calculated gas pressure, you don't need to to know anything about the particles except their speeds and masses. In particular, you don't need to know the history of how the system came to be that way, or any of the details about what is maintaining that system, to understand if it is a gas, and what its gas pressure is. Robitaille needs to stop pretending he understands things that in fact he does not even know the first thing about, but correcting his errors does serve a purpose because some of those errors are rather widespread.

Selfsim
2018-Dec-21, 03:12 AM
... Particles do not need surfaces to exhibit gas pressure, and they do not need to collide with anything either.
It should be noted, though this is not the key point, that most particles interact via forces such that the actual particles never strike against each other's "surfaces" anyway. But much more to the point, gas pressure does not even require interparticle forces.
...
Gas pressure is not reliant on collisions or interactions of any kind.

So what is gas pressure, and how does it push gas around, if it requires no forces between the particles and no surfaces? Gas pressure stems from exactly one thing: the motion of the particles. If you make the single assumption that the particle motions are randomly directed (called "isotropic"), then you have gas pressure, period. This is because gas pressure is simply about the way a collection of moving particles carries momentum around. When you have a "pressure gradient," which means the tendency to carry momentum around is a little greater in one area than a neighboring area, then what happens is momentum gets carried, by nothing but the motion of the particles, from the one area to another. Moving momentum from area A to area B will always look in every way just like a force between A and B, where here A and B are not individual particles but large collections of indistinguishable particles that are interchanging positions all the time. That's what gas pressure is, it is never anything else. When you have a wall, all it means is that the wall provides a force on the gas to balance the momentum that is being transported into it by the gas, because the wall is always assumed to be connected to something that keeps it from moving.

The situation is like when you step on a bathroom scale and say it is measuring your weight, but your weight does not come from the scale-- when weight is defined as the force of gravity on you, you realize that the bathroom scale is not measuring your weight, it is measuring the force the scale needs to provide to balance your weight. It registers your weight, but it is not producing your weight (even though when in freefall, we say you are "weightless"-- our language is often not precise and adds to the confusion of people like Robitaille). So it is with surfaces and gas pressure. Robitaille might as well be saying that if you are not standing on the ground, there cannot be a force of gravity on you-- the logic is precisely the same when he says there is not gas pressure without a surface under it.

So where do collisions come in when there is gas pressure? In one and only one place: they are often needed to keep the motions isotropic. That's it, that's all they do, and when there are other ways to do that (such as in the magnetic fields containing a plasma experiment), collisions aren't needed at all-- they simply have no role whatsoever in gas pressure when they are not needed to maintain the random directions of the particle motions.

Thus it should be clear that Dr. Robitaille does not know the first thing about gas pressure. It is easy to conclude that he also does not know the first thing about almost any other aspect of what a gas is. In particular, he never calculates the single most important quantity in determining if a bunch of particles will act like a gas-- the ratio of their average kinetic energy to their average interparticle (nearest neighbor) potential energy. Whenever that number is very large, you have a gas-- that's what a gas means. (It is very large for the Sun.) So when someone tells you something isn't a gas, and doesn't even know what the definition of a gas is, you should not spend any more time with them-- unless you want to use their foolishness as a vehicle to learn these things yourself.
Actually, as you can see from the above, kinetic motion is the one, and only, thing you need to have what we call "gas pressure". Any system of particles exhibiting random kinetic motions in all directions has an easily calculated gas pressure, you don't need to to know anything about the particles except their speeds and masses. In particular, you don't need to know the history of how the system came to be that way, or any of the details about what is maintaining that system, to understand if it is a gas, and what its gas pressure is. Robitaille needs to stop pretending he understands things that in fact he does not even know the first thing about, but correcting his errors does serve a purpose because some of those errors are rather widespread.Hi Ken;

Just to clarify, a gas molecule has a momentum 'mv' and when it collides with any surface, there is a change in momentum.
This change in momentum is the force exerted on the molecule by the surface, and is given by Newton's second law f = mdv/dt.

The pressure is simply the force per unit area of the surface, and is the sum of all the molecules that change momentum when colliding into the surface, divided by its surface area, no?

Ken G
2018-Dec-21, 05:36 AM
Hi Ken;

Just to clarify, a gas molecule has a momentum 'mv' and when it collides with any surface, there is a change in momentum.
This change in momentum is the force exerted on the molecule by the surface, and is given by Newton's second law f = mdv/dt.
All true, but none of that is gas pressure. You are describing the surface force that appears in the presence of gas pressure, much like the way the force from a bathroom scale when you stand on it is not the same thing as weight.


The pressure is simply the force per unit area of the surface, and is the sum of all the molecules that change momentum when colliding into the surface, divided by its surface area, no?No, that's not what gas pressure is, though it is often erroneously described that way. It's not really so wrong, because you get the right answer that way, but it feeds the unfortunate misconception that pressure has something to do with bouncing off something else-- which it doesn't. Gas pressure is there whenever you have a collection of particles with random isotropic velocities, period. So if you have a surface, then bouncing off the surface can be responsible for the random isotropic motions, but you can have those motions elsewhere in the gas without a surface. For example, inside a balloon, all the air is at the same gas pressure, not just the air next to the surface of the balloon. What you are describing is more like a way to figure out what the gas pressure is, rather than the guts of what the gas pressure is. Think about the bathroom scale analogy, versus the concept of weight. You use the force on a scale to determine the weight, but it's not what weight is, since weight is usually defined as the force of gravity on you (i.e., mg) regardless of whether there is any ground to stand on. Similarly, gas pressure is about how a collection of gas particles carry momentum around, even when there is no surface anywhere in sight. You don't even need the particles to collide with each other to have gas pressure.

Selfsim
2018-Dec-21, 05:49 AM
Hmm ..
I think temperature and pressure may be a little indistinct in the discussion. When molecules or atoms collide with each other, it is the temperature that is affected, yes?
The momentum of a gas, or more precisely, the velocity distribution of the molecules or atoms that make up the gas, follows a probability distribution.
The average kinetic energy of the gas of the distribution is a function of temperature.
The internal collisions result in energy and momentum being exchanged where the gas eventually reaches thermal equilibrium, which ultimately affects the pressure exerted by the surface of the container on the gas, no?

Ken G
2018-Dec-21, 05:54 AM
Hmm ..
I think temperature and pressure may be a little indistinct in the discussion. When molecules or atoms collide with each other, it is the temperature that is affected, yes?Temperature in a gas is something else again, it is 2/3 of the average kinetic energy per particle (divided by the Boltzmann constant). Pressure for a nonrelativistic gas is 2/3 of the kinetic energy per volume, rather than per particle. Neither of those definitions say anything about collisions, and neither require collisions. In practice, collisions can help those concepts be valid, but they can also be valid for other reasons-- without collisions.


The internal collisions result in energy and momentum being exchanged where the gas eventually reaches thermal equilibrium, which ultimately affects the pressure exerted by the surface of the container on the gas, no?You are describing how collisions can help the theorems of thermodynamics be applicable, but so can other things that do not involve collisions. Thermodynamics is mostly just about achieving the most likely distribution, regardless of how it gets achieved. That's the simplicity of thermodynamics, you not only don't need to know the details of the collisions, you don't even need collisions at all. But collisions help give you confidence the simplifications will apply, as they serve to help reach the most likely distribution.

Selfsim
2018-Dec-21, 08:25 PM
Thanks Ken. I'm still mulling this one over.

One thing is that I think the concept of 'gas pressure' (like 'weight') only becomes objective once its measured(?) .. and the method for measurement requires containment structures of some sort(?). Interestingly, I think the same applies for 'momentum'(?)
Perhaps in certain models, these quantities don't necessarily require explanatory mechanisms (eg: 'collisions'), however, the observation of 'pressure' readings do call for such a physical mechanism, no?

Ken G
2018-Dec-21, 09:52 PM
Thanks Ken. I'm still mulling this one over.

One thing is that I think the concept of 'gas pressure' (like 'weight') only becomes objective once its measured(?) .. and the method for measurement requires containment structures of some sort(?).It doesn't need to be measured that way, it can also be measured by its effect on the gas. For example, deep inside the Sun, you have gas pressure, and if it is a little higher in one region than another, it will cause expansion from the one region into the other. That caused expansion can be used to "measure" the presence of the gas pressure. It's quite analogous to the force of gravity (Newtonian picture), where we can "measure" how the force of gravity can cause an object to accelerate downward, or we can put the object on a scale and measure the force of gravity that way.


Perhaps in certain models, these quantities don't necessarily require explanatory mechanisms (eg: 'collisions'), however, the observation of 'pressure' readings do call for such a physical mechanism, no?Yes, but that can also be said for the force of gravity. If you want a device to register the force of gravity, you probably need to put the object down on a surface somewhere, as that is a handy way to encounter the presence of the force of gravity. But no one thinks the surface is required for there to be a force of gravity. Similarly, we should not think a surface is required for there to be gas pressure, it's just a handy way to encounter the consequences of gas pressure.

Selfsim
2018-Dec-22, 03:55 AM
Ok .. done some more thinking on this.

I understand that you're encouraging us to think of gas pressure as coming purely from the motion of particles, (with collisions not being essential):

Gas pressure stems from exactly one thing: the motion of the particles. If you make the single assumption that the particle motions are randomly directed (called "isotropic"), then you have gas pressure, period.
However, I think its also fair to say that the current kinetic theory of gases says that in order for a gas to experience a force (and ultimately exert pressure) the momentum of the particles must change with time according to Newton’s second law and this is accomplished in that theory, by making use of collisions. This is a fundamental point in most of the textbook references I've checked for the kinetic theory of gases.

So, you also quote the formula for pressure P, as being 2/3 of the average kinetic energy KE, of a single particle per volume V.
Mathematically this is P = (2/3)(KE)/V.
The physical interpretation of this formula (from what I've since read) is the volume V is confined by a physical barrier and the pressure is the force per area exerted through collisions of the particle with the barrier.

Ok .. so I also understand you're challenging the above textbook interpretation (and I'm also willing to 'try on' what you say) but I think that the textbook interpretation is also fairly clear. (I guess we can do the 'usual', and go into providing reference links etc to support what I've said .. but I suspect you might concur without my having to do that .. there's plenty of available references .. starting with wiki's first statement on the matter, here (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases)).

Ok .. so, the second equation you mention for a single particle is KE = (3/2)kT, where k is the Boltzmann constant.
This equation is derived from the first equation by using the well known empirical formula PV = nRT (note P and V are the same in both equations) and using n=1 mole and k = R/N for an individual particle, where k is Boltzmann’s constant, R is the gas constant, and N is Avogadro’s number for 1 mole of gas and equals 6.02 X 10²³ particles.

Note in the equation KE = (3/2)kT above, there is no P term and the average KE is purely a function of the temperature T, at which the single molecule exists.
When this equation is extended to include the distribution of KE (velocities) of all particles in the gas, we can note that “isotropic velocities” are a function of temperature and not pressure (as I think you said) .. Query?

Selfsim
2018-Dec-22, 07:03 AM
It doesn't need to be measured that way, it can also be measured by its effect on the gas. For example, deep inside the Sun, you have gas pressure, and if it is a little higher in one region than another, it will cause expansion from the one region into the other. That caused expansion can be used to "measure" the presence of the gas pressure. It's quite analogous to the force of gravity (Newtonian picture), where we can "measure" how the force of gravity can cause an object to accelerate downward, or we can put the object on a scale and measure the force of gravity that way.Ken,

Something else occurs upon considering your proposition in this thread. See, using the Sun as an example to illustrate why the collision mechanism in gas pressure is not necessary, appears as being odd.

The problem here is that the Sun is modelled in terms of fluid dynamics.
This is due to a simple observation, that the Sun is in hydrostatic equilibrium (https://en.wikipedia.org/wiki/Hydrostatic_equilibrium).
The Sun doesn't collapse under its own gravity, as fusion in the core provides the outward pressure that negates gravity, (yes)?
The Sun is behaving like a fluid in providing resistance to compression, instead of acting like a gas.
While fusion is a collision dependent process, the output is not the same as the process as described by the kinetic theory of gases.

While the kinetic theory of gases does not explain the outward pressure the Sun exerts to counter gravity, the flaw in the argument here appears to be the broad generalisation that collisions are not the mechanism for gas pressure, even though this is an explicit part of the kinetic theory of gases (as evidenced starting from the wiki reference in my previous post, to textbooks, etc)?

Ken G
2018-Dec-22, 09:23 PM
I understand that you're encouraging us to think of gas pressure as coming purely from the motion of particles, (with collisions not being essential):
Right on.


However, I think its also fair to say that the current kinetic theory of gases says that in order for a gas to experience a force (and ultimately exert pressure) the momentum of the particles must change with time according to Newton’s second law and this is accomplished in that theory, by making use of collisions.No, collisions are never an essential part of the kinetic theory of gases, they only help make the assumptions of the kinetic theory of gases hold. If you simply start with those assumptions (most importantly, the isotropic velocity distribution), then you don't need to include collisions unless you want to understand much more complicated issues than gas pressure.
This is a fundamental point in most of the textbook references I've checked for the kinetic theory of gases.Then get new textbooks. More advanced ones would never make that mistake.

Mathematically this is P = (2/3)(KE)/V.
The physical interpretation of this formula (from what I've since read) is the volume V is confined by a physical barrier and the pressure is the force per area exerted through collisions of the particle with the barrier.Again, that formula has nothing to do with "barriers." This should be pretty clear from the fact that we use that formula to understand the hydrostatic equilibrium in the Sun. The Sun is barrier free. One must therefore understand two things:
1) Gas pressure has nothing to do with barriers
2) What gas pressure actually is, such that is has nothing to do with barriers.


Ok .. so I also understand you're challenging the above textbook interpretation (and I'm also willing to 'try on' what you say) but I think that the textbook interpretation is also fairly clear. I'm not sure what you are claiming is the textbook interpretation of gas pressure, but both you, and the textbook, need to be quite clear that the Sun doesn't contain barriers, and it does contain gas pressure. If you turned off all collisions in the Sun, nothing would happen to its gas pressure structure, but its temperature structure would begin to change because collisions have a lot to do with heat transport.


I guess we can do the 'usual', and go into providing reference links etc to support what I've said .. but I suspect you might concur without my having to do that .. there's plenty of available references .. starting with wiki's first statement on the matter, here (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases)).The quote says "The kinetic theory of gases describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant, rapid, random motion." That's just what I said above, that's what the kinetic theory of gases is all about-- no collisions mentioned or required. Then the quote goes on to say "The randomness arises from the particles' many collisions with each other and with the walls of the container." This is a statement about the reason we normally get to use the kinetic theory of gases, and it is not entirely accurate, because there are plenty of collisionless applications to the kinetic theory of gases, they just aren't as common. To be correct, the Wiki should have said "The most common situation in which we invoke the randomness assumption is when there are frequent collisions with each other and/aor with walls of a container." In particular, cosmologists who work on the gas pressure of dark matter, while assuming it collides with nothing at all, would be very surprised to learn everything they are doing is not the kinetic theory of gases. (It is, though.)

None of the formal assumptions of the kinetic theory of gases involve collisions, but they are a convenient way to be confident of the assumptions of that theory, which I also said above. So here you must understand the difference between the set of assumptions that comprise the kinetic theory of gases, and the practical reasons why that theory can be assumed. In particular, gas pressure involves the former, not the latter. But rather than getting sidetracked into understanding the role of collisions, recognize that the kinetic theory of gases is all about random distributions of motion. You just don't care why the random distribution is there, that's a separate issue (and it often does involve collisions, because collisions are good at creating randomness.)

When this equation is extended to include the distribution of KE (velocities) of all particles in the gas, we can note that “isotropic velocities” are a function of temperature and not pressure (as I think you said) .. Query?As I said above, the kinetic energy appears in both temperature and pressure. Temperature is about kinetic energy per particle, pressure is about kinetic energy per volume. These are just facts.

Ken G
2018-Dec-22, 09:38 PM
The problem here is that the Sun is modelled in terms of fluid dynamics.A gas is an example of a fluid.

The Sun is behaving like a fluid in providing resistance to compression, instead of acting like a gas.A gas is an example of a fluid.

While fusion is a collision dependent process, the output is not the same as the process as described by the kinetic theory of gases.It is the same. Don't start to sound like Robitaille, he has no idea what a gas is.


While the kinetic theory of gases does not explain the outward pressure the Sun exerts to counter gravity,It certainly does, you just have to understand what gas pressure is.

the flaw in the argument here appears to be the broad generalisation that collisions are not the mechanism for gas pressure, even though this is an explicit part of the kinetic theory of gases (as evidenced starting from the wiki reference in my previous post, to textbooks, etc)?They aren't an explicit part of that theory, they are often (but not always) the reason we use the theory. Those two statements are different in ways that are necessary to understand, to understand how gas pressure works inside the Sun (and why it has nothing directly to do with collisions). Again, the key thing to realize is that if you wave a magic wand and turn off all the collisions in the Sun, absolutely nothing would happen to its gas pressure. However, for reasons that have to do with energy transport not pressure, the structure would gradually start to change, which would start to alter the gas pressure.

Selfsim
2018-Dec-23, 07:26 AM
Ken;

I'll distill a couple of points/observations from your previous two quotes (rather than get into the usual quote/response patterns).
Please note again, I present the below points only to promote discourse and hopefully promote a deeper understanding and as a contribution to the Q/A Forum.
I'm personally still undecided on the matter, as several of these points represent 'noteworthy obstacles':

i) With respect to your first response: I should make it clear that the Sun is modelled as a fluid .. (not as a gas) and therefore “physical barriers” are not a requirement.
ii) I haven't yet encountered any mainstream papers where the kinetic theory of gases is applied in descriptions of the physics of the Sun.
iii) Collisions appear to be a necessity even with the Sun modelled as a fluid, as collisions result in fusion which provides the outward pressure to counter gravity, resulting in hydrostatic equilibrium.

iv) The formula P = (2/3)(KE)/V.
The physical interpretation of this formula has to be that a gas occupies the volume which constrains it, (otherwise it doesn't make any sense to me).
In this case V is clearly intended as being a finite volume embedded in its surrounding space.
For a gas to occupy this volume, instead of the surrounding space, implies some kind of, (at least), momentary constraint.
Collisions with the boundary of that constraint, (whatever its nature is .. even imaginary), invokes a mechanism for pressure.

v) The Wikipedia link for Kinetic Theory of Gases (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases):
The link is fairly well explicit in defining the mechanism for pressure:

The theory posits that gas pressure results from particles' collisions with the walls of a container at different velocities.
I also note that the above text immediately followed the pre-amble which you quoted in your reply ... :)

vi) Your final sentence in your first response:
As I said above, the kinetic energy appears in both temperature and pressure. Temperature is about kinetic energy per particle, pressure is about kinetic energy per volume. These are just facts... calls upon a need to elaborate on the significance of the relevant equations:

The average KE = (3/2)kT, for a single particle, or when extended to many particles .. say Avogadro’s number N is:
KE = (3/2)RT.

The average KE for an Avogadro number of particles is also defined as:
KE= N(0.5Mû²) = 0.5Mû² where M is the molar mass of the gas.

Combining the two equations gives:
û² = 3RT/M
√û² = √3RT/M
√û² is simply the root-mean-square (rms) for speed.

What this emphasizes is that the distribution of isotropic velocities is a function of temperature (not pressure), as the rms for speed is also a function of the temperature T (and not pressure).

(The above information came from a physical chemistry undergrad textbook I referenced, which then goes goes into considerable mathematical detail in modelling the kinetic theory as collisions between molecules and the walls of a physical barrier).

vii)
A gas is an example of a fluid A gas is an example of a gas, (which I believe is the whole point of the discussion).

viii) In the kinetic theory, the gas occupies a volume .. if this was true of the Sun, then the solar atmosphere would be stripped .. as the gas would occupy the surrounding space. Given this doesn’t happen, it can be stated that the solar atmosphere behaves like a fluid in hydrostatic equilibrium.

ix) Your comment that collisions are not an explicit part of the kinetic theory of gases, I think, is still legitimately queryable, (as evidenced by the Wiki text quoted above), which still, (for better or for worse), makes it very clear that collisions are central to the theory. (I'll go looking for more later on).

x) Your statement that nothing would happen to the gas pressure if the collisions were turned off is a pretty big leap of faith to request, I think. For instance, a change alone in the condition for collision (=fusion), alters the gas pressure resulting in the star no longer being in a hydrostatic equilibrium.
A star going out of the main sequence stage by expanding into a red giant is such an example.

Cheers

Ken G
2018-Dec-23, 08:13 AM
Please note again, I present the below points only to promote discourse and hopefully promote a deeper understanding and as a contribution to the Q/A Forum.I completely understand, our goal is understanding.

i) With respect to your first response: I should make it clear that the Sun is modelled as a fluid .. (not as a gas) and therefore “physical barriers” are not a requirement.I do not know why you think modeling as a fluid implies not modeling as a gas. The latter is a subset of the former, and I have never seen a gas modeled as anything other than a fluid. Perhaps you have-- but I doubt it! It's more likely that you are making a false distinction.

ii) I haven't yet encountered any mainstream papers where the kinetic theory of gases is applied in descriptions of the physics of the Sun.And I have never seen a paper on the fluid dynamics of the Sun that did not use the kinetic theory of gases. This is why I'm telling you these things, your misconceptions are getting in the way of your understanding of why formulae like PV=NkT and P = 2/3 KE/V do indeed apply to the Sun. Any time you saw the phrase "ideal gas" in the same paragraph as "hydrodynamics" or "hydrodynamic equilibrium," you are being given an example of what you claim you've never encountered.

iii) Collisions appear to be a necessity even with the Sun modelled as a fluid, as collisions result in fusion which provides the outward pressure to counter gravity, resulting in hydrostatic equilibrium.Another common misconception: fusion does not "provide" either pressure or temperature. This should be clear-- the temperature and pressure go into calculating the fusion rate, they do not come out of it. Both are present prior to fusion, and neither changes when fusion begins, ergo fusion "produces" neither. (But fusion does cause a pause in the evolution of pressure and temperature, both of which existed prior to fusion and continue to rise after fusion is over. How could fusion possibly "produce" something that is there before there is fusion, and rises after fusion ends?)


iv) The formula P = (2/3)(KE)/V.
The physical interpretation of this formula has to be that a gas occupies the volume which constrains it, (otherwise it doesn't make any sense to me).Volume never requires "constraints". Also, that formula has nothing to do with collisions or barriers, and holds just fine for collisionless gases, because simple (i.e., scalar) gas pressure is not about collisions or barriers, it is about the transport of momentum by isotropic motions-- period.

In this case V is clearly intended as being a finite volume embedded in its surrounding space.Of course V is a volume, V is the first letter of volume. But the first letter of "barrier" is "B", a letter completely absent from that formula. So volumes matter, barriers don't.

For a gas to occupy this volume, instead of the surrounding space, implies some kind of, (at least), momentary constraint.Certainly not, volume is just volume, no constraints needed.

Collisions with the boundary of that constraint, (whatever its nature is .. even imaginary), invokes a mechanism for pressure.Again, no. That's just not what the mechanism for pressure is. Again: the mechanism for scalar gas pressure is exactly one thing: the transport of momentum by an isotropic velocity distribution of many particles. That's it, that's gas pressure-- that's all you ever need to derive everything you have ever seen about gas pressure. A good textbook will do all those derivations, never ever referring to any boundaries or constraints because they would be completely extraneous to the derivation. Bad textbooks might talk about bouncing off walls, ergo the common misconceptions that Robitaille has clearly fallen under (along with his misconceptions about the difference between a gas and a liquid).


v) The Wikipedia link for Fluid Dynamics (https://en.wikipedia.org/wiki/Fluid_dynamics):An example of a clearly wrong statement. You should not think Wikipedia never makes clearly wrong statements, and if you do, you have a perfect example in front of you. Why on Earth anyone who understands the first thing about gas pressure could think it "results from particles' collisions with the walls of a container" is beyond me, as that is obviously complete nonsense. It's obvious because one of the central equations of hydrostatic equilibrium in a star is dP/dr = - rho*g, where P is gas pressure (usually ideal gas pressure, in fact), rho is mass density, and g is the acceleration of gravity. You will not get past the first page of any analysis of stellar structure without encountering this equation, but here's something interesting about a star: no walls, no containers. The Wiki claim is therefore pure bunk. What they actually mean, even if they don't know it, is that you can help yourself to understand gas pressure by thinking about how it interacts with a wall, which is a whole lot like saying you can help yourself understand the force of gravity on you by thinking about its interaction with a bathroom scale. But no one in their right mind would say "the force of gravity on you results from standing on a bathroom scale," which essentially just the quoted nonsense about what gas pressure "results from."

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The average KE = (3/2)kT, for a single particle, or when extended to many particles .. say Avogadro’s number N is:
KE = (3/2)RT.

The average KE for an Avogadro number of particles is also defined as: (apologies .. the board can't render the latex symbol for \mu)
KE= N(0.5Mû²) = 0.5Mû² where M is the molar mass of the gas.
The formula is exactly what I'm talking about-- it requires nothing at all about walls or collisions, as should be obvious by inspection of the quantities that go into the formula.


Combining the two equations gives:
û² = 3RT/M
√û² = √3RT/M
√û² is simply the root-mean-square (rms) for speed.Now look at what you have written. All reference the motion of the particles, as I said. No walls, no containers, that's all baloney because it's obviously not in the formulae. Seriously, have you ever heard of something that is "produced by" something else that appears nowhere in its formula? It's nonsense.

What this emphasizes is that the distribution of isotropic velocities is a function of temperature (not pressure), as the rms for speed is also a function of the temperature T (and not pressure).All I can do is repeat these two simple facts:
1) temperature is about kinetic energy per particle
2) gas pressure is about kinetic energy per volume.
This is what all those formulae say, it's right there in the formulae, plain as day.


(The above information came from a physical chemistry undergrad textbook I referenced, which then goes goes into considerable mathematical detail in modelling the kinetic theory as collisions between molecules and the walls of a physical barrier).Well, that's what you get when you learn your physics from chemists! Get a better book, say a physics book on the kinetic theory of gases. Or a paper like https://arxiv.org/abs/1206.5804, which goes into way more detail than you need, but its very title illustrates the point I'm making. There's just a lot of nonsense that gets repeated about the kinetic theory of gases, but this is what you need to know:
The kinetic theory of gases requires assumptions about the distributions of velocities. It does not require any assumptions about how those distributions were realized, i.e., collisions or barriers. However, in many common applications, the assumptions are enforced by collisions. They can also be enforced in other ways, it simply doesn't matter to the basic theory.

viii) In the kinetic theory, the gas occupies a volume .. if this was true of the Sun, then the solar atmosphere would be stripped .. as the gas would occupy the surrounding space.You've lost me here, but I think we are seeing why the misconceptions that you have fallen victim to are limiting your understanding of the Sun. We have a concept of particle density, which is just the average number of particles per volume, taken at some point. That's it, that's density-- no walls, no barriers, but still the concept of "per volume." We have this concept, and none of the particles are leaking away, other than the flimsy solar wind.


[COLOR=#212121][FONT=&]Given this doesn’t happen, it can be stated that the solar atmosphere behaves like a fluid in hydrostatic equilibrium.Yes, it behaves like a fluid in hydrostatic equilibrium, everyone knows that. It is also a gas, with no walls or barriers-- most know that too. Robitaille doesn't know that, his views are nonsense. I'm trying to save you from the same fate!


ix) Your comment that collisions are not an explicit part of the kinetic theory of gases, I think, is still legitimately queryable, (as evidenced by the Wiki text quoted above), which still, (for better or for worse), makes it very clear that collisions are central to the theory. (I'll go looking for more later on).I'm well aware that the misconceptions are widespread. But my proof that they are wrong is very simple: the connections between T, rho, and P that you find in the ideal gas law, and the law of hydrostatic equilibrium, are all quite easy to derive from a few simple assumptions about the velocity distribution of the particles. The words "collision" or "barrier" never need to appear anywhere in those mathematical derivations, which is why nothing about collisions or barriers actually does appear in those equations. Collisions and barriers are commonly, yet misleadingly, cited for one simple reason: their presence makes the assumptions that you actually do need more likely to hold. But just make the assumptions, and poof, no collisions, no walls, no barriers. Find some other way to make the assumptions hold, and again, poof, no collisions, no walls, no barriers-- but all the same equations in the simple kinetic theory (like the ideal gas law, or dP/dr =-rho*g).

x) Your statement that nothing would happen to the gas pressure if the collisions were turned off is a pretty big leap of faith to request, I think. For instance, a change alone in the condition for collision (=fusion), alters the gas pressure resulting in the star no longer being in a hydrostatic equilibrium.
A star going out of the main sequence stage by expanding into a red giant is such an example.Look at what I said again. I was talking about short-term changes. Obviously as time passes, the stellar structure will evolve, which I also pointed out above. But what should be clear is that if there is no short-term change in gas pressure if collisions cease to exist, it is obvious that collisions cannot be what "produces gas pressure." Is that not basic logic? You would have to either say that gas pressure can be produced by collisions and barriers, or by other things, which is not what you're saying. But even saying that would be missing the point, because we already know what gas pressure is produced by: that which appears in its equation, the kinetic energy density of an isotropic velocity distribution. Period.

Ken G
2018-Dec-23, 08:52 AM
I can simplify all of the above with one simple challenge: show me some physical quantity, x, that is "produced by" some other phenomenon, Y, where none of the attributes of Y appear anywhere in the equation for x. Go.

chornedsnorkack
2018-Dec-23, 09:18 AM
There are two important assumptions about gas behaviour:
1) The pressure is dominated by kinetic energy of particles. Degeneracy pressure and attraction between particles are negligible.
That´s an important property of gas, and important way in which gas differs from liquid, both of them fluids.
And it is an important property of Sun that for the whole depth of Sun, pressure is dominated by thermal pressure, with negligible degeneracy pressure.
2) That kinetic energy and pressure are isotropized by collisions. Holds inside Sun. Does it hold in solar wind?

Ken G
2018-Dec-23, 09:27 AM
There are two important assumptions about gas behaviour:
1) The pressure is dominated by kinetic energy of particles. Degeneracy pressure and attraction between particles are negligible.Actually, believe it or not, degeneracy pressure is also a quintessential example of what we mean by gas pressure (just not "ideal gas pressure"), because it is also produced by kinetic energy density and is also all about the transport of momentum by an isotropic velocity distribution. This should be clear from the fact that (nonrelativistically), degeneracy pressure is also equal to 2/3 the kinetic energy density, just like ideal gas pressure! This little understood fact is the reason that we should think of degeneracy as a thermodynamic effect on the temperature, not an effect on the pressure which it does not alter, as long as we already understand the history of the gas that gives rise to its kinetic energy density. But I digress!


That´s an important property of gas, and important way in which gas differs from liquid, both of them fluids.
And it is an important property of Sun that for the whole depth of Sun, pressure is dominated by thermal pressure, with negligible degeneracy pressure.It is all too common to see language that suggests "degeneracy pressure" somehow augments "thermal pressure," such that one could be negligible compared to the other. But in any situation where you can track the kinetic energy history, as is usually pretty easy to do because of energy conservation and our interest in heat and work, there is no difference whatsoever between "thermal pressure" and "degeneracy pressure", in regard to the gas pressure, again because in both cases P = 2/3 KE/V. What is actually different is the temperature that this KE implies. Degeneracy is an effect on the thermodynamics (i.e., how the KE is partitioned among the particles), not a mechanical effect on pressure. The only reason we see the phrase "degeneracy pressure" is because it means the gas pressure you encounter when the gas is fully degenerate-- but the gas pressure is still perfectly normal gas pressure, and it still comes from the way particle motions transport momentum, which is why it still equals 2/3 KE/V. The point being, if I can track KE and therefore know KE/V, I can also know the gas pressure, without needing to know if it is degenerate or ideal or any "combination" thereof.

This calls for some clarification given how common is the phrase "degeneracy pressure". If you are not tracking the KE history of the gas, you can certainly write expressions that look like the pressure is a sum of two terms, one which looks like ideal gas pressure and one that looks like something that springs solely from the density. When you do that, it does make sense to think of the pressure as having a "thermal" and a "degenerate" contribution. But those expressions will involve temperature, so what is really happening there is that we are writing the connection between pressure and temperature, which of course includes the thermodynamics that controls the temperature and that's why degeneracy is coming into play. Put differently, any expression that refers to temperature will be thermodynamic in nature, and degenerate vs. ideal behavior is also thermodynamic in nature (by which I mean, involves not just the KE but its partitioning among the particles). But since you can also forget about temperature, and simply track the kinetic energy density, and get P = 2/3 KE/V without knowing anything about temperature or about what is "thermal" and what is "degenerate", it is clear that gas pressure does not, by itself, have anything to do with ideal or degenerate gases, it's just gases that have isotropic kinetic energy and that's all.

2) That kinetic energy and pressure are isotropized by collisions. Holds inside Sun. Does it hold in solar wind?But note that it matters not what isotropizes the motions, we only need to know that they are isotropic. So if it matters not what isotropizes them to have the normal concept of gas pressure, it is clear that what isotropizes the motions is not what "produces" the gas pressure, the gas pressure is produced by the isotropic motions and exists simply because the motions are isotropic for whatever reason.

As for the solar wind, it is often regarded as a "collisionless" gas (indeed, a plasma, but that is also a detail), and the isotropic motions in the fluid frame are maintained because you have a gradual drift of a distribution of particles that are flying upward and falling back downward. As long as individual particles are as likely to be going upward as downward, due to these gravity-and-electric-field-controlled trajectories, you still have the isotropic assumption even when collisionless. Of course, this is the basis of a simple understanding-- many more effects, such as magnetic fields and various types of plasma waves, come into play in a detailed analysis, and the "gradual drift" gets faster and faster as you go upward until it is not so gradual after all. We normally neglect all these complications when considering "gas pressure" in the solar wind, as we still expect an isotropic velocity distribution in the fluid frame (or at least we allow ourselves this simplifying assumption, even when it is not entirely true).

chornedsnorkack
2018-Dec-23, 03:36 PM
As for the solar wind, it is often regarded as a "collisionless" gas (indeed, a plasma, but that is also a detail), and the isotropic motions in the fluid frame are maintained because you have a gradual drift of a distribution of particles that are flying upward and falling back downward. As long as individual particles are as likely to be going upward as downward, due to these gravity-and-electric-field-controlled trajectories, you still have the isotropic assumption even when collisionless. Of course, this is the basis of a simple understanding-- many more effects, such as magnetic fields and various types of plasma waves, come into play in a detailed analysis, and the "gradual drift" gets faster and faster as you go upward until it is not so gradual after all. We normally neglect all these complications when considering "gas pressure" in the solar wind, as we still expect an isotropic velocity distribution in the fluid frame (or at least we allow ourselves this simplifying assumption, even when it is not entirely true).
But they aren´t going downward.
Suppose that in the lower part of solar wind, some particles are leaving Sun at 400 km/s and some at 500 km/s but none are going down. So average velocity 450 km/s, with dispersion of 50 km/s in vertical direction. Further suppose that it is there isotropic, with 50 km/s dispersion in horizontal direction as well.
Now at some distance from Sun, say at Earth, the dispersion in vertical direction is still 50 km/s. It would not be the case if solar wind were a single blast; because then the particles at 500 km/s would arrive separately (before) and particles at 400 km/s later. But if solar wind blows continuously, there are 400 km/s particles emitted earlier and 500 km/s particles emitted later which catch up with them at Earth.
But not in lateral direction. The particles which arrive at Earth come from the narrow angle to Sun, and therefore have a small relative speed in horizontal direction. It was not the case near Sun; but the particles which flew past them in different directions near Sun have continued their course somewhere else and are not near Earth.
So what is the real pressure of solar wind?

Ken G
2018-Dec-23, 04:42 PM
But they aren´t going downward.Sure they are, the fraction going downward depends on the ratio of the local thermal speed to the average bulk flow speed, and becomes a half when that ratio is large.

Suppose that in the lower part of solar wind, some particles are leaving Sun at 400 km/s and some at 500 km/s but none are going down.Actually one component of the solar wind has a fastest speed of about 300 km/s, and I'm talking about nearer to the base of the wind where we might take the speeds are more like 100 km/s than 450 km/s. But we can use your numbers too and see most of the effect.
So average velocity 450 km/s, with dispersion of 50 km/s in vertical direction. No, the local dispersion is caused by the temperature, i.e., the average kinetic energy per particle in the frame that comoves with the fluid. A typical temperature deep down in the wind is some 10 million K, which means the thermal speed of the protons is about 300 km/s for the protons, and over 1000 km/s for the electrons. So we see that especially the electron component is very much moving upward and downward, and that is even pretty much true of the protons also. To make all these velocities more isotropic, we simply enter the comoving frame of the wind.

Now at some distance from Sun, say at Earth, the dispersion in vertical direction is still 50 km/s. It would not be the case if solar wind were a single blast; because then the particles at 500 km/s would arrive separately (before) and particles at 400 km/s later. But if solar wind blows continuously, there are 400 km/s particles emitted earlier and 500 km/s particles emitted later which catch up with them at Earth.Yes, that is correct, the dispersion in a collisionless plasma is controlled by the trajectories of the individual particles, under the effect of gravity and the prevailing electric field. But this means that at any distance, the lower-kinetic-energy particles are still in orbit, so will still fall back down, even as far out as the Earth. But less and less of the particles will indeed fall back down the farther out you go, as a higher fraction of the particles have escape energy as those that don't get culled out. A similar effect is found in Earth's atmosphere, causing the air at the top of Mount Everest to be lower density than down here. Hence, we have two competing effects that cause density to drop-- some of the particles fall back down, and some are carried away by the overall drift of the distribution. The latter only dominates when the drift speed exceeds the local escape speed, which is not the case near the base of the solar wind, it is only true pretty far out from the Sun's surface.

It can also be noted in the Mount Everest analogy that air actually is not collisionless, but importantly, it would make little difference if it were-- the equations we use to understand air density at the top of Mount Everest make no reference to any collision rates, they purely involve the assumption of isotropic velocities and nothing else. Hence the density on top of Mount Everest would be mostly the same as it is now (it would be the same in the isothermal approximation), and the ideal gas law would still hold, if air was completely collisionless, or if you magically turned off all collisions in the air and neglected the minor differences between nitrogen and oxygen. This is another way to understand why pressure and collisions are two very different things.

But not in lateral direction. The particles which arrive at Earth come from the narrow angle to Sun, and therefore have a small relative speed in horizontal direction.Ah, but here you make a mistake, it's another common misconception! (Gas dynamics is rife with them, hence the thread.) Even a completely collisionless gas will maintain an isotropic velocity distribution (in the frame moving with the fluid) as you get farther from a central source of thermalized gas. All that happens is the density and temperature drop! All the while, P= 2/3 KE/V. That's scalar gas pressure, period.

So what is the real pressure of solar wind?It is P= 2/3 KE/V, as with all gas pressure. The real problem in the solar wind is that the electrons and protons don't have the same kinetic energy per particle (they decouple when there aren't collisions to transport heat between them), and you also have magnetic fields (which allow the kinetic energy component perpendicular to the field to be different from parallel). So life get more complicated when you can't rely on collisions to maintain thermodynamic equilibrium, and other ways to maintain it fail to pick up the slack. But those are all interesting details about plasmas-- in the simple case of a single component gas, the velocity dispersion stays isotropic as you get farther from a central source, all that happens is the density and temperature drop. The temperature drop is due to the overall bulk average velocity, called "adiabatic cooling from spherical divergence," and the density drop is a combination of the falling back down of the particles (which dominates whenever the average bulk velocity is less than the local escape speed, as is true in Earth's atmosphere, and then the flow speed is controlled by the density behavior rather than the other way around), and the spherical divergence effect (which dominates in the contrary situation).

Selfsim
2018-Dec-24, 12:51 AM
Ken;

The 'style' of parts of your previous response to me are getting a little too close to the 'style' of other conversations I'm more used to having with ideologically driven cranks on other forums .. so I'll gracefully decline in engaging with you on those specific parts.

However, the following is 'fair game' I think, as it gets to the heart of the issue, (so I'll 'have a go'):


.. And I have never seen a paper on the fluid dynamics of the Sun that did not use the kinetic theory of gases. This is why I'm telling you these things, your misconceptions are getting in the way of your understanding of why formulae like PV=NkT and P = 2/3 KE/V do indeed apply to the Sun. Any time you saw the phrase "ideal gas" in the same paragraph as "hydrodynamics" or "hydrodynamic equilibrium," you are being given an example of what you claim you've never seen. (You have.) Hmm .. I think the ball is in your court to demonstrate how the equations are relevant to describing the Sun, particularly the term 'V', which has a physical significance in the kinetic theory of gases, as the volume of a confined system.

Given that you concur there are no 'barriers' in the case of the Sun, as a starting point, I think it is encumbant upon you to explain what is the physical significance of 'V', and to then go on to derive the equations, from first principles, that are consistent with the Sun being in hydrostatic equilibrium.


The Wiki is really poor. Notice that it tries to distinguish the "average KE for a single particle" from the "average KE for an Avogadro's number of particles. What kind of nonsense is that distinction anyway? A cursory examination of the words shows the distinction is completely silly. The formula is useful, however-- and has nothing whatsoever to do with barriers or containers, as should be obvious by inspection of the quantities that go into the formula. I usually like Wiki articles, in fact they are usually a little too technically precise rather than not precise enough-- but not this time, that article is quite poor.

A closer read of the Wiki article may help in yielding a different interpretation because it doesn’t appear to even mention Avogadro's number of particles, let alone anything that is even remotely familiar in context. (The Wiki article does refer to the value 'N' .. however this isn't Avogadro's number used the average KE formula).


Well, that's what you get when you learn your physics from chemists! Get a better book, say a physics book on the kinetic theory of gases. Or a paper like https://arxiv.org/abs/1206.5804, which goes into way more detail than you need, but its very title illustrates the point I'm making There's just a lot of nonsense that gets repeated about the kinetic theory of gases, but this is what you need to know:
The kinetic theory of gases requires assumptions about the distributions of velocities. It does not require any assumptions about how those distributions were realized, i.e., collisions or barriers. However, in many common applications, the assumptions are enforced by collisions. They can also be enforced in other ways, it simply doesn't matter to the basic theory. This arxiv.org link refers to a collisionless system involving galactic dynamics.

Envisaging how this is even remotely relevant to the kinetic theory of gases, which has more mundane physical examples such what goes on inside an inflated balloon, or car tyre, is a question in itself, but would only add to the 'noise' in our discussion.


Don’t learn your physics from chemists
Umm .. the mathematics is standard and thus can be transplanted into a Physics, or Physical Chemistry treatment of the subject.

Here is a Physics textbook link, (so as avoid any 'contamination' from chemists, or your criticism of what you say is the 'poorly' written Wiki article containing imaginary references):
http://people.virginia.edu/~ben/Hue_Physics_152/BEN_Lect_16.pdf

This text appears to completely contradict your position (don't shoot me .. I'm just a carrier pigeon .. :) ).
As follows:
(1) The Kinetic theory of Gases is based on collisions (page 3).
(2) Force (and pressure) are defined in an enclosed system (page 4).
(3) Force is a function of collisions between molecules and the walls (page 4).
(4) Pressure is a function of collisions with molecules and the walls (page 5).
(5) Average KE is a function of temperature not pressure. (page 6).
(6) Average speed RMS is a function of temperature not pressure (page 7).
(7) The equations for average KE and average speed RMS are based on a closed system even after the elimination of the PV term to derive the equations. (Pages 3-7).

I've reached the conclusion that, (as much as you may disagree with it), the mathematics behind the above Physics textbook reference, the Wikipedia page, and the references from a physical chemistry textbook, are all the same and describe a collision based theory, as would likely also appear in any other treatment of the kinetic theory of gases.

Now, if you can see how I came to this conclusion, I don't mind discussing further on the basis that you're proposing a mainstream alternative to that consensus position .. (I would suggest the S&T forum .. and not Q&A though).

Have a happy and safe Christmas by the way! :)
Cheers

Ken G
2018-Dec-24, 01:22 AM
Hmm .. I think the ball is in your court to demonstrate how the equations are relevant to describing the Sun, particularly the term 'V', which has a physical significance in the kinetic theory of gases, as the volume of a confined system. What is done in the Sun is the use of the concept of "density" n=N/V. Poof, that's what happens to V, no containers anywhere but all the equations are the same as "the kinetic theory of gases." For example, the familiar ideal gas law PV=NkT becomes P = nkT.


Given that you concur there are no 'barriers' in the case of the Sun, as a starting point, I think it is encumbant upon you to explain what is the physical significance of 'V', and to then go on to derive the equations, from first principles, that are consistent with the Sun being in hydrostatic equilibrium.Done. This is all quite trivial, it's just gas dynamics 101.


This arxiv.org link refers to a collisionless system involving galactic dynamics.
So what? It's still gas dynamics, it uses the phrase "kinetic theory of gases" and "collisionless" in the same sentence. I'm afraid that fact is completely conclusive. But I already know all this, and you don't seem to want to, so it's not clear there is much point in continuing. You seem to like your misconceptions, even though they make it impossible for you to understand why the kinetic theory of gases applies to the Sun (without walls) and to collisionless gases in appropriate contexts (like that paper). So far it was fun though-- I enjoy explaining these things. But I need someone who wants to understand, not just quote the misconceptions I have already explained exactly why they are misconceptions, and why those misconceptions make it impossible for you to understand physical truths like why the Sun obeys the kinetic theory of gases without any walls, or why the Earth's atmospheric density would remain nearly the same if all collisions were suddenly turned off. You cannot understand that, can you? But it's easy for me to understand that, so that's the value of knowing this stuff. Also, I notice you have not attempted the challenge I put for you. If you don't try that challenge, I'm pretty sure you will never advance to understanding here.

As for your list of items, to make sure you don't think I'm leaving anything out, I will dispense of them as such:


(1) The Kinetic theory of Gases is based on collisions (page 3).I have stated above what the role of collisions is, and is not, in the equations we call the kinetic theory of gases. Whether you want to apply your own vague new term "based on collisions" is up to you, my correct statement is that collisions are not required, appear nowhere in the equations, and do not "produce gas pressure", all of which are true-- regardless of how you are interpreting what you read.


(2) Force (and pressure) are defined in an enclosed system (page 4).This is pure baloney, force and pressure appear all the time in unenclosed systems (like the Sun, the Earth's atmosphere, galaxies, dark matter, the early universe, etc. etc. etc.). If you think you read that on page 4, you should immediately throw any such book away, because it is so preposterous I don't even know where to start-- like, have you never seen a weather forecast where they talk about "high pressure" in the unenclosed system that is our air? Has an airplane pilot ever said that the pressure in the air drops with altitude, without any walls or enclosures in that air? You hear about these things because gas pressure is a property of air, empty, pristine air. The claim that you need a wall to have pressure is the mind-blowing misconception that is motivating all my answers-- I can't bear the idea that you should labor under this catastrophically disabling way of thinking about pressure.


(3) Force is a function of collisions between molecules and the walls (page 4).I can't interpret what you think that statement means. Obviously there are forces that have noting at all to do with collisions-- like gravity. If your book made that statement on page 4, throw it out immediately.

(4) Pressure is a function of collisions with molecules and the walls (page 5).Take my challenge above to see why this is wrong. Or don't, you don't have to understand this.

(5) Average KE is a function of temperature not pressure. (page 6).I also can't see what relevance you think this has. As I said, average KE per particle relates to temperature, average KE per volume relates to gas pressure. Since your statement isn't contradictory to those, it is just a bit confused, I have little to add.


(6) Average speed RMS is a function of temperature not pressure (page 7). Part of that is true, part is baloney. Average rms speed connects with temperature for an ideal gas (only), this is obvious from my statement that average kinetic energy per particle is how you get the temperature of an ideal gas. But it is confused to say it "is a function of temperature", because one can just as easily say the temperature "is a function of the rms velocity." What's more, pressure also depends on the average rms velocity, it's just that pressure is the kinetic energy per volume, so it depends on the density as well, whereas temperature does not. I've said all this above.

(7) The equations for average KE and average speed RMS are based on a closed system even after the elimination of the PV term to derive the equations. (Pages 3-7).Nonsense. I'm sorry, that's just plain nonsense. Since you are mixing your own personal misconceptions with what is said in your sources, and not being very careful to distinguish them, it's hard for me to know where to begin to refute this one. Most physicists know the ideal gas law as P=nkT, and that equation most certainly does not require a "closed system" because none of its quantities have anything to do with closed systems, although what you mean by "based on" a closed system is vague and unclear.

chornedsnorkack
2018-Dec-24, 07:02 AM
Ah, but here you make a mistake, it's another common misconception! (Gas dynamics is rife with them, hence the thread.) Even a completely collisionless gas will maintain an isotropic velocity distribution (in the frame moving with the fluid) as you get farther from a central source of thermalized gas. All that happens is the density and temperature drop! All the while, P= 2/3 KE/V. That's scalar gas pressure, period.
It is P= 2/3 KE/V, as with all gas pressure. The real problem in the solar wind is that the electrons and protons don't have the same kinetic energy per particle (they decouple when there aren't collisions to transport heat between them), and you also have magnetic fields (which allow the kinetic energy component perpendicular to the field to be different from parallel). So life get more complicated when you can't rely on collisions to maintain thermodynamic equilibrium, and other ways to maintain it fail to pick up the slack. But those are all interesting details about plasmas-- in the simple case of a single component gas, the velocity dispersion stays isotropic as you get farther from a central source, all that happens is the density and temperature drop. The temperature drop is due to the overall bulk average velocity, called "adiabatic cooling from spherical divergence,"

Demonstrate how the velocity distributions in different directions are coupled to each other in absence of collisions.

Ken G
2018-Dec-24, 07:27 AM
As I said above, you need something to make the velocity distribution isotropic in the fluid frame to use the kinetic theory. Period, that's what you need. It could be the cosmological principle that does it, like in "dust" models of the early universe (no collisions needed). It could be collisions in the past that are no longer present. It could be a lot of things! The key point I've been making above is that it doesn't matter what makes the distribution isotropic, so nothing about gas pressure requires that there be collisions, nor do any of the common elementary expressions encountered in gas dynamics refer to collisions in any way (which is obvious from the formulae, just inspect them). However, we all know that collisions are very good at making the velocity distribution isotropic, so that's why we often look to collisional gases when we apply these theorems. I also gave an example of an article which involves collisionless gases, yet still applies kinetic theory (which is quite a routine thing to do, you might look at papers on dark matter gases). You could simply look to that article for the answer to your question, but it's not clear to me exactly what question you are asking. If you are asking about why the velocity distribution in a collisionless gas remains isotropic as the density drops with height against gravity, like in a collisionless atmosphere of a planet with a very weak atmosphere, then you have collisions off the ground (though the system has no roof and is not "closed"). In the base of the solar wind, there is no "ground", there is merely a very high density gas which acts something like a ground, so you make a transition from a collisional to a collisionless environment, and you also make a transition from static to moving. Note that no change is required in the gas dynamics equations when these transitions occur, although other types of phenomena begin to appear in more detailed treatments (I mentioned above magnetic fields, and the tendency for electrons and protons to reach different temperatures). Which of these situations are you asking about, and why?

chornedsnorkack
2018-Dec-24, 08:14 AM
As the solar wind expands when travelling away from Sun in lateral direction (due to spherical divergence) but does not expand in the radial direction (that would require acceleration, for which there are no collisions and not much energy), it would make sense that adiabatic expansion diminishes the velocity dispersion in lateral direction while the velocity dispersion in radial direction stays unchanged. Thereby making velocity distribution anisotropic.

Note that both adiabatic expansion (in presence of collisions) and particle segregation by velocity (in absence of collisions) predict decrease of velocity on expansion. But segregation by velocity further specifies that anisotropic expansion affects the velocity directions independently and therefore causes the velocity dispersion to become anisotropic.

Ken G
2018-Dec-24, 03:51 PM
As the solar wind expands when travelling away from Sun in lateral direction (due to spherical divergence) but does not expand in the radial direction (that would require acceleration, for which there are no collisions and not much energy), it would make sense that adiabatic expansion diminishes the velocity dispersion in lateral direction while the velocity dispersion in radial direction stays unchanged. Thereby making velocity distribution anisotropic.Ah, I see what you are saying, and there are several issues going on at once here. You are saying that whenever the expansion of fluid elements is anisotropic, it can lead to anisotropic velocity dispersion in the absence of any kind of "stirring" between velocity directions. That is true, some stirring is needed. It is not true that you would need collisions to get that stirring, and it is not true that you can't have pressure without stirring, because you can have isotropic velocities without stirring if you don't have anisotropic expansion.

It is also not true that you need collisions to get radial acceleration of a spherically diverging wind. If you started out with particles released from a gravitating planetary surface with a Maxwell-Boltzmann distribution (say, by imagining that the particles pass from a collisional to a collisionless domain), with average velocity much less than the local escape speed, then you will get a drop in density with height (similar to what happens as you climb a mountain on Earth) due to the particles that fall back down before they reach that height. If there were no interparticle collisions, neither the temperature, nor its related velocity dispersion, would change with height, low to the surface. So low to the surface, you would just see a density drop, and no need for collisions between particles. All gas dynamics equations work fine.

However, there will be a small correction to the above, which is the appearance of a net outward drift, owing to the tail of the velocity distribution that does not fall back down. As you go higher up from the surface, this net drift speed will grow. In a fluid dynamical treatment (where you average over small volumes), this increasing drift appears because of acceleration due to the gas pressure gradient (due to the falling density). Note this gradient acts just like a force on the fluid, even though there are no actual forces on any of the particles other than gravity (and the fact that the particles bounce off the ground if we are using that picture to maintain the situation). So we see radial acceleration of the gas, though collisions are not the cause of that acceleration-- pressure gradients are.

Now if we go even farther out, eventually we will start to notice the spherical divergence, and will start to get adiabatic cooling, which just means the kinetic energy associated with velocity divergence will start to be converted into kinetic energy associated with bulk drift (the "windspeed"). This happens more and more as the windspeed approaches and ultimately exceeds the local escape speed. This is also the domain you are talking about-- where anisotropic expansion (more and more azimuthal rather than radial) in the wind would mess up the isotropic velocity dispersion if there was nothing present to "stir" the gas. Point taken, it's just not what I'm talking about above.

What I'm talking about is the misconception that pressure either requires collisions, or worse, comes from collisions. Even in the above situation, where you have anisotropic expansion (the worst case scenario for maintaining isotropic velocities) collisions are not necessary, as long as there is some other mechanism in place to yield the necessary "stirring." In the absence of such stirring, we would not be able to use a scalar pressure, we would need a tensor pressure. It's still pressure, it's just not the easy flavor of pressure. But yes, some form of stirring is needed to maintain the simple concepts we are talking about in this thread in applications that include anisotropic expansion. In the solar wind, plasma electromagnetic perturbations may serve to produce sufficient "stirring" without any collisions between particles, but there can also be situations where the isotropic distribution is not maintained, and you can also get a different temperature in the electrons and the protons, as I mentioned above. In the solar wind, the anisotropy in "parallel" and "perpendicular" temperature typically appears in relation to the local magnetic field direction, rather than the radial direction (the magnetic field is generally not radial), so the anisotropic expansion of fluid elements is a difference in expansion along the field versus perpendicular to the field. But your overall point holds there.

So my point in all the above has not been that you never, in any situation, need any stirring to maintain isotropy. It is that if you don't need collisions in all situations where you can use the pressure concept, because any time you have isotropic motions, you have simple pressure, and if you don't, you have more complicated tensor pressure. In neither case do "collisions produce pressure," that should be obvious from all the applications in which we apply the pressure concept without any collisions at all. To repeat, those contexts include dust models of dark matter in early universe models under the cosmological principle, and galactic dynamics of stars treated as a collisionless gas. In the former, isotropy is inserted as an assumption of the cosmological principle, and in the latter, isotropy is maintained by something else, possibly the "stirring" produced by random fluctuations in the local gravitational field, or maybe it follows from the steady-state assumption in spherical symmetry. The point is, it doesn't matter where the isotropy comes from-- if you have it, you have simple pressure in kinetic theory.

All this raises an important question: if collisions really have nothing directly to do with gas pressure, why do so many elementary sources claim that pressure comes from collisions, or worse, comes from bouncing off walls that aren't even present in all those astrophysical applications which use the pressure concept? Why does Robitaille think you can't have pressure in uncontained gases like the Sun, and why am I getting sources quoted to me on this thread that claim pressure is about walls? It's hard to say how these misconceptions get so entrenched, but in this case I think it's clear enough: people are simply confusing a convenient way to be able to apply the postulates of some theory with the useful theoretical constructs invoked in that theory, and they are confusing the way we measure some quantity with the theoretical entity being measured. That's why I brought up the example of a bathroom scale, which is a very convenient way to measure the force of gravity on you-- but is not what produces that force and is not required to be able to invoke the theoretical construct of a "force of gravity." So it is with the "force of simple gas pressure", which is really just the way isotropic particle motions transport momentum through empty space in a volume-averaged treatment of a large collection of particles-- and nothing else, that's just exactly what pressure is.

An interesting sidelight of all this is that when you realize what I'm saying, you realize that pressure is a strange kind of force because it completely goes away when you look at the individual particles. It's not a force on a particle, it's only an effective force on a large number of particles. This is the nature of gas pressure. To see the difference, note that if you think that gas pressure requires collisions, you would think that a collisionless gas could not propagate a sound wave. If you understand the way gas pressure actually works, you understand that a collisionless gas can indeed propagate a sound wave, in a very similar way as a collisional gas does. You also understand that the "scale height" concept in the Earth's atmosphere would apply in a very similar way if the air involved no interparticle collisions. All this is the power of the pressure concept, once you escape the misconception that it is produced by collisions. Hence, quoting all these sources that say it is produced by collisions, or worse, comes from bouncing off walls, is highly counterproductive to an actual understanding of how the pressure concept helps us understand gas phenomena.

Ken G
2018-Dec-24, 05:45 PM
It might be a good time to summarize all the interesting gas dynamics results we have learned from the above about simple "gas pressure":
1) It is about momentum carried by isotropic particle motions, and its gradient acts like a force on a large number of particles, even though it is not a force on any individual particle, remarkably.
2) It does not require collisions, and it does not require walls, because the equations can be applied without either and don't refer to either, if the assumptions are valid.
3) It equals 2/3 of the kinetic energy per volume in a frame that moves with the average speed of the gas, so it is obviously dependent on the existence of that kinetic energy-- not collisions or walls. What's more, equations like p = 2/3 KE/V and force per volume equals the gradient of p, are easy to derive directly from any isotropic nonrelativistic particle distribution. So it is obvious that p and the fluid force it produces depend only on the presence of KE/V. This is basic logic, no matter what you think sources are telling you, and you need to consult more advanced sources.
4) It holds for ideal gases and degenerate gases alike.
5) It requires an isotropic velocity distribution, which can be violated by anisotropic expansion if there are not collisions and/or random force field fluctuations. When this happens, we simply generalize the pressure concept and use language like parallel and perpendicular velocities, and pressure becomes a tensor.
6) Collisions only help in the way they tend to make valid the necessary assumptions that you actually do need in the kinetic theory of gases that support the gas pressure concept. A common application where they are not needed is in the dark matter gas dynamics of the early universe, where you will see "gas pressure" used in an absolutely invaluable way.

Now contrast these very useful facts about gas pressure that are used constantly in fluid dynamics with the kind of useless and even untrue statements we've seen quoted from various sources that convey a number of misconceptions about gas pressure. This is the importance of understanding these concepts yourself-- not turning your brain over to your sources. Some sources "dumb down" the physics because they don't think you can handle the truth, but actually, the concepts themselves are much more powerful, and often not so difficult after all.

Selfsim
2018-Dec-25, 10:54 PM
Hmm;

Interesting ... I note that the arxiv.org link to the paper: 'Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics", is the very first link that comes up following a simple Google search on: 'arxiv.org: Kinetic Theory of Gases Collisionless' (https://www.google.com/search?ei=FJgiXM3lAczYvATPsrWwDA&q=arxiv.org%3A+Kinetic+Theory+of+Gases+Collisionle ss&oq=arxiv.org%3A+Kinetic+Theory+of+Gases+Collisionl ess&gs_l=psy-ab.3...12774.20234..21979...0.0..0.451.4954.2-8j6j2......0....1..gws-wiz.......33i160j33i21.RaWJIJJtygo).

I cannot agree that this paper is pertinent to the topic under discussion.
It still appears as being incongruous with the discussion and the mainstream science answer pertaining to the physical explanation of 'gas pressure'.



Hmm .. I think the ball is in your court to demonstrate how the equations are relevant to describing the Sun, particularly the term 'V', which has a physical significance in the kinetic theory of gases, as the volume of a confined system.
What is done in the Sun is the use of the concept of "density" n=N/V. Poof, that's what happens to V, no containers anywhere but all the equations are the same as "the kinetic theory of gases." For example, the familiar ideal gas law PV=NkT becomes P = nkT.

The formula n=N/V defines 'number density'. It is the number of particles per volume.

Dividing both sides by V, and renaming the N/V term as number density, doesn’t make the closed system disappear because V no longer appears in the equation.
What happens when gas is compressed in that system?
The number of particles doesn’t change during compression in that system .. the number density increases because the enclosed volume decreases. Conversely, increasing the volume in that system, decreases the number density.

All that is accomplished here, is redefining the closed system under a different variable.



Given that you concur there are no 'barriers' in the case of the Sun, as a starting point, I think it is encumbant upon you to explain what is the physical significance of 'V', and to then go on to derive the equations, from first principles, that are consistent with the Sun being in hydrostatic equilibrium.Done. This is all quite trivial, it's just gas dynamics 101.
Disagree. This hasn't been accomplished.

Leaving the above mentioned number density issue aside, the above request requires deriving the equations from first principles.
This entails taking the (previously agreed) assumption of the Sun being in hydrostatic equilibrium, to construct a mathematical framework in order to derive the equations.

An example of deriving the equations from first principles is found in the Wikipedia article (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases) based on the assumptions posited by the kinetic theory of gases.



This arxiv.org link refers to a collisionless system involving galactic dynamics.

So what? It's still gas dynamics, it uses the phrase "kinetic theory of gases" and "collisionless" in the same sentence. I'm afraid that fact is completely conclusive. But I already know all this, and you don't seem to want to, so it's not clear there is much point in continuing. You seem to like your misconceptions, even though they make it impossible for you to understand why the kinetic theory of gases applies to the Sun (without walls) and to collisionless gases in appropriate contexts (like that paper). So far it was fun though-- I enjoy explaining these things. But I need someone who wants to understand, not just quote the misconceptions I have already explained exactly why they are misconceptions, and why those misconceptions make it impossible for you to understand physical truths like why the Sun obeys the kinetic theory of gases without any walls, or why the Earth's atmospheric density would remain nearly the same if all collisions were suddenly turned off. You cannot understand that, can you? But it's easy for me to understand that, so that's the value of knowing this stuff. Also, I notice you have not attempted the challenge I put for you. If you don't try that challenge, I'm pretty sure you will never advance to understanding here.

The title of paper says it all “Kinetic Theory of Collisionless Self-Gravitating Gases……..”.
This has nothing to do with the “kinetic theory of gases” under discussion, as the gases are not self gravitating.

The “supporting” paper does not distinguish the issue under discussion. (More like the opposite).

Moving forward, and addressing the responses to the list of items from the Physics theory textbook:


(1) The Kinetic theory of Gases is based on collisions (page 3).

I have stated above what the role of collisions is, and is not, in the equations we call the kinetic theory of gases. Whether you want to apply your own vague new term "based on collisions" is up to you, my correct statement is that collisions are not required, appear nowhere in the equations, and do not "produce gas pressure", all of which are true-- regardless of how you are interpreting what you read.
(2) Force (and pressure) are defined in an enclosed system (page 4).

This is pure baloney, force and pressure appear all the time in unenclosed systems (like the Sun, the Earth's atmosphere, galaxies, dark matter, the early universe, etc. etc. etc.). If you think you read that on page 4, you should immediately throw any such book away, because it is so preposterous I don't even know where to start-- like, have you never seen a weather forecast where they talk about "high pressure" in the unenclosed system that is our air? Has an airplane pilot ever said that the pressure in the air drops with altitude, without any walls or enclosures in that air? You hear about these things because gas pressure is a property of air, empty, pristine air. The claim that you need a wall to have pressure is the mind-blowing misconception that is motivating all my answers-- I can't bear the idea that you should labor under this catastrophically disabling way of thinking about pressure.
(3) Force is a function of collisions between molecules and the walls (page 4).

I can't interpret what you think that statement means. Obviously there are forces that have noting at all to do with collisions-- like gravity. If your book made that statement on page 4, throw it out immediately.
(4) Pressure is a function of collisions with molecules and the walls (page 5).

Take my challenge above to see why this is wrong. Or don't, you don't have to understand this.
(5) Average KE is a function of temperature not pressure. (page 6).

I also can't see what relevance you think this has. As I said, average KE per particle relates to temperature, average KE per volume relates to gas pressure. Since your statement isn't contradictory to those, it is just a bit confused, I have little to add.
(6) Average speed RMS is a function of temperature not pressure (page 7).

Part of that is true, part is baloney. Average rms speed connects with temperature for an ideal gas (only), this is obvious from my statement that average kinetic energy per particle is how you get the temperature of an ideal gas. But it is confused to say it "is a function of temperature", because one can just as easily say the temperature "is a function of the rms velocity" What's more, pressure also depends on the average rms velocity, it's just that pressure is the kinetic energy per volume, so it depends on the density as well, whereas temperature does not. I've said all this above.
(7) The equations for average KE and average speed RMS are based on a closed system even after the elimination of the PV term to derive the equations. (Pages 3-7).

Nonsense. I'm sorry, that's just plain nonsense. Since you are mixing your own personal misconceptions with what is said in your sources, and not being very careful to distinguish them, it's hard for me to know where to begin to refute this one. Most physicists know the ideal gas law as P=nkT, and that equation most certainly does not require a "closed system" because none of its quantities have anything to do with closed systems, although what you mean by "based on" a closed system is vague and unclear.

The physics texbook reference, the chemistry textbook reference, the Wikipedia link and the math based physical descriptions, weren’t submitted for making interpretations but as a presentation of observations about what they say about the kinetic theory of gases .. which may or may not happen to run counter to other interpretations, such as; that the theory stands independent from collision mechanisms, or closed systems.

The above physics textbook points represent a simple observation and notes what the texbook document says .. which is; the theory postulates that gas pressure is due to particle collisions in a closed system.
Noting what it actually says is a critical factor in understanding the distinction of how 'interpretations' can easily differ amongst individuals, whilst also acknowledging the core consensus (agreements) already come to, on some base topic.

I sincerely hope Ken can see the difference between arguing over interpretations of what it says .. as distinct from what it actually says about the consensus position(?)

Ken G
2018-Dec-26, 12:41 AM
I cannot agree that this paper is pertinent to the topic under discussion. The article is the tip of the iceberg of a subfield of astronomy that applies the kinetic theory of gases to the stars in a galaxy. It is obviously pertinent-- the stars are being treated precisely as a gas, in precisely the same say as the molecules in the air around you are (they also move in a mean gravitational field, by the way). What's more, they don't collide, and even the star-star gravity is neglected, so they are a collisionless gas, to which kinetic theory is being applied. These are just facts. It appears your logic will be "kinetic theory only applies to collisions because any time it is applied in the collisionless context I will claim it is not pertinent." Above you said the discussion is feeling like one you would have with a crank, but you are missing the one who is using crank logic-- the logic that ignores facts.



Dividing both sides by V, and renaming the N/V term as number density, doesn’t make the closed system disappear because V no longer appears in the equation.I'm sorry, I have no idea what significance you think that statement has. How does a closed system disappear? You are the only one even thinking about closed systems, I don't care about them at all. Gas dynamics does not require a closed system, nor does the kinetic theory of gases. This is completely obvious, both of those fields are applied all the time in astronomy. Astronomy is not a closed system.

Part of the problem is you have never defined what you mean by a "closed system", but the deeper problem is you don't understand how fluid dynamics works. Start with the air in your lungs right now. That is not a "closed system", because you are exchanging air molecules with your surroundings. Nevertheless, what is in your lungs right now will be treated as a fluid in any theoretical medical description. In that fluid treatment, you will find concepts like "pressure" and "temperature", and the first will refer to the kinetic energy per volume, and the second will refer to the kinetic energy per particle. These are facts, if you want to understand fluid mechanics, start there. Forget "closed systems."

You see, the way fluids work is you decide you have too many particles to track, so you will turn this limitation into a benefit by averaging over volumes of many particles. They don't need to be the same particles-- because you are not tracking particles, you don't care at all if ten particles leave the imagined volume you are picturing (any volume you like,no walls needed), as long as ten different particles take their place. That's not "closed," but it is fluid dynamics.

As for the rest of what you are saying, I can't even tell what claims you are making, or which claims of mine you are disputing. Everything I said in the summary in post 57 is not only correct, it is all quite essential for understanding gas dynamics, kinetic theory, and what role gas pressure actually plays in those theories. If you want to understand those theories, understand post 57. If you don't, and you just want to quote dumbed-down sources, that's up to you, but note I'm not asking you to take anything I say on faith-- I have provided crystal clear logical arguments at every step, it should be quite easy to follow the reasoning that leads to every one of my statements.



All that is accomplished here, is redefining the closed system under a different variable.It sounds like you are saying I am "redefining" a closed system, but actually I'm simply defining it, not redefining. The definition of a "closed system" can be looked up easily, as in its Wiki: "A closed system is a physical system that does not allow certain types of transfers (such as transfer of mass and energy transfer) in or out of the system." That's what I mean by a closed system, yet the concept of gas pressure, and all the other concepts of gas dynamics and kinetic theory, are often applied in systems that include transfer of mass and energy, especially the exchange of particles with the immediate environment. Like your lungs, and the medical treatment of gas pressure used to keep you alive if you go into surgery.


An example of deriving the equations from first principles is found in the Wikipedia article (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases) based on the assumptions posited by the kinetic theory of gases. Exactly what I've been telling you all this time. Now all you have to do is go through that very link you just gave, and actually look at what is going into that derivation. Notice what isn't there: any attribute of any kind of collision! Now recall my challenge from above: give me any example where some attribute x in theory X is produced by phenomena Y, but the quantity x does not depend in any way on any quantity from phenomena Y. Good luck, it's nonsense. But that nonsense is just what you are claiming here-- when theory X is kinetic theory, attribute x is gas pressure, and phenomena Y is collisions.


The physics texbook reference, the chemistry textbook reference, the Wikipedia link and the math based physical descriptions, weren’t submitted for making interpretations but as a presentation of observations about what they say about the kinetic theory of gases ..Again I really have no idea what this sentence is trying to say. You made the statement "gas pressure is produced by collisions." Now, is that a presentation of observations or a making an interpretation? I just can't tell what distinctions you are trying to draw. All I can tell you is that gas pressure is not produced by collisions, it is produced by the random kinetic energy in a large collections of particles, whether they collide or not. I have shown you why that's true, given you examples of collisionless gases that support the concept of gas pressure (and kinetic theory), and I have pointed out that if you actually look at the mathematical derivation of the equations of kinetic theory, you will see where they assume isotropic velocities, and you will not see anywhere that any attributes of collisions appear. Finally, I have told you why collisions get mentioned at all-- they help guarantee that the isotropic assumption is good, but that assumption may be good for a host of other reasons that are not collisional. I just can't say it any more clearly.

So what I must try to do is ask you one simple thing: can you use kinetic theory to understand why a collisionless gas can support a sound wave? Because I can. So if you can't, that should really make it quite obvious why the approach I'm describing is the superior one.


I sincerely hope Ken can see the difference between arguing over interpretations of what it says .. as distinct from what it actually says about the consensus position(?)And I sincerely hope you can follow the simple and straightforward logic I just gave you above. I don't care at all about what a source actually says, I care about what is correct. I care about understanding gases, not being blocked by misconceptions. And don't bother claiming my position is ATM, you are just using sources that are too elementary. There's a difference between mainstream physics and physics that has been dumbed down because they don't expect you to really understand gas pressure. A lot of elementary texts will tell you how to calculate gas pressure, and how to understand gas pressure in the context of how it works next to a wall, but then a lot of diet books will tell you how to measure your weight by explaining how bathroom scales work. If you really want to understand the force of gravity in the Newtonian pricture, it has nothing to do with the surface you are standing on, and if you really want to understand gas pressure, it has nothing to do with any walls the gas may or may not be contained in.

Swift
2018-Dec-26, 03:31 AM
This derailment/side discussion about gas behavior has been split off from this thread (https://forum.cosmoquest.org/showthread.php?170689-Is-this-guy-obviously-incorrect-to-say-the-sun-is-liquid-hydrogen).

In the future, it would be appreciated if certain people didn't completely derail Q&A threads.

Ken G
2018-Dec-26, 05:56 AM
One of the things I often try to do on this forum is explain how the physics of some theory actually works, rather than parrot elementary sources that often get this wrong, or at least, explain it in a weak or hamstrung kind of way. People complain it's ATM, but the real problem is their sources are too elementary, and they are simply not attempting to actually understand. Normally, we do have to trust elementary sources, but it's also important not to turn off our brains in the process. Here is a classic example: what is gas pressure?

The main fallacy in Robitaille's argument in his erroneous argument that the Sun is a liquid not a gas is that he doesn't understand gas at all, especially gas pressure. This is why the question was indeed relevant to that thread. But who cares, all that matters is this: which of you wants to understand gas pressure, and which don't care? If you don't care, stop reading immediately. If you do, and you google "How do molecules cause pressure?", you may get:

"The rapid motion and collisions of molecules with the walls of the container causes pressure (force on a unit area). Pressure is proportional to the number of molecular collisions and the force of the collisions in a particular area. The more collisions of gas molecules with the walls, the higher the pressure."

Reading this, you might conclude gas pressure requires a wall, since we have just been told by some authority that walls cause it, and surely we need the cause to have the effect.
That's certainly what Robitaille thinks, apparently because he can read sources like that one. The problem is, the first sentence is nonsense if taken as an explanation of what gas pressure is, because you can have gas pressure without any walls. All that statement is is a description of one common way to measure gas pressure, and therefore can help many people understand its effects by considering the effect it has on a wall. It's fine to gain insight into some theoretical quantity by considering its effect in some given situation, but one should not mistake the situation for what that entity actually is. The second and third sentences are true, but they become highly misleading when following the first. To see the problem, imagine the quote said:

The repulsion between the molecules in your feet and the atoms in your bathroom scale cause your weight (the force of gravity on you). Weight is proportional to the force the scale exerts on you to keep you from falling through the floor. The more the atoms in the scale push up on your atoms, the higher your weight.

The two statements are almost precisely the same, in how they combine true and misleading statements to yield a completely mistaken overall concept. The only difference is that you do see the first, and not the second, in common sources. The reason both statements are virtually the same is explained carefully above, not much point in repeating here. But it is certainly true that if you want to know what your weight is, you do step on a bathroom scale, so that's why the second version could be something you might see if we did not already have a much better understanding of Newtonian gravity. People generally lack a similar understanding of gas pressure, so mistake it for how you would use its effect on a surface to measure it. But that's the problem-- if you already understand something, you don't need to be told what it is, and if you don't already understand it, you shouldn't be filled with misconceptions that mistake the thing for how you would use a surface to measure it.

Now, maybe you think, as Presocratis suggested above, that you don't need a wall to have gas pressure, because collisions between the particles can do it too, but you still need either a wall (as Selfsim and Robitaille think), or the "walls" of the particles themselves (as in Presocratis' suggestion). These ideas are bringing you closer, but you have not understood gas pressure, because it doesn't require collisions between the particles either. It requires the one thing you need to calculate it: an amount of random kinetic energy per volume. It doesn't matter why you have random kinetic energy, it only matters that you do, and then you have gas pressure. That's why it is gas pressure in the Sun, and in the solar wind, and in the dark matter universe, and in stars treated as a gas in a galaxy.

No one who doesn't understand what I am saying here can possibly understand why Robitaille is wrong about the Sun, but if it must be a separate thread, so be it.

Selfsim
2018-Dec-26, 09:38 AM
I'm afraid that Ken's interpretation: that a gas can either be modelled as a fluid or a gas, is seriously flawed.

They are not interchangeable, the equations for the kinetic theory of gases cannot be used for a gas behaving as a fluid, as much as fluid dynamics is useless when the gas is behaving as a gas.

The best way for differentiating between the two models, is by considering physical examples.

The air inside an inflated tyre is described by the kinetic theory of gases.
In this case, the gas is behaving like a gas; it expands and fills out to the volume of the tyre.
The tyre pressure is due to collisions of molecules with the tyre walls.

The atmosphere behaves like a fluid.
It is in hydrostatic equilibrium because the pressure gradient results in an upward force that is cancelled by gravity.

Let's look at the math for the atmosphere that Ken omitted, (or rather boldly claimed that the Wiki article supports his interpretation, which it doesn't) ..
There is a pressure gradient which is a function of height z .. lets call it: P(z).
Consider a slice of atmosphere which starts at a height z, and ends at the height z + dz and has a cross sectional area A.

The upward force is therefore F = [P(z)-P(z+dz)]A
The downward force, due to gravity, is simply the weight of the slice and is F =-ρgAdz, where ρ is the density, and g is the acceleration.

The condition for hydrostatic equilibrium is therefore:
[P(z)-P(z+dz)] - ρgdz = 0
Which reduces to dP/dz = -ρg

Using the ideal gas law: PV = nRT,
P= nRT/V = ρRT.

Substituting ρ = P/RT into the differential equation gives:

dP/dz = -gP/RT
or dP/P = (-g/RT)dz

Solving the equation gives
P= P₀(exp(-zg/RT)), where P₀ is the surface pressure.

But hang on ..
This equation bears no resemblance to the equation for pressure P, used in the kinetic theory of gases: P = (2/3)(KE)/V​.

There is a straightforward physical explanation for this:
In the case of the atmosphere, the molecules have a limited degree of freedom and the atmosphere behaves as a solid mass, where pressure increases with depth and is at a maximum on the surface where z=0.

In the kinetic theory of gases, the molecules can freely move in an enclosed volume and pressure is dependent on the kinetic energy supplied for collisions.

I believe this puts to rest, once and for all, that the equations for the kinetic theory of gases can be applied to fluid mechanics.

Until this issue can be properly confronted, collisionless self-gravitating gas papers, lungs and bathroom scales, only serve to contribute to 'the noise' in this thread.

Len Moran
2018-Dec-26, 09:56 AM
Would there be a concept of weight without the bathroom scales though? I don't see Newtonian gravity as existing as "something" to be understood at a deeper fundamental level with weight being an incidental subset of that deeper level. Weight seems to be an equal part of the whole picture that encompasses a notion of gravity that involves modeling forces between bodies. The kitchen scales seems no less or more fundamental than any other part of that model, the scales are needed when modeling weight but can be discarded if weigt is not being considered.

You are saying that gas has pressure without walls in the same way that gravity exists without a bathroom scales. It's an analogy that doesn't quite fit with me and brings to the forefront many discussions we have had concerning modeling. We can model gravity as exising without a bathroom scales, but to model weight the bathroom scales are fundamental. We can model the motion of particles without any walls receiving the impact of that motion, but to model pressure, do we not require the walls just as much as we require thebathroom scales to model weight?

Using the gravity analogy strikes me as saying that the manifestation of weight is not contained in the weighing scales, rather it is contained in the fundamental notion of gravity. I wouldn't disagree with that in essence, but what I would say is that the manner in which weight is contained within gravity is "something different" to weight as I understand it in relation to a bathroom scales.

So I simply ask, is gas pressure as related to particles and a wall and all of the manifestations of that pressure "something different" when considered without any walls?

profloater
2018-Dec-26, 10:33 AM
What at interesting Christmas present to read this thread on boxing day! The epiphany for me is that stars are a collision free gas and thus there is a cosmic pressure. Personally i find the explanation very lucid, pressure is just velocities. It explains the role of the mean free path and, now speculating, the statistical nature of collisions as the mean free path reduces and velocity increases. All that is left for me to understand is spin in a gas or fluid,

Selfsim
2018-Dec-26, 11:11 AM
... The epiphany for me is that stars are a collision free gas and thus there is a cosmic pressure. Personally i find the explanation very lucid, pressure is just velocities. .. except as I have shown in post#30 (https://forum.cosmoquest.org/showthread.php?171201-lt-Gas-behavior-gt&p=2471434#post2471434), pressure in fluid dynamics bears no resemblance to gas pressure in the kinetic theory of gases. The paper (which I think you are referring to) on collisionless self-gravitating gases, uses a model based on the Collisionless Boltzmann Equation (CBE), which is pure fluid dynamics and not a gas behaving as a gas.

George
2018-Dec-26, 02:28 PM
Would there be a concept of weight without the bathroom scales though? I don't see Newtonian gravity as existing as "something" to be understood at a deeper fundamental level with weight being an incidental subset of that deeper level. Weight seems to be an equal part of the whole picture that encompasses a notion of gravity that involves modeling forces between bodies. The kitchen scales seems no less or more fundamental than any other part of that model, the scales are needed when modeling weight but can be discarded if weigt is not being considered.

You are saying that gas has pressure without walls in the same way that gravity exists without a bathroom scales. It's an analogy that doesn't quite fit with me and brings to the forefront many discussions we have had concerning modeling. We can model gravity as exising without a bathroom scales, but to model weight the bathroom scales are fundamental. We can model the motion of particles without any walls receiving the impact of that motion, but to model pressure, do we not require the walls just as much as we require thebathroom scales to model weight? But don't forget the second part of his scale analogy -- free fall. If the scale reads zero, it might be wise to look out the window, or perhaps not. ;) Gravity is present regardless of how we choose to measure it. For pressure, we are accustomed to seeing pressure gauge readings, which involves putting the gas pressure to work (literally: Fxd)) on a diaphragm. I think I'm inclined to also see gas pressure as something that has efficacy but Ken's point seems to be, more correctly, that we are putting the cart before the horse.

Consider the pressure readings as we decrease the size of the diaphragm. If it has great response time, an atomic-sized diaphragm will produce a very erratic reading. Did the gas pressure change?

Ken G
2018-Dec-26, 03:01 PM
What at interesting Christmas present to read this thread on boxing day! The epiphany for me is that stars are a collision free gas and thus there is a cosmic pressure. Personally i find the explanation very lucid, pressure is just velocities. It explains the role of the mean free path and, now speculating, the statistical nature of collisions as the mean free path reduces and velocity increases. All that is left for me to understand is spin in a gas or fluid,Precisely, I'm glad my efforts were not wasted.

Ken G
2018-Dec-26, 03:02 PM
.. except as I have shown in post#30 (https://forum.cosmoquest.org/showthread.php?171201-lt-Gas-behavior-gt&p=2471434#post2471434), pressure in fluid dynamics bears no resemblance to gas pressure in the kinetic theory of gases. Post 30 is completely wrong, but perhaps it is wrong in ways that could be made into something useful.

In that post, you give two equations that start out looking like "pressure equals something." Those two expressions are both correct in the case of an "ideal gas" (only), which is a thermodynamic subset of "gases." But the real error in that post is in thinking that if you have two true equations, one must be true for fluids and the other for gases. That's just nonsense, an ideal gas is both a gas and a fluid, and both equations for pressure are true equations in that context.

But where we really have something to learn is in the distinction between what is the mechanical elements of gas pressure (which connects to the random kinetic energy per volume because it is about the transport of momentum and does not matter how the kinetic energy is partitioned among the particles) versus the thermodynamics of a gas (which connects to temperature and the partition of kinetic energy among the particles). This crucial distinction is rarely made in contexts where you see the "ideal gas law," so I will offer to you a much better way to understand that law:

Split it into its actual two key elements. The mechanical part is p = 2/3 KE/V, that is what gas pressure is, and applies to all simple nonrelativistic gases-- not just "ideal gases". The thermodynamic part is kT = 2/3 KE/N, where KE is the total kinetic energy and N is the number of particles, and this is the only place where the "ideal" assumption comes in. Notice the KE is the key aspect of both equations, which puts proper attention on the fact that the way a gas contains random kinetic energy is the crucial thing to understand, especially since energy is a conserved quantity so is easy to track over the history of the preparation of the gas. The "ideal gas law" comes from combining those two key concepts, so it results not in "the equation that determines the pressure", as many people (unfortunately) think it to be, it results in what it actually is: a simple constraint on pressure, temperature, and density that stems from other physics. If you think of the ideal gas law, and all other "equations of state," in those terms, you will finally understand what they are. You can also understand why p = nkT and p = 2/3 KE/V are both true for ideal gases, in the fluid description.



The paper (which I think you are referring to) on collisionless self-gravitating gases, uses a model based on the Collisionless Boltzmann Equation (CBE), which is pure fluid dynamics and not a gas behaving as a gas.I hope no one pays any attention to this statement, it is just utterly wrong.
the equations for the kinetic theory of gases cannot be used for a gas behaving as a fluid, as much as fluid dynamics is useless when the gas is behaving as a gas.Another good statement to ignore. Let's just pretend this was never said.

Ken G
2018-Dec-26, 03:05 PM
But don't forget the second part of his scale analogy -- free fall. If the scale reads zero, it might be wise to look out the window, or perhaps not. ;) Gravity is present regardless of how we choose to measure it. For pressure, we are accustomed to seeing pressure gauge readings, which involves putting the gas pressure to work (literally: Fxd)) on a diaphragm. I think I'm inclined to also see gas pressure as something that has efficacy but Ken's point seems to be, more correctly, that we are putting the cart before the horse. Exactly. If you set up a sinusoidal sound wave in a collisionless gas, it will propagate completely normally, and your ear will hear it completely normally, as long as the gas can push on the hairs in your ear. How could we possibly hamstring our understanding of gas pressure any worse than to imagine the gas pressure appears in our ear, but is not present in the gas that is propagating the sound wave? It's not about semantics, it's about understanding.

Ken G
2018-Dec-26, 03:28 PM
Would there be a concept of weight without the bathroom scales though?It is a question of terminology. Words like "weight" and "weightless" get used in common parlance in different ways than their precise meanings in physics. That's why when I talk about "weight", I generally say "where weight is defined as the force of gravity on an object." That's how physicists use the term. But you are right, people in common parlance may mean the force on a bathroom scale, and if they are on a bathroom scale in an elevator whose cable breaks, they will take the fact that the scale reading goes to zero to mean they are "weightless." But when you write down Newton's theory of nonrelativistic gravity, you will find a simple equation for the force of gravity on an object, and it will not include bathroom scales. Similarly, when you derive gas pressure from kinetic theory as used in nonrelativistic gas dynamics, you will find that gas pressure equals 2/3 KE/V, with no mention of any walls.
The kitchen scales seems no less or more fundamental than any other part of that model, the scales are needed when modeling weight but can be discarded if weigt is not being considered.Again, in physics, "weight" means "the force of gravity on an object." You are welcome to interpret everything I said above using that definition, just like "gas pressure" is "the effective force that acts on large collections of particles in a gas that stems from the random motions of those particles." One of the most important things to understand about gas pressure is that it is not a force on any individual particle, it is a force that doesn't even appear until you take a fluid description. (A "fluid description" simply means you are replacing the detailed motions of all the particles with volume-averaged quantities like density, temperature, and, yes, gas pressure.)


You are saying that gas has pressure without walls in the same way that gravity exists without a bathroom scales.Much more than that. I'm saying that we can understand the physics of motions of gravitating bodies by not imagining that "weight is produced by scales," and we can understand the physics of the motions of gases by not imagining that "gas pressure is produced by bouncing off walls," or "gas pressure is produced by collisions."
It's an analogy that doesn't quite fit with me and brings to the forefront many discussions we have had concerning modeling.Replace "weight" with "the force of gravity" and try the analogy again.

So I simply ask, is gas pressure as related to particles and a wall and all of the manifestations of that pressure "something different" when considered without any walls?
That's exactly the point. The answer is "no, gas pressure is exactly the same notion in the absence of walls," and that's precisely what Robitaille gets wrong in his absurd claim that the gas in the Sun cannot be a gas because it isn't encountering any walls (which is almost as absurd as Selfsim's claim it can't be a gas because it is a fluid.) It is misconceptions like this that I am attempting to replace with understanding, because I like understanding, and I hate baloney.

The "baloney" in all this is that either kinetic theory, or simple gas dynamics, are theories that require collisions, or are about collisions. What is actually true is that we often apply these theories when there are collisions because collisions are one way to enforce the actual assumptions of these theories, and collisions might be one of the phenomena we wish to include in our applications. The simple fact that there are many collisionless applications of gas dynamics and kinetic theory should put the lie to this commonly seen claim. (Now some people will trot out all kinds of examples of seemingly authoritative sources saying you must have collisions to have kinetic theory and/or simple gas dynamics, and all I can say to them is, turn on your brain instead of just your eyeballs.) But note the real issue here is not semantic, any more than saying "the force of gravity on you is produced by a bathroom scale" is a matter of semantics. It's about understanding what gas pressure is, so you can properly use the concept when you need it. For the opposite possibility, just look at what Robitaille said about the Sun, or what Selfsim is saying about gases and fluids. And I don't mean to be insulting to Selfsim-- indeed I am quite indebted to him for making my argument that these concepts are actually important to understanda, nor are his misconceptions unusual (especially given how poorly these concepts are often explained in seemingly authoritative sources.)

Len Moran
2018-Dec-26, 04:40 PM
It is a question of terminology. Words like "weight" and "weightless" get used in common parlance in different ways than their precise meanings in physics. That's why when I talk about "weight", I generally say "where weight is defined as the force of gravity on an object." That's how physicists use the term. But you are right, people in common parlance may mean the force on a bathroom scale, and if they are on a bathroom scale in an elevator whose cable breaks, they will take the fact that the scale reading goes to zero to mean they are "weightless." But when you write down Newton's theory of nonrelativistic gravity, you will find a simple equation for the force of gravity on an object, and it will not include bathroom scales. Similarly, when you derive gas pressure from kinetic theory as used in nonrelativistic gas dynamics, you will find that gas pressure equals 2/3 KE/V, with no mention of any walls.Again, in physics, "weight" means "the force of gravity on an object." You are welcome to interpret everything I said above using that definition, just like "gas pressure" is "the effective force that acts on large collections of particles in a gas that stems from the random motions of those particles." One of the most important things to understand about gas pressure is that it is not a force on any individual particle, it is a force that doesn't even appear until you take a fluid description. (A "fluid description" simply means you are replacing the detailed motions of all the particles with volume-averaged quantities like density, temperature, and, yes, gas pressure.)
Much more than that. I'm saying that we can understand the physics of motions of gravitating bodies by not imagining that "weight is produced by scales," and we can understand the physics of the motions of gases by not imagining that "gas pressure is produced by bouncing off walls," or "gas pressure is produced by collisions."Replace "weight" with "the force of gravity" and try the analogy again.


Ah yes thanks, the analogy takes shape when the force of gravity replaces weight and as pointed out by George, in free fall the scales are at zero weight but the force of gravity hasn't gone away. So the analogy is a big help there in at least taking on board the idea that pressure is there even when walls or collisions are not.

Ken G
2018-Dec-26, 04:45 PM
So the analogy is a big help there in at least taking on board the idea that pressure is there even when walls or collisions are not.Right, that was the point of it. The main problem is that pressure has units of force per unit area, so it is easy (yet misleading) to explain it as a force per unit area on a wall. But it is better to think of pressure as a momentum per second per unit area, which has the same units-- but requires no walls. (Another interesting point is that since we are imagining isotropic random velocities, you might think the momentum carried per second per area would cancel out to zero. But actually a leftward momentum transported from right to left represents a positive momentum flux across the surface, and a rightward momentum transported from left to right also represents a positive momentum flux across that same surface, that's how vector fluxes become scalars-- they don't cancel out.)

When you insert a wall, all that happens is the pressure goes to zero on the other side of the wall, so the gas pressure goes from whatever it is, to zero. This is why actual forces are gradients in pressure, not pressure itself-- as you can see from the equation dp/dr = -rho*g as the force balance against gravity-- it's not p, it's dp/dr. Hence, rather than thinking of pressure as a force per unit area, it is more powerful to think of the gradient of pressure as being a force per unit volume.

George
2018-Dec-26, 06:56 PM
Exactly. If you set up a sinusoidal sound wave in a collisionless gas, it will propagate completely normally, and your ear will hear it completely normally, as long as the gas can push on the hairs in your ear. How could we possibly hamstring our understanding of gas pressure any worse than to imagine the gas pressure appears in our ear, but is not present in the gas that is propagating the sound wave? That's another nice analogy since a pressure wave can be propagated without a requirement of smacking the neighboring particles; it's more about flux density of the energy (or momentum). It's almost a potential energy since we expect pressure to do some real work or produce a force at least, but that force is the cart not the horse.

Another example, and the first that I recall that sorta matches what you say, is that B-flat wavelength -- I forget how many octaves one must go to get there -- that was discovered propagating across a galaxy. It's a little easier to see that it's a flux density wave and not necessarily a bumping action.

Ken G
2018-Dec-26, 07:09 PM
Yes, there is great interest in the fluctuations in the CMB, because they tell us about dark matter gas pressure waves. Dark matter is regarded as collisionless.

Selfsim
2018-Dec-26, 08:49 PM
The point needs to be made that I am not defending or advocating for Robitaille, or for anything else in his paper.

The fact is that I haven't even mentioned him, apart from in the immediately above sentence.
He can be dealt with later as far as I'm concerned.

As I have clearly stated and supported with objective evidence throughout this thread, I am presenting the documented in textbooks (& widely taught) mainstream Physics view on the topic.

Ken however, is advocating that view as being a misconception.

Ken G
2018-Dec-26, 08:55 PM
The point needs to be made that I am not defending or advocating for Robitaille, or for anything else in his paper.
Fair enough, but I never said you agree with him, I said that you have made the same mistake as him, which you have-- neither of you realize that a gas is a fluid, which is part of why neither of you understand gases.


As I have clearly stated and supported with objective evidence throughout this thread, I am presenting the documented in textbooks (& widely taught) mainstream Physics view on the topic.All I can say is, if you want to understand ideal gases, read post 36 again where I show you how to derive the ideal gas law. Then go back to your post 30, and you wlll be able to see all the nonsense there-- nonsense that is not in any source, such as your claim that because p can be put in two different equations that start p=, that somehow implies gases aren't fluids. I mean, you didn't find that in a source, now did you? No, you didn't, because it's nonsense.

But, the error is not all yours, because some of the sources you have quoted are indeed quite misleading. The important thing to remember is, when trying to understand physics, there are three things to keep separate:
1) what the sources say
2) what you think the sources are saying
3) what is actually true
Your post 30 is an excellent example of just how different those three things can be, and it is basically the same thing as the learning process to differentiate those three things.
That's more or less the opportunity that Robitaille gave us, but I don't know if it would have been as effective without your assistance, so you have made an important contribution by your willingness to enter into discourse on the matter. Perhaps you will even benefit yourself, though this remains to be seen.

Selfsim
2018-Dec-26, 09:13 PM
Fair enough, but I never said you agree with him, I said that you have made the same mistake as him, which you have-- neither of you realize that a gas is a fluid, which is part of why neither of you understand gases.Again .. I am presenting the Physics arguments for why a gas is a gas.

Math is used as a rigorous method for maintaining the consistency of arguments .. especially in Physics derivations from first principles .. so that is what was done did in post#30 .. and it highlighted an inconsistency. No further wordsmithing needed.

Ken G
2018-Dec-26, 09:38 PM
Again .. I am presenting the Physics arguments for why a gas is a gas.Pity, I guess you have not benefitted, and will continue to labor under the errors of post 30. Oh well, others will take the benefits instead.

Selfsim
2018-Dec-26, 09:43 PM
Pity, I guess you have not benefitted, and will continue to labor under the errors of post 30. Oh well, others will take the benefits instead.
Your interpretation is noted.

It is being subjected to the appropriate scrutiny, (with no cover-ups), whilst taking note of the weight of the opposing arguments.

profloater
2018-Dec-26, 10:01 PM
I think many of us laboured under the impression that a sound or pressure wave propagates by collisions and not by momentum fluctuations because we are told about collisions as a model, especailly at walls.

Ken G
2018-Dec-26, 11:23 PM
What we see all the time, when there are misconceptions, is some are willing to let them go, while others cling very tightly. I'm sure we've all encountered this, it's human nature-- and credit to those willing to let go.

Selfsim
2018-Dec-27, 12:49 AM
So, we have seen that there is no relationship between the fluid derived equation: P= P₀(exp(-zg/RT)) and; the kinetic gas derived equation: P = (2/3)(KE)/V, which both describe different respective physical conditions.
There are no limit conditions that exist, where one equation breaks down to the other. (Akin to the way GR equations reduce to the gravitational potentials of Newtonian gravity, in the weak limit condition for gravity).

One can use the first equation to show that the pressure gradients, (which Ken champions), plays no role at small scales:
Take the case of a pressure gradient inside a car tyre which has a diameter say of 0.6 metres at a temperature of 20⁰ C = 293K.
Plugging in the values z= 0.6 metres, g = 9.8 m/s², R= 8.31 J K⁻¹ (mol)⁻¹ and T = 293K gives:
P = 0.9976P₀
The pressure gradient, using the air pressure of the tyre nearest the ground (P₀), and at the top of the tyre (P), is insignificantly small and cannot explain the force and overall pressure in the tyre.
The situation is even worse if the tyre is on its side, in which case z is now the width of the tyre!

Needless to say, no such issues exist using the collision theory of the kinetic theory of gases.

In fact, I'd like to see the explanation for how the pressure of a tyre increases when inflated, if collisions play no role in pressure?

Ken G
2018-Dec-27, 01:15 AM
So, we have seen that there is no relationship between the fluid derived equation: P= P₀(exp(-zg/RT)) and; the kinetic gas derived equation: P = (2/3)(KE)/V, which both describe different respective physical conditions. Here is the relationship between them. The second equation is why we have an ideal gas law. The first equation is how the ideal gas law determines the density structure. Since in the ideal gas law, the pressure connects with the density and temperature, you end up with a way to know the pressure given other constraints (g, T, Po) that come from the history of the gas. None of this alters the fact that the reason you have an ideal gas law in the first place is because p=2/3 KE/V. How do we know this? Find any derivation of the ideal gas law you like, and I will show you where p = 2/3 KE/V came into play.


There are no limit conditions that exist, where one equation breaks down to the other.You are completely confused. Those are not two equations for p that apply in different situations, they are just two completely different true expressions involving p. I'm sorry you can't tell the difference between those things, but to help you, let's consider two true equations for the particle density in the same situation: n = no e-zmg/kT and n=N/V. Recognize the similarity? I hope you can also see that the second equation is just what density is in every situation, and the first equation is what the density works out to be in that particular situation. Are you starting to see the nonsense in your argument?


One can use the first equation to show that the pressure gradients, (which Ken champions), plays no role at small scales:Utter nonsense. All pressure forces come from pressure gradients, that's just a fact. I'm sorry if you don't understand it, but I can't see how to explain it any better. Maybe someone else can see what you aren't getting here. Do you really think dp/dr = -rho*g doesn't apply inside a tire? So you have no idea what would happen if you release a small helium balloon inside a tire?


In fact, I'd like to see the explanation for how the pressure of a tyre increases when inflated, if collisions play no role in pressure?Let's ask the same question this way: I'd like to see the explanation for how the reading on a bathroom scale increases when a person puts on a backback, if the force coming from a bathroom scale plays no role in the weight of a person? George already told you the answer: cart before the horse-- but you have to listen.

profloater
2018-Dec-27, 10:36 AM
Now i remeber bernoulli for fluids in motion P + 1/2 ro v^2 + ro g h = constant

In many cases especially gases we tend (as engineers) to ignore the g term but the possibility for oscillation is immedately clear with three partial differentials and there is no hint in Bernoulli of collisions, indeed to consider them complicates the situation! I mean in x y and z.

profloater
2018-Dec-27, 10:53 AM
I am still thinking about spin . Because I have been experimenting with smoke ring projection. With a simple drum type smoke ring generator you can send a stable annular smoke ring across a room of still air. The smoke annulus has spin hence velocity to lower pressure in the ring. When contacting a wall or another smoke ring they mutually disintegrate into a puff of smoke. In general flow visualisations, spinning vortices are generated at, it seems, every transition and this must include micro vortices in a body of fluid. These must reinforce and cancel all the time and reresent at any instant part of the manifestation of momentum.

Ken G
2018-Dec-27, 11:13 AM
Now i remeber bernoulli for fluids in motion P + 1/2 ro v^2 + ro g h = constant
Good point, the Bernoulli equation is just a conservation law, that's all. You can change the rho and v with force fields, or with walls, the equation doesn't care which.

Ken G
2018-Dec-27, 12:29 PM
This thread started out debunking the misconceptions about gases held by Robitaille about the Sun. So now that we have cleared away most of the baloney that people believe about gases, let's make sure we understand what is actually going on with gases and fluids.

Gases are not defined by having lots of interactions between particles, actually the definition is quite the opposite-- interparticle interactions must be relatively rare. A good way to measure that rarity is to form the ratio of the average particle-particle potential energy to the average particle kinetic energy. When that is small, you have a gas. When it is not small, you are starting to make a transition to a liquid or a solid.

So to have a gas, you have lots and lots of particles that, most of the time, are just moving freely, or moving under some mean external force field. This implies some ghastly number of degrees of freedom for the motion, so you cannot track particles individually and you must find a way to turn this difficulty into an asset. The way you do this is to average over small volumes, and replace the particles with fluid concepts like density, temperature, gas pressure, and fluid flow velocity. So that's how gases end up getting treated as fluids-- it is all from this averaging process. It also shows us how absurd it is to think gases and fluids are two completely different things with separate sets of equations, as we were told above. By throwing away a vast quantity of information you don't really care about, you focus on a small number of parameters that you actually do care about-- hence a fluid is a good way to treat a gas.

Now let's talk about interparticle collisions, and collisions with walls. We want these to be rare, as I said, but it is handy if they do occur, because the main simplifying assumption in the fluid treatment is that we can average over a locally (in the fluid frame) isotropic velocity distribution. Real gases won't always have isotropic velocity distributions in the frame of the fluid, but if they are close enough, then we can get away with the simple (scalar rather than tensor) fluid treatment. So although collisions are handy for this reason, many sources miss the important point that gas dynamics in the fluid treatment is not about collisions and does not require collisions, it is about isotropic velocities for whatever reason they exist. And in particular, gas pressure has nothing to do with being near a wall, it has to do with the way many particles transport momentum around-- period. If you are near a wall, you can use the force on the wall to determine the pressure, but that's not what gas pressure is-- because it's still there when the wall isn't.

So what then is "kinetic theory"? That's just a general term for how you understand macro averaged quantities like density, pressure, and temperature in terms of the microscopic particle motions. It doesn't require that you assume isotropic velocities, and it certainly doesn't require collisions (a point made in some detail above), but it is much simpler when you can assume isotropic velocities (so that's what is normally done), and it helps, but is not always necessary, to have collisions if you want to assume that.

So now we can see all the misconceptions being sown by the standard language you find in elementary "dumbed-down" sources that say things like, as does the Wiki on the kinetic theory of gases, "The kinetic theory of gases describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant, rapid, random motion. [true, except the particles certainly do not have to be "submicroscopic"] The randomness arises from the particles' many collisions with each other and with the walls of the container. [not necessarily, no]" and, worse, "The theory posits that gas pressure results from particles' collisions with the walls of a container at different velocities." [that is what fooled Robitaille in the first place.] Wiki is usually quite good, and the error here is subtle-- it is the difference between what gas pressure is (i.e., momentum transport by many many particles), and a good way to picture what it does in action in a particular situation (i.e., near a wall). I hope the subtle but crucial distinction is by now crystal clear, at least for most.

profloater
2018-Dec-27, 01:34 PM
So if I imagine now a volume of gas, and introduce a point energy rise such as a spark, the local particles get a kick of extra momentum which travels out as a spherical surface without needing collisions. The void then fills with a wave of low pressure chasing the first. Is there a resonance determined only by the gas? How would a resonance be communicated?

chornedsnorkack
2018-Dec-27, 03:10 PM
So, gases are defined by the following constraints:
1) Collisions between particles are frequent enough that momentum distributions are kept isotropic, kinetic energies of different types of particles are kept equal and distribution of different energies is Maxwell one. Otherwise pressure and temperature lose sense
But 2) the interactions between particles are sufficiently remote and infrequent that both degeneracy pressure and liquid cohesion stay insignificant compared to gas pressure.

You can claim that degeneracy pressure somehow is also "kinetic energy", but you cannot claim the same about cohesion pressure. You can easily handle mercury at precisely zero pressure, or a significant negative pressure. Does not mean that the atoms have negative kinetic energy, or negative absolute temperature.

Ken G
2018-Dec-27, 04:10 PM
So, gases are defined by the following constraints:
1) Collisions between particles are frequent enough that momentum distributions are kept isotropic, kinetic energies of different types of particles are kept equal and distribution of different energies is Maxwell one. Otherwise pressure and temperature lose senseNo, gases are most certainly not defined by having a Maxwellian distribution. This can be understood better when you understand some very important differences between pressure and temperature. Pressure is mechanical-- it comes from momentum transport, and all you need to know is the kinetic energy density, period. Temperature is thermodynamic-- which means it relates to heat transport, but more importantly in this context, it relates to the partition of KE among the particles. So temperature does require a Maxwell distribution, but pressure does not. As such, gas pressure is a much more general concept than temperature. Unfortunately, this point is rarely clarified, because everyone always jumps to the ideal gas law, which is highly thermodynamic in quality, so they fail to distinguish purely mechanical aspects of gases. Indeed, in astrophysics we often encounter gases that are non-Maxwellian.


But 2) the interactions between particles are sufficiently remote and infrequent that both degeneracy pressure and liquid cohesion stay insignificant compared to gas pressure.
Degeneracy pressure is gas pressure, and the particles in a fully degenerate gas do not collide at all! So degeneracy pressure is not about "frequent" interactions, it is about a special partition of the kinetic energy and momentum among the particles, which is more like a thermodynamic constraint among the particles than it is like "interactions". Indeed, a key aspect of the concept of "interaction" is the distinguishable identities of the interacting elements, but degeneracy works because the particles do not have individual identities at all. Nevertheless, we still talk about "degenerate gases" because we are using all the mechanical aspects of gas dynamics in our fluid descriptions-- with the different thermodynamics. Mechanically, degenerate gases are the same as ideal gases, a powerful insight to have!

There is a widespread misconception that degenerate pressure somehow "adds to" thermal pressure, and only the thermal "component" of pressure is gas pressure, but this isn't right when gas pressure is understood as its bare essential: "the pressure that arises just from the momentum transport of the particles, and equals 2/3 the kinetic energy density as a result." That's the good way to understand gas pressure, and it applies equally to degeneracy pressure, ideal gas pressure, and any combination thereof. Indeed, this general character is exactly why it's the "good way" to think of gas pressure (where "gas pressure" is an internal attribute of a gas, not its interactions with walls that are not even present inside a gas). You can measure gas pressure by getting it to interact with a surface, but that's not what it is-- the many sources that define it as something that does not even exist in the interior of the gas are simply not recognizing the difference between what a theoretical construct is and how you might choose to measure it (there are other ways that don't involve walls).

So why do we often see gas pressure represented as a kind of sum of thermal and degeneracy components? It is because if you are tracking temperature instead of kinetic energy, so you are involving yourself in the thermodynamics (even though this is unnecessary to understand the gas pressure, as I mentioned), then you can write an equation of state as a sum of those two pressure components, and only the "thermal contribution" to the equation of state equation involves the temperature. My point is, an equation of state should generally not be thought of as what sets the pressure, even though they are (by convention) often written as p=something. Instead, an equation of state should be thought of simply as a constraint equation connecting pressure, density, and temperature, which can pull out any of those variables and treat the equation of state as a way to get that parameter if you know the other two.

A constraint equation is much different from the cause of the variable you are solving for when you have knowledge of the others. A classic example is the ideal gas law as you climb a mountain. Even though we write the constraint p = nkT, no one thinks the ideal gas law is what determines the gas pressure as you climb a mountain-- everyone knows the pressure is set by the weight of air above you, which you can know without even knowing the ideal gas law. Nor does the ideal gas law set the temperature, that's set by the greenhouse effect and the Sun and atmospheric convection. The ideal gas law sets the density, because it is a constraint that acts on whatever parameter is the one that is subservient to the other two. So it should be clear that the ideal gas law should only be thought of as the physics that sets the pressure in special situations, such as when you push gas into a balloon. You need to know the overall situation before you can know how to interpret the causality in an equation of state, but (nonrelativistic) pressure is always 2/3 KE/V, even for a degenerate gas, because that's just what gas pressure is. This means if you are tracking the KE in a given volume, you always know the gas pressure, and you don't need to know anything thermodynamic, or what the gas is made of, or much of anything other than that your assumptions hold.


You can claim that degeneracy pressure somehow is also "kinetic energy", but you cannot claim the same about cohesion pressure.This thread is about gas pressure. Here it sounds like you are trying to find fault in an explanation of gas pressure by noting it is different from cohesion pressure.

Selfsim
2018-Dec-27, 11:02 PM
Here is the relationship between them. The second equation is why we have an ideal gas law. The first equation is how the ideal gas law determines the density structure. Since in the ideal gas law, the pressure connects with the density and temperature, you end up with a way to know the pressure given other constraints (g, T, Po) that come from the history of the gas. None of this alters the fact that the reason you have an ideal gas law in the first place is because p=2/3 KE/V. How do we know this? Find any derivation of the ideal gas law you like, and I will show you where p = 2/3 KE/V came into play.Hmm .. note to self: .. response is opinion (belief) based .. excludes any mathematical foundations ...

A quick read of the Wiki link and the physics textbook link I provided, reveals that p = 2/3 KE/V is not based on the ideal gas law.
When the ideal gas law is applied to this equation, it is the resultant Temperature-KE equation (https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Temperature_and_kinetic_en ergy), which then becomes based on the ideal gas law.

Also, I asked you to derive the equation P = (2/3)(KE)/V using the hydrostatic equilibrium condition which I notice thus far, you have completely sidestepped by boldly asserting the proof was in the Wiki link, despite the Wiki page, having been corroborated by evidence from Physics and Chemistry textbooks, as being based on the collision mechanism and not on hydrostatic equilibrium!!!!!!!

Also, the definition of an ideal gas (https://en.wikipedia.org/wiki/Ideal_gas), which you appear to be claiming above as being the basis of 'the relationship' I requested, still specifically includes the collision mechanism:
An ideal gas is a theoretical (https://en.wikipedia.org/wiki/Scientific_theory) gas (https://en.wikipedia.org/wiki/Gas) composed of many randomly moving point particles (https://en.wikipedia.org/wiki/Point_particle) whose only interactions are perfectly elastic collisions (https://en.wikipedia.org/wiki/Elastic_collision).



There are no limit conditions that exist, where one equation breaks down to the other.
You are completely confused. Those are not two equations for p that apply in different situations, they are just two completely different true expressions involving p. I'm sorry you can't tell the difference between those things, but to help you, let's consider two true equations for the particle density in the same situation: n = no e-zmg/kT and n=N/V. Recognize the similarity? I hope you can also see that the second equation is just what density is in every situation, and the first equation is what the density works out to be in that particular situation. Are you starting to see the nonsense in your argument?'My argument' is textbook Physics and it is crystal clear .. provided one looks with unbiased, crystal clarity.

A nonsense argument results however, when one wants to make a case about the equations involving pressure, but then inexplicably changes tack by discussing density!!

Adding clarity on the other hand: the difference in the equations, and their environments, is simply a case of counting.
In the first equation there are two pressure terms which reflects a pressure gradient; in the second equation there is only one pressure term, as there is no pressure gradient since the pressure is uniformly distributed in the enclosed volume.

When one appears as not being willing (or able) to derive either equation, it puts one in the position of being unable to make any form of informed weight-carrying judgements about basic Physics arguments derived from first principles ... (so they can be dismissed as being belief-based).

One can use the first equation to show that the pressure gradients, (which Ken champions), plays no role at small scales: ...Oh lord, help us. Now we are in la la land. All pressure forces come from pressure gradients, that's just a fact. I'm sorry if you don't understand it, but I can't see how to explain it any better. Maybe someone else can see what you aren't getting here. Do you really think dp/dr = -rho*g doesn't apply inside a tire? So you have no idea what would happen if you release a small helium balloon inside a tire?
When the argument from incredulity fallacy is invoked, it is sure sign that one has thrown in the towel!

I thought my post made it abundantly clear that at small scales, pressure gradients are shown as being negligible.

Regarding your helium balloon; you appear to have misunderstood the issue I raised on the impacts of the (tiny) magnitude of a pressure gradient in a tyre, so let’s clarify it with some more simple maths:

In my previous post #50 (https://forum.cosmoquest.org/showthread.php?171201-lt-Gas-behavior-gt&p=2471491#post2471491), over a 0.6 metre distance which corresponds to the diameter of a tyre, P = 0.9976P₀.
In a tyre typically inflated to around 200 kPa, P = 200 kPa and P = 0.9976 X 200 = 199.5 kPa
The pressure gradient is thus: 200 – 199.5 = 0.5 kPa.
Therefore, as a contribution to the total pressure, the gradient of it is (0.5/200) x 100 = 0.25%

Notice a problem here?
According to your interpretation it’s all about pressure gradients, so how do you account for the missing 99.75% pressure?



In fact, I'd like to see the explanation for how the pressure of a tyre increases when inflated, if collisions play no role in pressure?
Let's ask the same question this way: I'd like to see the explanation for how the reading on a bathroom scale increases when a person puts on a backback, if the force coming from a bathroom scale plays no role in the weight of a person? George already told you the answer: cart before the horse-- but you have to listen.So, the answer to the question as to why tyre pressures increase when inflated is to hide behind another poster’s analogy?

I ask the question again, including quantification:
Why do tyre pressures increase when inflated, particularly when at typical inflation pressures, the gradient only accounts for 0.25% of the pressure?

Ken G
2018-Dec-27, 11:36 PM
A quick read of the Wiki link and the physics textbook link I provided, reveals that p = 2/3 KE/V is not based on the ideal gas law.Yes, I've told you that quite a few times now. You are starting to get it-- don't stop now, but you won't learn anything just saying thing I've already told you many times.


Also, I asked you to derive the equation P = (2/3)(KE)/V using the hydrostatic equilibrium condition which I notice thus far, you have completely sidesteppedWell, I "sidestepped" it because that would be a nonsensical thing to do. Let me explain. P = 2/3 KE/V comes from the meaning of gas pressure, and that's what it must be derived from. It certainly does not come from hydrostatic equilibrium, so it would be quite silly to derive it from that. It doesn't come from hydrostatic equilibrium for one very obvious reason: We use the notion of gas pressure even when not in force balance. This is the value of actually understanding, and you should read this as many times as it takes. I'm serious here, you will be wasting both our time as long as you cannot follow what I just said here.



Also, the definition of an ideal gas (https://en.wikipedia.org/wiki/Ideal_gas), which you appear to be claiming above as being the basis of 'the relationship' I requested, still specifically includes the collision mechanism:No, the ideal gas law certainly does not specifically include any collision mechanisms, because it can also hold for collisionless gases, as long as what it actually does require holds true. What it actually does require is an isotropic velocity distribution in the fluid frame, and also the thermodynamics of an ideal gas. The derivation is straightforward, and extremely illuminating. Indeed, if you could only understand the next two lines, you would actually understand the ideal gas law:
1) Mechanical piece: p = 2/3 KE/V, which comes from tracking the momentum flux in all directions of any nonrelativistic isotropic velocity distribution
2) Thermodynamic piece: kT = 2/3 KE/N, which comes from the fact that in thermodynamic equilibrium, freely moving particles will have 1/2 kT of KE in each dimension for each particle, on the average.
Now, combine those two by eliminating KE, and poof, you have the ideal gas law. The reason this is a good thing to understand is that it quite clearly shows you what actually goes into that law. Notice I never had to even mention "collisions," because the ideal gas law has nothing to do with collisions-- though collisions commonly help its assumptions to hold, and that's why so many sources go on about them.



Adding clarity on the other hand: the difference in the equations, and their environments, is simply a case of counting.I'm afraid I haven't the vaguest idea of what you are trying to say in that sentence. To me, it just sounds like " is simply a case of counting." I don't get much from that.


I thought my post made it abundantly clear that at small scales, pressure gradients are shown as being negligible.All that statement is doing is proving what I already know: you don't understand gas pressure at all. I asked you a simple question: what happens when you put a helium balloon inside a tire? You couldn't answer, presumably because you believe this preposterous statement you just made. When you do understand what happens to a helium balloon inside a tire, you will have moved forward, but until then, there's just not much point.


Regarding your helium balloon; you appear to have misunderstood the issue I raised on the impacts of the (tiny) magnitude of a pressure gradient in a tyre, so let’s clarify it with some more simple maths:....
Notice a problem here?Yeah, I do-- you didn't answer the question. So again: what happens to a helium balloon when you put it inside a tire?

According to your interpretation it’s all about pressure gradients, [I]so how do you account for the missing 99.75% pressure? No idea what you think that means. I told you that pressure forces come from pressure gradients, which they do.


So, the answer to the question as to why tyre pressures increase when inflated is to hide behind another poster’s analogy?
Oh this is getting silly. I'm not hiding, I'm trying to show you that others understand what you do not. I can tell you why tire pressure increases when inflated-- it is because the KE/V increases. I can also tell you why the KE/V increases, it is because the density increases, if we take the temperature as fixed. Fixing T means KE/N is fixed, and so, trivially, p = 2/3 KE/V = 2/3 KE/N * N/V = nkT. It really doesn't get any easier than that, but notice the two things I didn't use or need: walls and collisions!

Why do tyre pressures increase when inflated, particularly when at typical inflation pressures, the gradient only accounts for 0.25% of the pressure?
Both aspects have been answered. The tire inflates because the pressure gradient at the boundary of the tire rises. The helium balloon rises because of the pressure gradient inside the tire. (Oops, I gave you the answer!) Both answers are all about pressure gradients. That's because pressure forces are about pressure gradients. This 0.25% quantity you have calculated is irrelevant. You seem to think that because the pressure only varies by 0.25% inside the tire, that means you can neglect the pressure gradient in there, but that's why you don't know what helium balloons do.

Selfsim
2018-Dec-28, 04:30 AM
... Well, I "sidestepped" it because that would be a nonsensical thing to do. Let me explain. P = 2/3 KE/V comes from the meaning of gas pressure, and that's what it must be derived from. It certainly does not come from hydrostatic equilibrium, so it would be quite silly to derive it from that.

It doesn't come from hydrostatic equilibrium for one very obvious reason: We use the notion of gas pressure even when not in force balance. This is the value of actually understanding, and you should read this as many times as it takes. I'm serious here, you will be wasting both our time as long as you cannot follow what I just said here.Let's get one thing clear .. I do understand what you are saying and I have substantial justification for treating it as nothing more than "Ken G's interpretation".
I'll make a separate post to explain this when/if I get the chance.

also;
Ok .. so specifically 'hydrostatic equilibrium' isn't the issue .. basing your argument on fluid dynamics, is!
As I originally said, from post#30 (https://forum.cosmoquest.org/showthread.php?171201-lt-Gas-behavior-gt&p=2471434#post2471434):
I'm afraid that Ken's interpretation: that a gas can either be modelled as a fluid or a gas, is seriously flawed.

They are not interchangeable, the equations for the kinetic theory of gases cannot be used for a gas behaving as a fluid, as much as fluid dynamics is useless when the gas is behaving as a gas.

The best way for differentiating between the two models, is by considering physical examples.

The air inside an inflated tyre is described by the kinetic theory of gases.
In this case, the gas is behaving like a gas; it expands and fills out to the volume of the tyre.
The tyre pressure is due to collisions of molecules with the tyre walls.

The atmosphere behaves like a fluid.
It is in hydrostatic equilibrium because the pressure gradient results in an upward force that is cancelled by gravity.
Ie: the behavior of 'the atmosphere' is not the same as the behavior of 'a gas'.


No, the ideal gas law certainly does not specifically include any collision mechanisms, because it can also hold for collisionless gases, as long as what it actually does require holds true. What it actually does require is an isotropic velocity distribution in the fluid frame, and also the thermodynamics of an ideal gas. The derivation is straightforward, and extremely illuminating. Indeed, if you could only understand the next two lines, you would actually understand the ideal gas law:
1) Mechanical piece: p = 2/3 KE/V, which comes from tracking the momentum flux in all directions of any nonrelativistic isotropic velocity distribution
2) Thermodynamic piece: kT = 2/3 KE/N, which comes from the fact that in thermodynamic equilibrium, freely moving particles will have 1/2 kT of KE in each dimension for each particle, on the average.
Now, combine those two by eliminating KE, and poof, you have the ideal gas law. The reason this is a good thing to understand is that it quite clearly shows you what actually goes into that law. Notice I never had to even mention "collisions," because the ideal gas law has nothing to do with collisions-- though collisions commonly help its assumptions to hold, and that's why so many sources go on about them.
The derivation of the formula P = (2/3)(KE)/V is a purely Newtonian model and is based on collisions of particles with the wall. Whether the gas is ideal or not, is also, arguably, irrelevant - as the equation does not deal specifically with collisions and interactions between the particles themselves.
When the above equation is combined with the ideal gas equation, to give the KE temperature formula, KE = (3/2)RT, the concept of an ideal gas becomes relevant, as the KE is also affected by particle collisions, as well the collisions with the walls.


I'm afraid I haven't the vaguest idea of what you are trying to say in that sentence. To me, it just sounds like "[insert something I don't understand] is simply a case of counting." I don't get much from that.Never mind .. noise .. (don't worry about this). The 'counting I was referring to was counting up to two, because there are two equations .. but you broke the sentence away from its accompanying explanation.


All that statement is doing is proving what I already know: you don't understand gas pressure at all. I asked you a simple question: what happens when you put a helium balloon inside a tire? You couldn't answer, presumably because you believe this preposterous statement you just made. When you do understand what happens to a helium balloon inside a tire, you will have moved forward, but until then, there's just not much point.
Yeah, I do-- you didn't answer the question. So again: what happens to a helium balloon when you put it inside a tire?No idea what you think that means. I told you that pressure forces come from pressure gradients, which they do.

Oh this is getting silly. I'm not hiding, I'm trying to show you that others understand what you do not. I can tell you why tire pressure increases when inflated-- it is because the KE/V increases. I can also tell you why the KE/V increases, it is because the density increases, if we take the temperature as fixed. Fixing T means KE/N is fixed, and so, trivially, p = 2/3 KE/V = 2/3 KE/N * N/V = nkT. It really doesn't get any easier than that, but notice the two things I didn't use or need: walls and collisions!
Both aspects have been answered. The tire inflates because the pressure gradient at the boundary of the tire rises. The helium balloon rises because of the pressure gradient inside the tire. (Oops, I gave you the answer!) Both answers are all about pressure gradients. That's because pressure forces are about pressure gradients. This 0.25% quantity you have calculated is irrelevant. You seem to think that because the pressure only varies by 0.25% inside the tire, that means you can neglect the pressure gradient in there, but that's why you don't know what helium balloons do.Since the helium balloon has become the next central theme of your argument, the irony is, the balloon well and truly kills it.

First of all, the balloon doesn't rise because of pressure gradients, it is due to buoyancy forces due to the difference in densities of helium and the air in which the helium balloon is submerged. It's like pressing down on a piece of cork in a glass of water, when you release the cork, it rises to the surface.
For thread readers: a more technical treatment is in this video:
https://www.youtube.com/watch?v=V9nahX_ty9k

The shape of the balloon is the real killer.
The reason why it is spherical, is that the surrounding air exerts an even pressure on the surface of the balloon, (and yes .. it is due to collisions).
If there was a pressure gradient of any magnitude, the pressure at the bottom of the balloon is going to be greater than the top, and you will not end up with a spherical shape.

So, now that the helium balloon is revealed to be a red herring, would you now please re-answer the tyre inflation question?

There is another point that needs to be made:
In the inflated tyre example, the equations for pressure P, for P= P₀(exp(-zg/RT)) and P = (2/3)(KE)/V, equations are similar. This leads to a problem, if you multiply both equations by A, which is the inside surface area of the tyre, you obtain the corresponding forces.

However, pressure is a scalar quantity, whereas force is a vector quantity.

In the first equation, the force opposes gravity and therefore acts in a specific direction, in the second equation, the force is not direction specific, it acts in all directions, since the pressure is equally distributed everywhere on the surface.

Hence the two equations are not describing the exact same thing. The second equation can only apply to collisions.

Selfsim
2018-Dec-28, 04:57 AM
Just noticed this also:


Oh this is getting silly. I'm not hiding, I'm trying to show you that others understand what you do not. I can tell you why tire pressure increases when inflated-- it is because the KE/V increases. I can also tell you why the KE/V increases, it is because the density increases, if we take the temperature as fixed. Fixing T means KE/N is fixed, and so, trivially, p = 2/3 KE/V = 2/3 KE/N * N/V = nkT. It really doesn't get any easier than that, but notice the two things I didn't use or need: walls and collisions!"p = 2/3 KE/V = 2/3 KE/N * N/V = nkT?????
????Really??????

Word salad!!! You should at least get the math right before declaring victory, Ken!
Its nonsensical, because p = 2/3(KE)/V does not imply p= nkT, as this would violates the ideal gas law, which is pV = nkT!

This is really getting embarrassing!

Ken G
2018-Dec-28, 05:23 AM
Just noticed this also:

p = 2/3 KE/V = 2/3 KE/N * N/V = nkT?????
????Really??????Yup, really.


Word salad!!! You should at least get the math right before declaring victory, Ken!The math is right. What nonsense are you on about now? (N is number of particles, as I said above, in some detail.) My remarks are only for those who can follow the simple math, it's just too hard otherwise.
First of all, the balloon doesn't rise because of pressure gradients, it is due to buoyancy forces due to the difference in densities of helium and the air in which the helium balloon is submerged. I'm pretty sure I'm not going to get you to see the error in this statement, but I'm also pretty sure everyone else does.

Jens
2018-Dec-28, 05:42 AM
Word salad!!! You should at least get the math right before declaring victory, Ken!


Is that what it really is about, winning an argument? I guess I was laboring under the delusion that we were here to deepen our knowledge. :)

PetersCreek
2018-Dec-28, 06:41 AM
Tone, folks. Tone. Keep it civil. If you find yourself irritated or outright angry, best that you not post until your aren’t.

Selfsim
2018-Dec-28, 06:50 AM
Yup, really.
The math is right. What nonsense are you on about now? (N is number of particles, as I said above, in some detail.) My remarks are only for those who can follow the simple math, it's just too hard otherwise.I'm pretty sure I'm not going to get you to see the error in this statement, but I'm also pretty sure everyone else does.Not only does P = nkT violate the ideal gas law, it is not even dimensionally (https://en.wikipedia.org/wiki/List_of_physical_quantities) correct.

P pressure has the dimensions MT⁻²L⁻¹

For nkT n (moles) is dimensionless, as it is a measurement of relative mass.
k, Boltzmann constant has the dimensions ML²T⁻²Θ⁻¹.
T, Temperature has the dimension Θ.


Hence nkT has the overall dimensions ML²T⁻²

In order for the equation to be dimensionally correct, there needs to be an L³ term multiplied to the dimensions of pressure.
L³ is the dimension for volume V.


Hence PV = nkT is the correct equation.

chornedsnorkack
2018-Dec-28, 07:36 AM
This thread is about gas pressure. Here it sounds like you are trying to find fault in an explanation of gas pressure by noting it is different from cohesion pressure.

Yes.

Ken G
2018-Dec-28, 07:56 AM
Not only does P = nkT violate the ideal gas law, it is not even dimensionally (https://en.wikipedia.org/wiki/List_of_physical_quantities) correct. Nope. It's hard to learn anything about gases when you keep tying us up in your own errors.


For nkT n (moles) is dimensionless, as it is a measurement of relative mass.And there is your error. Follow my math, and it is easy to see that n=N/V. That is, n is particle density. I said it above, but it's still safer to just assume that it means what makes the formula correct, because this is formula is mother's milk to a physicist.



Hence PV = nkT is the correct equation.No, you have made a second error. To you, n is moles, and then the equation is not what you have, but rather p = nRT. But as I said, n is particle number density, that's what physicists use because moles is actually a kind of silly unit.

Ken G
2018-Dec-28, 07:58 AM
Yes.Which makes no sense at all. You are the only one talking about cohesion pressure, I regard it as irrelevant to gas pressure so why would I care about trying to explain it?

Ken G
2018-Dec-28, 08:07 AM
With all the distractions, it must be hard to follow what I'm saying, so I will repeat:
Gas pressure does not require collisions, it requires isotropic velocities in the fluid frame. When you have that, it is trivial to derive, from momentum flux considerations, what gas pressure actually is: p = 2/3 KE/V. That is a mechanical result, that applies to ideal gases, to degenerate gases, to collisionless gases, to any nonrelativistic gases, because that's what gas pressure actually is-- as long as the isotropic assumption holds. Collisions are nothing more than a good way to insure the assumption holds, and walls are merely a good way to see what gas pressure does when it encounters a wall (but it's still there when the wall isn't). The ideal gas law is when the gas also obeys a particular thermodynamics, to wit, kT = 2/3 KE/N, which is 2/3 of the average KE per particle (in 3 dimensions). Notice that whenever you are tracking KE, which is easy to do because of the second law of thermodynamics, the ideal gas law is nothing more than a constraint obeyed by p and T because of how p is generated (by 2/3 KE/V) and how kT is generated (by 2/3 KE/N).

Now you understand, for those who can separate that much from all the baloney that has been raised in objection to these very simple and important facts about gas pressure. The reason this is relevant is because Robitaille said the Sun isn't a gas because it doesn't have walls. You can see how such a misguided opinion can be formed, whenever gas pressure is regarded as something that is "produced by" walls, or is some kind of force on walls and that's all it is. Yet, we were told these same things in this very thread, so we can see that Robitaille's misconceptions are not limited to him. What a gas actually is is a large collection of particles that most of the time are following ballistic trajectories through empty space, under the influence of mean external fields but not particle-particle interactions. When interactions become very important, you begin to make a phase transition to a liquid or solid, so you can see how thinking that gases are defined by interactions is more or less exactly the opposite of the truth. However, it is helpful if there are at least some collisions, since that really helps make the assumptions that define simple (isotropic) kinetic theory more likely to hold. Unfortunately, simple sources are not terribly clear on these points, ergo Robitaille's misconceptions, and ergo this thread. Ironically, some people will now quote sources that say Robitaille had it right (that you need walls to have gas pressure) and that what I'm saying is somehow ATM, but sadly, they have it exactly backward. Those who can understand this, good, those who cannot, I've done all I can.

chornedsnorkack
2018-Dec-28, 08:13 AM
Which makes no sense at all. You are the only one talking about cohesion pressure, I regard it as irrelevant to gas pressure so why would I care about trying to explain it?

It's not irrelevant, because it's vital as one of the limits where gas treatment breaks down. And cohesion pressure becomes a significant contributor on the side of still "gas".
Pressure is the derivative of total energy with respect to to volume, right?
And total energy is the sum of kinetic and potential energy.
Potential energy of interparticle interactions can be repulsive or attractive, or sum of both types of contributions.
And when "gas pressure" is derived from just kinetic energy part, a necessary assumption is that both interparticle interaction potential energy and its derivative with respect to volume are negligible relative to kinetic energy and its derivative.
You may argue that interparticle repulsive potential energy due to degeneracy is somehow also "kinetic energy", but you cannot make the same argument about interparticle attractive potential energy.

Selfsim
2018-Dec-28, 08:14 AM
Not only does P = nkT violate the ideal gas law, it is not even dimensionally (https://en.wikipedia.org/wiki/List_of_physical_quantities) correct.

P pressure has the dimensions MT⁻²L⁻¹

For nkT n (moles) is dimensionless, as it is a measurement of relative mass.
k, Boltzmann constant has the dimensions ML²T⁻²Θ⁻¹.
T, Temperature has the dimension Θ.


Hence nkT has the overall dimensions ML²T⁻²

In order for the equation to be dimensionally correct, there needs to be an L³ term multiplied to the dimensions of pressure.
L³ is the dimension for volume V.


Hence PV = nkT is the correct equation.
Ha!
Correction ... a couple of minor errors ...


For nkT n (moles) is dimensionless as it is a measurement of relative mass.

Should read:

For nkT n (moles) is the number of particles has dimension N.

and;

k Boltzmann constant has the dimensions ML²T⁻²Θ⁻¹

Should read:

k Boltzmann constant has the dimensions ML²T⁻²Θ⁻¹ N⁻¹
meh ... it happens ...

Ken G
2018-Dec-28, 09:21 AM
It's not irrelevant, because it's vital as one of the limits where gas treatment breaks down.Obviously. I've already pointed out above that interparticle interactions move a system toward phase changes, and away from being a gas, so it's not what we care about when we look at things that are gases-- like the Sun. That point was already made above, to point out that very frequent interactions is not only not necessary for a gas, it actually takes you more toward a liquid or a solid. You want collisions to be rare, though it's nice if they are not absent.

Pressure is the derivative of total energy with respect to to volume, right?Not necessarily, that is only that if the system is insulated from any heat transport, so it is a special case. But it's also a more general type of pressure, including things other than gas pressure. By contrast, when I said gas pressure was 2/3 KE/V, that's true even if there is heat transport, it's just plain what gas pressure always is (nonrelativistically, and in the simple scalar treatment that you get from isotropic velocities).


And total energy is the sum of kinetic and potential energy.Well, if you include potential energy, you are not talking about gas pressure-- but I am. You would have a kind of effective pressurelike quantity that would include other contributions as well, like what is sometimes called "gravitational pressure", but now you've gone far afield from "gas pressure." We're having enough trouble understanding what gas pressure is, you don't want to bring in other types of pressurelike quantities!


And when "gas pressure" is derived from just kinetic energy part, a necessary assumption is that both interparticle interaction potential energy and its derivative with respect to volume are negligible relative to kinetic energy and its derivative.Yes, as I've said, gas pressure applies in the absence of interparticle interactions, which would move the material toward a phase change into a liquid or solid. What is meant by a "gas" neglects these, except it does allow a mean field. But when there is a mean field, gas pressure does not care about that field, it is still just 2/3 KE/V.


You may argue that interparticle repulsive potential energy due to degeneracy is somehow also "kinetic energy", but you cannot make the same argument about interparticle attractive potential energy.
There is no such thing as "interparticle repulsive potential energy due to degeneracy," that's not what degeneracy is at all. As I said above, degeneracy pressure is gas pressure, all that is different about it is its thermodynamics-- the way the KE is partitioned among the particles. No potential energy, no repulsion between particles, just 2/3 KE/V. As for when there is some kind of interparticle potential, then you don't have a simple gas any more, you have something else that is moving in the direction of some kind of phase change. Corrections for those things are certainly possible, but they're just not what is being discussed-- we're talking about gases in their idealized form, without any such corrections. In particular, gases in the Sun.

chornedsnorkack
2018-Dec-28, 04:07 PM
Obviously. I've already pointed out above that interparticle interactions move a system toward phase changes, and away from being a gas, so it's not what we care about when we look at things that are gases-- like the Sun. That point was already made above, to point out that very frequent interactions is not only not necessary for a gas, it actually takes you more toward a liquid or a solid. You want collisions to be rare, though it's nice if they are not absent.
Well, if you include potential energy, you are not talking about gas pressure-- but I am. You would have a kind of effective pressurelike quantity that would include other contributions as well, like what is sometimes called "gravitational pressure", but now you've gone far afield from "gas pressure." We're having enough trouble understanding what gas pressure is, you don't want to bring in other types of pressurelike quantities!
Yes, as I've said, gas pressure applies in the absence of interparticle interactions, which would move the material toward a phase change into a liquid or solid. What is meant by a "gas" neglects these, except it does allow a mean field. But when there is a mean field, gas pressure does not care about that field, it is still just 2/3 KE/V.

No potential energy, no repulsion between particles, just 2/3 KE/V. As for when there is some kind of interparticle potential, then you don't have a simple gas any more, you have something else that is moving in the direction of some kind of phase change. Corrections for those things are certainly possible, but they're just not what is being discussed-- we're talking about gases in their idealized form, without any such corrections. In particular, gases in the Sun.
Remember the original challenge that is the basis of this thread. That Sun consists of liquid, not gaseous hydrogen.
Happens not to be true. But this is not the null hypothesis now.
We need to understand precisely how fluid deviates from gas behaviour towards liquid-like behaviour, to know which deviations to look for to verify their absence or insignificance in Sun and confirm that Sun indeed behaves mostly like gas.
And before you dismiss the issue of checking beforehand, Sun obviously has some conspicuously un-gaslike properties.
Density of liquid hydrogen is 0,071 kg/l.
Average density of Sun is 1,4 kg/l. The density at centre of Sun is estimated at 140 kg/l. More like liquid than like gas.
I agree that Sun behaves more like gas than liquid in most other relevant respects. I am sure it can be demonstrated. But we still need to present such a demonstration.

Ken G
2018-Dec-28, 04:38 PM
Remember the original challenge that is the basis of this thread. That Sun consists of liquid, not gaseous hydrogen.Oh, I remember, that's why I stated in my very first post:

"In particular, he never calculates the single most important quantity in determining if a bunch of particles will act like a gas-- the ratio of their average kinetic energy to their average interparticle (nearest neighbor) potential energy. Whenever that number is very large, you have a gas-- that's what a gas means. (It is very large for the Sun.)"

Having dispensed with the gas vs. liquid issue, I then moved on to the other misconceptions about gases, so from that point on it's been all about neglecting interparticle potentials (which spawned a new thread because somehow better understanding gases is not relevant to understanding gases).


And before you dismiss the issue of checking beforehand, Sun obviously has some conspicuously un-gaslike properties.
Density of liquid hydrogen is 0,071 kg/l.
Average density of Sun is 1,4 kg/l.Comparing densities is not a good way to tell if something is a gas. It's not that I don't check, it's that I do understand the difference between a gas and a liquid-- and it isn't just density.


The density at centre of Sun is estimated at 140 kg/l. More like liquid than like gas.That would be true if being a liquid was all about density, but it isn't. The core of the Sun is an excellent ideal gas, that's why people who model the solar interior use the ideal gas law. Even white dwarfs are excellent gases, and their density is 10,000 times the core of the Sun!


But we still need to present such a demonstration.Just do an order of magnitude estimate of the quantity I mentioned in my very first post. I didn't do it because I know the answer, and anyone who doesn't can do it themself. But if it helps, one can note that the average interparticle distance in the core of the Sun is a few tenths of an Angstrom, so the interparticle potential is comparable to a hydrogen atom. In temperature units, that's a few 100,000 K. But the kinetic temperature is 14 million K, so is almost two orders of magnitude larger. It's a good gas. Or, look at the surface, where the interparticle potential is some 11 orders of magnitude less, and the temperature is only about 3 orders of magnitude less-- an even better gas. It's gas all the way through.

Since I mentioned white dwarfs, we can look at those as well. They are 100 times smaller than the Sun, so their electrons have about 100 times the kinetic energy. This means their interparticle Coulomb potential is actually comparable to the electron kinetic energy. However, the quantum mechanics forbids the electrons in a highly degenerate gas to scatter off the protons, so they act like they are moving freely, and it's still a good gas. Don't miss the irony-- white dwarf electrons are a good gas because they are rarely allowed to collide, not because they collide a lot!

chornedsnorkack
2018-Dec-28, 08:27 PM
Now, let us try to derive the relationship of pressure to kinetic energy.
Assume still gas - that interparticle forces are negligible.
Let a volume V have uniform thickness L and area S orthogonal to thickness such that V=L*S
Now the volume V contains mass M.
Suppose that precisely one half of the particles are moving towards the wall, with speed u, and the other half is moving away from the wall, also with speed u (velocity then -u).
The mass of the half of gas travelling towards wall is M/2, and its momentum thus Mu/2.
As it collides with wall and recoils with unchanged speed, it confers momentum 2*Mu/2=Mu
The half gas collides with wall in time L/u, so the force is F=Mu/(L/u)=Muˇ2/L
Pressure is P=F/S=Muˇ2/LS, but since LS=V, then P=Muˇ2/V
Now, while only the particles travelling towards the wall contribute to pressure, both directions of particle movement contribute to total enclosed kinetic energy. Therefore the kinetic energy is E=Muˇ2/2
And so Muˇ2 cancels out: Muˇ2=2E, and thus P=2E/V.
Note that I was not assuming Maxwell distribution. I assumed distribution at just two discrete and opposite velocity.
Since the velocity cancels out, the pressures and kinetic energies are proportional to Muˇ2 for any part of any distribution of velocities, including Maxwell, on one condition: that for each M and u separately, the amounts of particles travelling in opposite directions are equal.
Now, let us consider particles travelling in directions other than towards or away from wall.
These directions do not contribute to pressure, but do contribute to kinetic energy. Therefore the energy is tripled, and pressure is not. Thus indeed leading to
P=2E/3V
Note the initial assumption of equal numbers of particles travelling in each direction (and eventually, at each M and u combination severally). It may be more insightful to remember that space has 6 directions, not 3, and therefore a more revealing presentation is to refrain from cancelling:
P=4E/6V.

Ken G
2018-Dec-28, 08:45 PM
Yes, that is a way to do the derivation. So we can agree-- what gas pressure is is 2/3 KE/V, more generally than the thermodynamics of the ideal gas law. It produces a force per unit area on a wall in the way so many sources explain, but what they fail to explain is that the gas pressure is already there if the KE is-- and the wall isn't.

Selfsim
2018-Dec-28, 10:01 PM
Not only does P = nkT violate the ideal gas law, it is not even dimensionally (https://en.wikipedia.org/wiki/List_of_physical_quantities) correct.Nope. It's hard to learn anything about gases when you keep tying us up in your own errors.



For nkT n (moles) is dimensionless, as it is a measurement of relative mass.
{Corrected to}:For nkT n (moles) is the number of particles has dimension N.
And there is your error. Follow my math, and it is easy to see that n=N/V. That is, n is particle density. I said it above, but it's still safer to just assume that it means what makes the formula correct, because this is formula is mother's milk to a physicist.



Hence PV = nkT is the correct equation.
No, you have made a second error. To you, n is moles, and then the equation is not what you have, but rather p = nRT But as I said, n is particle number density, that's what physicists use because moles is actually a kind of silly unit.

Unfortunately Ken picked an inappropriate variable to define number density, as in thermodynamics “n” is the number of moles.

Had he left the equation as P = (N/V)kT, like everyone else uses, ρ = N/V, and there would have been no confusion.

I think it’s about time to dispel the argument, once and for all, that the ideal gas law P = ρkT is:

- indicative of the pressure,
- P is independent of volume (ie no barriers) and collisions,

by examining the schematics of how the gas law is measured in a laborator (http://members.iinet.net.au/~sjastro/astrophysics/gas.jpg)y.

The above linked diagram is self explanatory; it measures the gas law at a constant temperature and volume and the number of moles of gas is varied to measure the pressure.
If pressure is independent of volume, this amounts to removing the chamber in the diagram.
The obvious question becomes how do you measure the pressure of the gas without using volume?

One might think 'the escape clause' is to treat the gas as a fluid, but even in this case, the ideal gas law applies as the gas is modelled as a compressible fluid.
Here the test for the gas law can be based on keeping the number of moles constant and changing the volume to measure the pressure.
In either case pressure and volume are linked.

Furthermore as already pointed out, the ideal gas law is based on perfectly elastic collisions between particles and walls, even when describing a fluid:
https://www.youtube.com/watch?v=kOw8OON0Es4

It's no coincidence the experimental design of the test is based on collisions.
Since in 'Ken's interpretation', this is not the case, I request that Ken provides us with the schematics of an experimental design where pressure can be tested without volume, in particular the case where the volume is not constant .. (.. please ..).

Ken G
2018-Dec-28, 11:08 PM
The obvious question becomes how do you measure the pressure of the gas without using volume? And the obvious answer is, look at how the gas responds to that force. This can be done either by watching the gas accelerate, if there is not force balance, or measuring the force that is doing the balancing, if there is force balance. The "lightbulb" moment is when you understand that gas pressure gradients produce forces per unit volume on the gas. So yes, you should think of gas pressure as pushing on gas, and surface forces are what resist that-- when surfaces are present. That is, if you want to understand.

You see, the way you always get a force on a surface is by invoking the same constraint that surfaces always produce-- the "normal force." Gas pressure is no different from all the other ways you can push on surfaces. Hence my analogy with a bathroom scale, an analogy you can understand when you realize that gas pressure produces forces on the gas, the way gravity produces your weight and that's a force on you. Surfaces merely pony up whatever forces needed to keep the gas out-- exactly like they do when you stand on the ground, or lean against a wall. The important realization is that when sources say "gas pressure is a force per unit area on a surface," they are simply mistaking a force on the gas (gas pressure gradients) for a force on the surface (the standard action/reaction to the "normal force", which works the same way no matter what is pushing on the thing the surface is keeping out, be it gas, a person standing on a scale, or a ladder leaning against a wall-- so why on Earth do all those silly sources single out gas pressure like it was any different from all the other ways of generating a normal force? Think about it, we must use our brains instead of blind adherence to sources that may not provide the best insights.) When you understand these things, you see that this is precisely true. When you don't, well you go on endlessly about the ideal gas law, like it matters at all in understanding the mechanics of gas pressure! (It doesn't-- the ideal gas law is about the thermodynamics, as I showed, it rarely sets the pressure in an ideal gas and never sets the pressure in a non-ideal gas.)

Since in 'Ken's interpretation', this is not the case, I request that Ken provides us with the schematics of an experimental design where pressure can be tested without volume, in particular the case where the volume is not constant .. (.. please ..). Determining gas pressure gradient forces can be done in many ways, I gave some examples above that have nothing to do with walls or volumes. You may as well challenge me to find a way to measure the force of gravity without a scale, it's the same challenge and not any more difficult.

Geo Kaplan
2018-Dec-28, 11:13 PM
I think it’s about time to dispel the argument, once and for all, that the ideal gas law P = ρkT is:

- indicative of the pressure,
- P is independent of volume (ie no barriers) and collisions,

by examining the schematics of how the gas law is measured in a laborator (http://members.iinet.net.au/~sjastro/astrophysics/gas.jpg)y.

The above linked diagram is self explanatory; it measures the gas law at a constant temperature and volume and the number of moles of gas is varied to measure the pressure.
If pressure is independent of volume, this amounts to removing the chamber in the diagram.
The obvious question becomes how do you measure the pressure of the gas without using volume?

One might think 'the escape clause' is to treat the gas as a fluid, but even in this case, the ideal gas law applies as the gas is modelled as a compressible fluid.
Here the test for the gas law can be based on keeping the number of moles constant and changing the volume to measure the pressure.
In either case pressure and volume are linked.

Furthermore as already pointed out, the ideal gas law is based on perfectly elastic collisions between particles and walls, even when describing a fluid:
https://www.youtube.com/watch?v=kOw8OON0Es4

It's no coincidence the experimental design of the test is based on collisions.
Since in 'Ken's interpretation', this is not the case, I request that Ken provides us with the schematics of an experimental design where pressure can be tested without volume, in particular the case where the volume is not constant .. (.. please ..).

This is one of the weakest arguments you've put up here, selfsim. To conflate how one measures things with how one defines things is a rather serious conceptual error, and hardly "puts things to bed, once and for all."

As a non-pressure example, one defines the electrical potential one way (the energy per elementary charge acquired in falling through a field), and measures it another way (e.g., classically, the magnetic deflection of a needle affixed to a coil). By your logic, voltage must be magnetic if one uses an older-style analogue voltmeter to measure it.

You are, in effect, saying that a voltage does not exist unless a voltmeter is there to measure it; that a pressure does not exist unless a wall is there to define it. Worse, you are saying that how one measures a quantity actually defines what it is. I suppose you are free to hold that position, but it is not particularly useful. Nor does it acknowledge that we routinely define quantities in physics that cannot be directly measured non-perturbatively.

Selfsim
2018-Dec-29, 03:00 AM
To conflate how one measures things with how one defines things is a rather serious conceptual error, and hardly "puts things to bed, once and for all."Let's try and not get off track by generalizing here, eh? ... (The reason being that the discussion is, thus far, confined to Gas behavior).
A gas (https://en.wikipedia.org/wiki/Gas) happens to be specifically defined through using its specific physical properties, and by direct controlled (confined) measurement. Historically, these same measurements also then led directly onto the development of the ideal gas law.
This also stands as a classic example of where experiment, (ie: objective controlled measurements), came before theory:

Because most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussacand Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below).

And so, a 'physical property (https://en.wikipedia.org/wiki/Physical_property)' is:
A physical property is any property that is measurable, whose value describes a state of a physical system.[1] The changes in the physical properties of a system can be used to describe its changes between momentary states. Physical properties are often referred to as observables. They are not modal properties. Quantifiable physical property is called physical quantity.


As a non-pressure example, one defines the electrical potential one way (the energy per elementary charge acquired in falling through a field), and measures it another way (e.g., classically, the magnetic deflection of a needle affixed to a coil). By your logic, voltage must be magnetic if one uses an older-style analogue voltmeter to measure it.

You are, in effect, saying that a voltage does not exist unless a voltmeter is there to measure it; that a pressure does not exist unless a wall is there to define it. Worse, you are saying that how one measures a quantity actually defines what it is. I suppose you are free to hold that position, but it is not particularly useful. Nor does it acknowledge that we routinely define quantities in physics that cannot be directly measured non-perturbatively.
This is a more complex and controversial analogy and I am extremely hestitant to engage on it in this thread ... 'more complex' because the physical properties which you describe, can be either intensive or extensive, depending on the way the subsystems are arranged in your example and; 'controversial'​ because intense ideologies exist on the topic. I am not arguing 'gas pressure' from an ideological basis .. rather, just from the plain old 'mainstream science (consensus)' viewpoint. Suffice it to say also, confined measurement technique is shared with the 'gas pressure' topic.

Ken G
2018-Dec-29, 03:04 AM
Let's try and not get off track by generalizing here, eh? ... (The reason being that the discussion is, thus far, confined to Gas behavior).
A gas (https://en.wikipedia.org/wiki/Gas) happens to be specifically defined through using its specific physical properties, and by direct controlled (confined) measurement. Historically, these same measurements also then led directly onto the development of the ideal gas law.It almost sounds like you don't realize that an "ideal gas" that obeys the "ideal gas law" is not the same thing as a "gas." A "gas" is a more general entity, I told you above what it requires. What's more, all simple gases (not ideal gases, I mean any gas with isotropic nonrelativistic velocities) obey p = 2/3 KE/V, but they do not all obey the "ideal gas law." If you don't know these things, you really shouldn't dig yourself any deeper. Come on, you don't really know anything about gases, now do you? All you can do is insert contextually isolated verbiage from sources you don't really understand, and it's not lending any insight into this discussion, since you're not open to learning anything, and it appears all the others already have.

Here are the key takeaways that most seem to be getting:
1) gas pressure is 2/3 KE/V, that's just exactly what it is (for simple nonrelativistic gases, which include but are not limited to ideal gases), and
2) forces on walls are action/reaction pairs to what gets called "the normal force," show up in all kinds of situations, are constraint forces from how walls work, and in no way distinguish gas pressure from any other forces, including standing on the floor or leaning against the wall. There is no reason whatsoever to single out gas pressure and pretend that that force, compared to all the other ways of pushing and pulling on objects, somehow comes from a wall! That so many sources say that is just a broad misconception.

Selfsim
2018-Dec-29, 06:11 AM
The obvious question becomes how do you measure the pressure of the gas without using volume?
And the obvious answer is, look at how the gas responds to that force. This can be done either by watching the gas accelerate, if there is not force balance, or measuring the force that is doing the balancing, if there is force balance. The "lightbulb" moment is when you understand that gas pressure gradients produces forces per unit volume on the gas. The way you get a force on a surface is by invoking the same constraint that surfaces always produce-- the "normal force." Hence my analogy with a bathroom scale, an analogy you can understand when you realize that gas pressure produces forces on the gas, the way gravity produces your weight and that's a force on you. Surfaces merely pony up whatever forces needed to keep the gas out-- exactly like they do when you lean against a wall. The important realization is that when sources say "gas pressure is a force per unit area on a surface," they are simply mistaking a force on the gas (gas pressure gradients) for a force on the surface (the standard "normal force", which works the same way no matter what is pushing on the thing the surface is keeping out, be it gas, a person standing on a scale, or a ladder leaning against a wall.) When you understand these things, you see that this is precisely true. When you don't, well you go on endlessly about the ideal gas law, like it matters at all in understanding the mechanics of gas pressure! (It doesn't-- it's about the thermodynamics, as I showed.)

Since in 'Ken's interpretation', this is not the case, I request thatKen provides us with the schematics of an experimental design where pressure can be tested without volume, in particular the case where the volume is not constant .. (.. please ..).
Please don't try to interpret what I say, you never get it right. Either quote what I say, or leave me out of your misunderstanding.

Why do you persist in promoting the idea it is all about pressure gradients when it has already been explained in detail the gradients are negligible at small scales?
Your helium balloon example was sunk like a lead one, as you couldn’t explain why the balloon was spherical if pressure gradients prevail; the uplift was due to buoyancy forces rather than gradients; or why inflating a tyre results in an even force distribution on the surface, (rather than being directional opposite to gravity, if pressure gradients are the cause).

Then of course, there was no explanation forthcoming for the missing 99.75% of the pressure in a tyre ...

Selfsim
2018-Dec-29, 06:20 AM
One further response to this one:

This is one of the weakest arguments you've put up here, selfsim. To conflate how one measures things with how one defines things is a rather serious conceptual error, and hardly "puts things to bed, once and for all."

As a non-pressure example, one defines the electrical potential one way (the energy per elementary charge acquired in falling through a field), and measures it another way (e.g., classically, the magnetic deflection of a needle affixed to a coil). By your logic, voltage must be magnetic if one uses an older-style analogue voltmeter to measure it.

You are, in effect, saying that a voltage does not exist unless a voltmeter is there to measure it; that a pressure does not exist unless a wall is there to define it. Worse, you are saying that how one measures a quantity actually defines what it is. I suppose you are free to hold that position, but it is not particularly useful. Nor does it acknowledge that we routinely define quantities in physics that cannot be directly measured non-perturbatively.

I believe you may have also missed the point of my post.

The kinetic theory of gases explicitly states the change in momentum with time, is the result of particles colliding with a wall.

We have an alternative POV .. call it a 'hypothesis', which states something like (admittedly my wording):
'At scales at which laboratory experiments pertaining to the theory are performed, to inflating car tyres and balloons; a wall may not required to explain pressure'.

And then we have a 'hypothesis' which makes a definite prediction .. ie: 'no walls are required'.

The challenge is to show whether such experiments exist to support this hypothesis, or to devise a “no wall” experiment where the hypothesis can be tested.

I’m almost 100% certain the challenge will not succeed, and there will be no seismic paradigm shift that is going to overturn a theory that has its origins from the early 18th century.

Ken G
2018-Dec-29, 06:32 AM
Why do you persist in promoting the idea it is all about pressure gradients when it has already been explained in detail the gradients are negligible at small scales? Trust me, no one else on this thread has any idea why you are so obsessed with "small scales." The rest of us understand that a helium balloon a foot wide rises in the 10-mile-high atmosphere of the Earth, and we know why this happens-- because the gas pressure force on the helium balloon comes from a pressure gradient. Yes, a pressure gradient, on a "small scale." It doesn't matter to us at all whether the scale is big or small, if it is small, you get a small force, if the scale is big, you get a big force. The force is still due to pressure gradients, either way. It's just a fact, you are totally lost here and you should stop doubling down on your confusion. I've given you the tools to understand, you have to take them.


Your helium balloon example was sunk like a lead one, as you couldn’t explain why the balloon was spherical if pressure gradients prevail;Nope, I have no trouble explaining that at all, just look at the pressure gradient across the rubber surface of the balloon. Easy.

the uplift was due to buoyancy forces rather than gradients;Goodness, where to start. Buoyancy forces come from pressure gradients. This is the first thing to understand about buoyancy. Ever notice what happens in your ears when you dive down below the water? Pressure gradient. Buoyancy. Get it?


or why inflating a tyre results in an even force distribution on the surface, (rather than being directional opposite to gravity, if pressure gradients are the cause).
Again, there are two pressure gradients in a tire. One is vertical, and explains why a helium balloon would rise inside a tire. The second is across the rubber surface of the tire, and is why tires inflate. Pressure gradients.



Then of course, there was no explanation forthcoming for the missing 99.75% of the pressure in a tyre ...I cannot explain questions that make no sense and stem from your misunderstanding, there is just nothing to explain there. It's why I couldn't explain why you thought the ideal gas law had different units than it does, it's beyond explanation.

Geo Kaplan
2018-Dec-29, 07:02 AM
One further response to this one:


I believe you may have also missed the point of my post.

Your belief is misplaced.


The kinetic theory of gases explicitly states the change in momentum with time, is the result of particles colliding with a wall.

Regrettably, repetition of such a profound misapprehension does nothing to increase its validity. Your error has been explained quite clearly in several different ways.


We have an alternative POV .. call it a 'hypothesis', which states something like (admittedly my wording):
[I]'At scales at which laboratory experiments pertaining to the theory are performed, to inflating car tyres and balloons; a wall may not required to explain pressure'.

Bizarre. Simply bizarre.

I will leave you with one thought to ponder in quieter moments: If a point source sprays out particles radially from that point, one may most definitely define a pressure everywhere (or do you insist that standing next to an exploding bomb is safe?). Yet, there is no wall.

And with that I leave you to your beliefs. I cannot hope to explain your errors better than Ken G already has, nor do I have his patience. One can only lead someone else to knowledge; the final step must be taken by that individual.

profloater
2018-Dec-29, 10:13 AM
Quick thought. If you replace the helium balloon with a lead solid model of it, the buoyancy force is identical and is caused by a pressure gradient in the surrounding fluid. The helium (or the density )is not relevant to the buoyancy force.

LaurieAG
2018-Dec-29, 01:29 PM
So if you regard V as 1, i.e. unitary, 1^3 = 1, you could argue that V is not necessary numerically by redefining what the hidden V actually represents.

Now if this 'constant' unitary V represents a constant 'density' of any gas at different pressures an actual experimental 'Volume' can be back calculated from the 'desired' density or pressure and this would be expected to change while discretely 'measuring' different gasses and pressures.

This could be tested easily although you would have to adjust the results of the equation without V by the actual experimental volumes used to get 'V' = 1, and also add L^3 to the units, to normalize the two different equations and compare apples with apples and oranges with oranges in any 'general' application of the concept.

Ken G
2018-Dec-29, 02:09 PM
This sounds unnecessarily complicated-- can we not simply say that that concept of volume exists independently of the concept of containers, and be done with it?

Ken G
2018-Dec-29, 02:24 PM
I cannot hope to explain your errors better than Ken G already has, nor do I have his patience.
Thanks Geo, I confess that my patience comes mostly from the fact that I always learn things myself in discussions like this. For example, in this discussion, in all honesty I had not appreciated chornedsnorkack's point that anisotropic expansion of a collisionless gas will lead to anisotropic velocities unless the different directions receive some type of stirring (though as I pointed out above, the stirring does not need to come from interparticle collisions, even though many sources would have us believe our understanding of gases is lost without collisions).

And more fundamentally, I also had not realized that so many common sources so badly conflate the interesting and physically unique specifics of gas pressure with completely generic elements of the everyday normal force, as though the latter "produced" the former. So in all fairness, the misconception being promoted by Selfsim that you were pointing out did not start with him, it starts in these seemingly authoritative sources and the bizarre approach they take of describing a physical effect in terms of what it does when it encounters a surface. It would be like saying you only have a force of gravity on you when you are standing on the ground, or that a refrigerator magnet is only magnetic when it is against a metal surface, which no one would tolerate for an instant but we don't bat an eye when the sources do exactly that with gas pressure! Without Selfsim's participation, I would not have recognized how widespread is this misidentified role of surfaces in gas pressure, and so I would not have understood where Robitaille is getting his misconceptions from. It was quite a surprise, that for some reason, sources that are normally quite dependable cannot tell a "normal force" action/reaction pair from whatever interesting and unique physical effect is the cause of the generation of that force pair! So there is always some learning that occurs in discourses, and in this case I believe I may have succeeded in learning more from Selfsim's involvement than he did from mine, ironically-- though perhaps there is still hope.

grant hutchison
2018-Dec-29, 03:00 PM
Quick thought. If you replace the helium balloon with a lead solid model of it, the buoyancy force is identical and is caused by a pressure gradient in the surrounding fluid. The helium (or the density )is not relevant to the buoyancy force.And if you remove the source of the pressure gradient (gravity), the buoyancy force disappears.

Grant Hutchison

Ken G
2018-Dec-29, 03:14 PM
Right, but you see, the key point here is we must understand differently the cause of the gas pressure itself (which is internal random motions, a property of the gas itself that requires no participation from any walls) from how we understand the various external causes of pressure gradients (which could be due to walls, or gravity, or electric fields, or the history of the preparation of the system-- even there, nothing special about walls). Not doing that is precisely the error being made by all those many sources that say gas pressure is "produced by" walls! Once you understand this, you won't be able to look up "gas pressure" without a handy source of antacid nearby.

Swift
2018-Dec-29, 03:49 PM
It almost sounds like you don't realize that an "ideal gas" that obeys the "ideal gas law" is not the same thing as a "gas." A "gas" is a more general entity, I told you above what it requires. What's more, all simple gases (not ideal gases, I mean any gas with isotropic nonrelativistic velocities) obey p = 2/3 KE/V, but they do not all obey the "ideal gas law." If you don't know these things, you really shouldn't dig yourself any deeper. Come on, you don't really know anything about gases, now do you? All you can do is insert contextually isolated verbiage from sources you don't really understand, and it's not lending any insight into this discussion, since you're not open to learning anything, and it appears all the others already have.

Here are the key takeaways that most seem to be getting:
1) gas pressure is 2/3 KE/V, that's just exactly what it is (for simple nonrelativistic gases, which include but are not limited to ideal gases), and
2) forces on walls are action/reaction pairs to what gets called "the normal force," show up in all kinds of situations, are constraint forces from how walls work, and in no way distinguish gas pressure from any other forces, including standing on the floor or leaning against the wall. There is no reason whatsoever to single out gas pressure and pretend that that force, compared to all the other ways of pushing and pulling on objects, somehow comes from a wall! That so many sources say that is just a broad misconception.
In particular:

Come on, you don't really know anything about gases, now do you? All you can do is insert contextually isolated verbiage from sources you don't really understand, and it's not lending any insight into this discussion, since you're not open to learning anything, and it appears all the others already have.
This is completely inappropriate. Do not make public judgements about other members' abilities nor their interest in learning.

If this rudeness continues, there will be points for the next infraction.

Ken G
2018-Dec-29, 03:55 PM
All right, those words did sound personal. I don't actually have anything personal in mind, there is, in this thread, the information needed to understand gases and what causes both gas pressure (random particle motions)and what causes forces on gas from gas pressure (pressure gradients), as well as the difference between all that and the mundane elements of the normal force which do not "produce" gas pressure any more than the normal force of my bottom on my chair right now "produces" the force of gravity. I present all this for those who can get it, and I doubt I can say it any more clearly, so I can't imagine why I would need to add anything more.

grant hutchison
2018-Dec-29, 04:10 PM
Right, but you see, the key point here is we must understand differently the cause of the gas pressure itself (which is internal random motions, a property of the gas itself that requires no participation from any walls) from how we understand the various external causes of pressure gradients (which could be due to walls, or gravity, or electric fields, or the history of the preparation of the system-- even there, nothing special about walls).You don't need to persuade me.
I'm bemused anyone finds this objectionable.

Grant Hutchison

Ken G
2018-Dec-29, 04:48 PM
Isn't it remarkable how many sources talk about gas pressure as if it was an interaction with a wall instead of a property of a gas? You rarely see such situation-dependent thinking in such a completely general physics concept. I'm normally pretty impressed by how carefully thought out physics concepts are in the widespread sources on the topic, so this one is pretty disappointing. Maybe it's the chemists!

grant hutchison
2018-Dec-29, 05:54 PM
I guess, given the importance of Bernoulli and osmotic pressure in my line of work, I've long been used to thinking of pressure as implying energy density.

Grant Hutchison

Ken G
2018-Dec-29, 06:43 PM
Me too, so I haven't looked at the common sources much lately. That's why I was so shocked what googling "gas pressure" will get you!

George
2018-Dec-29, 06:47 PM
Isn't it remarkable how many sources talk about gas pressure as if it was an interaction with a wall instead of a property of a gas? It's not that surprising to me being more in the engineering and the heavy equipment world. When definitions simply state it as a force per unit area it's hard not to have a wall come up (pun intended, of course). It's as if the cart is so big that the horse is hard to see, which makes it all the more interesting.

Your points have broadened my understanding of it and how it applies to stars is especially interesting. I'm sure there are engineering efforts that require this more accurate definition of gas pressure as well, perhaps fusion reactor containment designs or other energy field work.

Len Moran
2018-Dec-29, 06:48 PM
Just for my benefit, I would like to clarify some thoughts I have on this issue at I would say a fairly basic level. So any comments would be appreciated to aid this clarification.

(1) From Wikipedia:
Pressure means how much something is pushing on something else. It is expressed as force per unit area: P=F/A

(2) If I'm banging a nail into a piece of wood, I will be pushing a hammer which in turn pushes a nail which in turn pushes a piece of wood. But to obtain the required end result (work), the piece of wood has to be fixed in position and thus creating an opposing force.

(3) If the piece of wood was not fixed in position, then my arm,hammer,nail and piece of wood will be pushing against air pressure. If I was doing all of this in a vacuum then the whole assembly of my arm, hammer,nail and piece of wood would not be encountering an opposing force.

In (2), going by the definition (1) pressure seems to be intuitive as well as scientific.

In (3) it would seem that in terms of the definition (1) pressure is not present intuitively or scientifically when everything takes place in vacuum.

But I would assume that in the case of (3) any presence of anything (no matter how weak the opposing force) the other side of my bit of wood would give an opposing force, so then, in terms of the definition, pressure is present scientifically if not intuitively (i.e. atmospheric pressure on the other side of my bit of wood is hardly going to facilitate the nail being driven home).

So the obvious question I have is, if a gas is expanding into a vacuum where there is no opposing force, is there actually a gas pressure?

I appreciate that this is sort of going over old ground in that we can ask is there weight without some bathroom scales. There isn't weight as such, but the force of gravity is still there. Place the scales on a descending platform and there will be some weight, place the scales on a free falling platform and there will be no weight. But the force of gravity is there unchanged in all of these scenarios.

But...place some gas in a container with the container being in a very large vacuum, the definition of pressure in (1) works admirably well. Make a little pinhole and the pressure drops. Remove the walls and the pressure drops to nothing because there is no opposing force, all the gas has as a boundary is a vacuum. But at all times within these scenarios the gas has isotropic momentum.

In the gravity analogy, we confine weight to the weighing scales and acknowledge that the force of gravity is always present regardless of the status of the weighing scales in terms of its presence or descending motion.

In dealing with gas, the consensus is that pressure is not confined to the equivalent of the weighing scales, rather it is there all the time, even if the boundary of a gas is a vacuum despite definition (1) suggesting that pressure is something pushing against something else.

So perhaps, what I should be asking for is a definition of gas pressure that doesn't involve "something pushing on something else".

In none of the above am I making the suggestion that pressure is "made" by the opposing force of a barrier, just as I would never suggest that a weighing scales makes weight. It just seems to me that the term pressure is just a word to describe the effect of something pushing on something else, I don't see that the term has any intrinsic properties, that it is "something" out there waiting to come into existence like a flame or explosion. It just seems to be a descriptive term when something pushes against something else. You know it is happening when you produce work, its not that the work produces something magical with intrinsic properties of "pressure", rather the intrinsic property is work, be it an explosion from a ruptured gas container to a harmless measurement. It is work that is the intrinsic entity, the term "pressure" just seems to be our way of noting the work in a convenient and easy, manner.

Hornblower
2018-Dec-29, 06:56 PM
Don't forget that in Ken G's model with no collisions between the gas particles, the gas cloud is gravitationally bound, if I am not mistaken. That is what we have with a star. I envision the particles in his model as buzzing around like the stars in a globular cluster. If we could magically turn off the gravity, the cloud would expand, with a corresponding drop in the gas pressure.

Len Moran
2018-Dec-29, 07:57 PM
Don't forget that in Ken G's model with no collisions between the gas particles, the gas cloud is gravitationally bound, if I am not mistaken. That is what we have with a star. I envision the particles in his model as buzzing around like the stars in a globular cluster. If we could magically turn off the gravity, the cloud would expand, with a corresponding drop in the gas pressure.

That helps - that allows my definition of pressure being "something pushing against something else". It also allows me to continue to prefer the term "work" to pressure. The gravitational field is providing an opposing force to the isotropic particle velocities, so work is being done there. Magically switch off the gravitational field and the gas particles have no opposing force, so no work gets done. But all of the particle velocities are still intact.

So the work is there with the gravitational barrier in place, reduce the force of that barrier and less work gets done. Remove it completely and the work is zero. So work is dependent on the barrier, it isn't there when the barrier is removed.

....I think.

Ken G
2018-Dec-29, 08:04 PM
(1) From Wikipedia:
Pressure means how much something is pushing on something else. It is expressed as force per unit area: P=F/AYes, that is the problem. This is a very limited way to think about pressure, because pressure is a much more general (and powerful) concept than that! It is true that pressure has units of F/A, and that's how it acts when there is a sudden pressure discontinuity (as when a wall is present), but the concept is so much more general than that so it's really unfortunate to get misguided by those units. After all, it also has the units of energy density, and if you want forcelike units, notice that a force is a rate of change of momentum, so F/A is a flux density of momentum. Also, pressure gradients have units of force per unit volume, and both of those latter ways of thinking about gas pressure are powerful when you realize that the gas pressure force is a force on the gas. Defining it as a force on the enclosure of the gas simply confuses the pressure force with the action/reaction pair forced called the "normal force," which appears in many different situations involving surfaces and has nothing to do with the nature of the forces that are making the normal force appear.



(2) If I'm banging a nail into a piece of wood, I will be pushing a hammer which in turn pushes a nail which in turn pushes a piece of wood. But to obtain the required end result (work), the piece of wood has to be fixed in position and thus creating an opposing force. Not so, and this is very much the point. You can hit a nail with a hammer in free space, and accelerate the nail, without any wood present. Is that somehow a different hammer force than if the wood is present? Yet that's how you see gas pressure forces explained, astonishingly.


(3) If the piece of wood was not fixed in position, then my arm,hammer,nail and piece of wood will be pushing against air pressure. See how you are imagining a hammer must push against something? No, the nail has inertia, so the hammer can push on it, there is no need for any resistance. There the work done will simply show up as kinetic energy in the nail, should we really consider that to be a different kind of force?


In (2), going by the definition (1) pressure seems to be intuitive as well as scientific.And wrong! Note how it led you to a wrong conclusion, you thought you cannot push against a nail unless something "opposes it." That's wrong, and it's also wrong for gases-- gases can be pushed around by their own pressures, no resistance needed other than their own inertia.


So the obvious question I have is, if a gas is expanding into a vacuum where there is no opposing force, is there actually a gas pressure?A useful question-- have you ever heard of gas pressure in the early universe? Is that not exactly the scenario you are describing? How about light pressure after the era of recombination (where photons are noncollisional), doesn't that appear in cosmological models? (It happens to be a small contribution, but it could have been large and it would be the same equations.)

But the force of gravity is there unchanged in all of these scenarios.Precisely, and so is the gas pressure. This is very important, gas pressure is just gas pressure-- it doesn't change at all when you put the gas next to a wall. What the wall does is create a discontinuity in gas pressure, which you can agree is something quite different.


But...place some gas in a container with the container being in a very large vacuum, the definition of pressure in (1) works admirably well. And that's the problem-- that's the only situation where it works, just like bathroom scales are the only situation where weight is easily confused for a normal force. But gas pressure is a much more general concept, just like gravity is.

Remove the walls and the pressure drops to nothing because there is no opposing force, Oh really? Remove a all and the gas pressure instantly drops to nothing? See how you are making errors based on the misconception you are analyzing?


In dealing with gas, the consensus is that pressure is not confined to the equivalent of the weighing scales, rather it is there all the time, even if the boundary of a gas is a vacuum despite definition (1) suggesting that pressure is something pushing against something else.Right, now you see it.


So perhaps, what I should be asking for is a definition of gas pressure that doesn't involve "something pushing on something else". Yes, that's what you should be demanding from those sources that let you down so badly. I can give you a conceptual definition, and then a more precise (but more mathematically complicated) one. The conceptual one is that gas pressure quantifies the tendency of a gas to expand. The mathematical one is that gas pressure is the tensor that determines the rate the gas particles carry momentum across imaginary surfaces you can mentally insert anywhere you like without any effect on the gas. This tensor quantity simplifies to a scalar behavior in the simple case of isotropic motions, so that's why this simplification has been inserted so much above. The scalar gives the rate, per area, that momentum is carried across any imaginary surface, with the subtle point I mentioned above that when leftward momentum is carried from left to right, and rightward momentum is carried from right to left, they both contribute positively to the pressure scalar. The reason is that if you make an imaginary box, momentum carried one way into the box adds positive momentum to the box, whereas momentum carried the other way out of the box subtracts negative momentum from the box, both of which produce the same force (when you think of force as vector momentum deposition rate).

It just seems to me that the term pressure is just a word to describe the effect of something pushing on something else, I don't see that the term has any intrinsic properties, that it is "something" out there waiting to come into existence like a flame or explosion.You are right, that is how the word is being used in those sources, but that's exactly the problem. This is a terrible way to think about what gas pressure is, because it is far more powerful to think of it in a much more general way-- a property of the gas itself.


It just seems to be a descriptive term when something pushes against something else. We already have a term for that-- it's called "the normal force." I agree that "the normal force" is a very generic term and is not widely understood outside of physics, because it is really just a constraint force that bears no particular connection to whatever other forces are causing it to appear, but it is much worse to mistake gas pressure for a normal force on a wall. It's just as bad as mistaking gravity for the normal force on the chairs we are sitting on.

It is work that is the intrinsic entity, the term "pressure" just seems to be our way of noting the work in a convenient and easy, manner.And so you see the problem-- gas pressure can do work without any walls, and to see that, simply blow out a candle.

profloater
2018-Dec-29, 08:18 PM
And if you remove the source of the pressure gradient (gravity), the buoyancy force disappears.

Grant Hutchison
Yes and it is surprising that pressure is not understood by some as within a gas, (it was the removal of the need for collisions that helped me earlier) when we experience weather such as wind all our lives, (not the other kind of wind) and surely we know that pressure gradient drives winds? No surfaces required.

Len Moran
2018-Dec-29, 09:11 PM
And so you see the problem-- gas pressure can do work without any walls, and to see that, simply blow out a candle.

Well that helps thanks. To understand gas pressure as being a real and proper property of gas in its own right helps to place the kind of definition "pressure is something pushing against something else" in a better context. That definition starts you off with a mindset that sees gas pressure as being "a"(a gas) pushing against "b"(a wall), from that point on it's difficult to think of "a" as being separated from "b" in terms of pressure. But your (as always) detailed look under the conventional approaches allows us to simply start and finish with "a" as a system with a self contained property of pressure.

That (for me at any rate) is quite a departure from how I have always thought about gas pressure.

Ken G
2018-Dec-29, 09:28 PM
Apparently that's because it's a departure from how it's normally taught. To the standard approach, a wind isn't a thing, it's something that blows against your cheek. We're usually so adept at abstract concepts in physics, it's odd to find an example that is so pinned down to concrete experience. The topic of gas pressure must have a very different history than we normally find in physics-- temperature and density have much more formal meanings that sound more like intrinsic properties.

Selfsim
2018-Dec-29, 09:37 PM
...
And more fundamentally, I also had not realized that so many common sources so badly conflate the interesting and physically unique specifics of gas pressure with completely generic elements of the everyday normal force, as though the latter "produced" the former. So in all fairness, the misconception being promoted by Selfsim that you were pointing out did not start with him, it starts in these seemingly authoritative sources and the bizarre approach they take of describing a physical effect in terms of what it does when it encounters a surface. It would be like saying you only have a force of gravity on you when you are standing on the ground, or that a refrigerator magnet is only magnetic when it is against a metal surface, which no one would tolerate for an instant but we don't bat an eye when the sources do exactly that with gas pressure! Without Selfsim's participation, I would not have recognized how widespread is this misidentified role of surfaces in gas pressure, and so I would not have understood where Robitaille is getting his misconceptions from. It was quite a surprise, that for some reason, sources that are normally quite dependable cannot tell a "normal force" action/reaction pair from whatever interesting and unique physical effect is the cause of the generation of that force pair! So there is always some learning that occurs in discourses, and in this case I believe I may have succeeded in learning more from Selfsim's involvement than he did from mine, ironically-- though perhaps there is still hope.
There is no misconception being promoted by SelfSim.

What we have here, is a clear-cut case of an Against the Mainstream advocation by yourself.

In all my time reading threads on this site, I have never seen anything as clear-cut as what you are doing, which is what I have been distinguishing for others, all along. There is a line and your argument clearly steps over it.

And, with your above statements, it seems even you now concur with the depth and breadth of mainstream consensus sharply contrasting with your idea.

This is not a comment directed at you personally, Ken and I assure you, I do appreciate and understand deeply your overall idea ... however, the responsibility for taking appropriate actions on how this thread should be treated, lies somewhere beyond both of us.

The point is, that the onus is on yourself for defending your idea with your own objective experimentation evidence in the face of the vast weight of countering mainstream evidence.

Ken G
2018-Dec-29, 09:50 PM
There is no misconception being promoted by SelfSim.

What we have here, [B]is a clear-cut case of an Against the Mainstream advocation by yourself.I thought you might say that. It certainly would seem to be true, but only for someone who really doesn't understand everything else that is being said in this thread. Aren't you ignoring all those posts by other contributors? Why would you do that?


And, with your above statements, it seems even you now concur with the depth and breadth of mainstream consensus sharply contrasting with your idea. Well, what the evidence has shown me is that common "mainstream" explanations of what gas pressure is are often quite poor, as they have led to a stream of false statements by you and other people on the thread who fell victim to those misconceptions. This was demonstrated above. Sadly, it sometimes happens that widespread seemingly good sources can make a hash of some particular concept, and then you have to either use your own brain, or consult more advanced sources. Graduate level textbooks are often the best for the latter option, but are hard to give people access to, so I normally resort to the former option on this forum. Ultimately, it just comes down to whether or not you want to understand gas pressure. You've made your choice, so have the others.



The point is, that the onus is on yourself for defending your idea with your own objective experimentation evidence in the face of the vast weight of countering mainstream evidence.Actually, the arguments I've provided are the only "defense" I require or intend. As I said, the rest is up to each person who reads the thread, I can't explain it any better.

grant hutchison
2018-Dec-29, 10:21 PM
What we have here, is a clear-cut case of an Against the Mainstream advocation by yourself.Sorry, but that seems like complete nonsense to me, and no more defensible for being delivered in Bold Italic Underline.
Ken has done nothing here but explain an understanding of pressure with which I've been familiar for decades. Whereas your own erroneous comments about buoyance forces suggest you have a deep misunderstanding somewhere.

Grant Hutchison

Selfsim
2018-Dec-29, 10:38 PM
I thought you might say that. It certainly would seem to be true, but only for someone who really doesn't understand everything else that is being said in this thread.Appearances can be deceptive.

How else would a 'foil' going up against your clearly tightly held idea, come away as appearing any other way?

Anyway how I appear doesn't really matter so much .. as long as the distinction of what 'mainstream' means has been clarified (a little?)


.. Well, what the evidence has shown me is that common "mainstream" explanations of what gas pressure is are often quite poor, as they have led to a stream of false statements by you and other people on the thread who fell victim to those misconceptions. This was demonstrated above.
I admitted and disclosed any personally made oversights and misreads. I think you'll find honesty there. My not responding to those posters who defend your idea is merely out of necessity and efficiency .. and no disrespect is intended.


Sadly, it sometimes happens that widespread seemingly good sources can make a hash of some particular concept, and then you have to either use your own brain, or consult more advanced sources. Graduate level textbooks are often the best for the latter option, but are hard to give people access to, so I normally resort to the former option on this forum. Ultimately, it just comes down to whether or not you want to understand gas pressure. You've made your choice, so have the others.
Unfortunately, in the process your argument, you have not provided sufficient evidence for distinguishing the speaker of 'your idea', from a myriad of other countless other conversations of the same type, which I've had with ideologicially driven acolytes, (similar topics), whose basis of agumentation is identical.
The 'tools' of which you speak, unfortunately, lack the necessary backing to hold up in the face of those arguments.

As I said, all you've provided here is yet another idea where: 'I'm right and everyone else is wrong'.


Actually, the arguments I've provided are the only "defense" I require or intend. As I said, the rest is up to each person who reads the thread, I can't explain it any better.You don't have to explain that .. I get it .. and your idea simply doesn't get to the level where I can make use of it, I'm afraid.

Cheers

Ken G
2018-Dec-29, 10:51 PM
I admitted and disclosed any personally made oversights and misreads. I think you'll find honesty there.I'm certain you are not being dishonest, but honesty isn't the issue, misunderstanding is. I see a clear connection between the misconceptions you have about gas pressure, and your errors involving the ideal gas law, the difference between a gas and a fluid, and the source of buoyancy. These are all concepts that follow quite easily from a better understanding of what gas pressure is, yet you resist that better understanding. So your mistakes don't surprise me at all, this is the whole point of what I'm trying to do here-- provide a better understand to help avoid mistakes and false conclusions. I've seen this work well with other posters, and you should have seen that too-- just by reading carefully. Yet you resist. That's a personal thing, it's none of my business.



As I said, all you've provided here is yet another idea where: 'I'm right and everyone else is wrong'.Not everyone else.


You don't have to explain that .. I get it .. and your idea simply doesn't get to the level where I can make use of it, I'm afraid.Yes, I reached that conclusion some time ago. Unfortunately, this means you likely will also not understand gases and fluids, the ideal gas law, and buoyancy, as well as a host of other pressure-related topics that didn't come up, like how gas pressure appears in general relativity. But you don't have to care, as I said, it's a personal choice.

grant hutchison
2018-Dec-30, 12:11 AM
Unfortunately, in the process your argument, you have not provided sufficient evidence for distinguishing the speaker of 'your idea', from a myriad of other countless other conversations of the same type, which I've had with ideologicially driven acolytes, (similar topics), whose basis of agumentation is identical.And that looks very much like the Argument of the Squid.

Grant Hutchison

Jens
2018-Dec-30, 02:53 AM
I realize that the issue is a bit deeper, but in a sense this reminds me of the question of whether a falling tree makes a sound if there is nobody there to hear it. You can make the argument, which I find fairly silly, that the vibrations in the air, which definitely occur, are not sound until somebody hears them. It seems that Wikipedia and other sources are almost making the same mistake for pressure. So I have no problem with Ken’s argument and I also don’t understand why it’s controversial.


Sent from my iPhone using Tapatalk

Ken G
2018-Dec-30, 05:00 AM
Yes you're right, it's a bit like asking if a sound wave is a pressure pattern in the air, or something that happens in your ears. It isn't the semantics we care about, we have to call these things something, it's that we want to understand what is happening in the air-- not what is happening in our ears.

chornedsnorkack
2018-Dec-30, 07:40 AM
Note the reasoning that the condition of pressure summing up as
4E/6V
is that M should be equal for every opposite u

Yes, if Mu do not cancel out then we have a net wind of the bulk.
But the momentum is given by Mu - pressure by Muˇ2
You can easily have momentum cancelling out (no net wind) but pressures unequal in opposing directions if the velocity distribution is such that at one u, particles move in one direction, and at another u, in opposite direction.

Ken G
2018-Dec-30, 10:04 AM
It's not opposing directions that matter (as I mentioned, momentum transport along opposing directions just adds to the gas pressure, never "cancelling out"), but rather perpendicular ones. That's why gas pressure is most generally a tensor. But as I've said many times, to keep things simple, and to make pressure act like the scalar we all know and love, the assumption of isotropic velocities in the fluid frame is necessary. This is the core assumption of a simple gas-- not collisions. Indeed, frequent particle-particle interactions don't make the behavior more gaslike, it makes it closer to a phase transition to a liquid. However, some small collisionality is everyone's favorite way to enforce isotropic velocities, though it can also come from other things (such as the cosmological principle, in the case of cosmic photon pressure, which is highly noncollisional after the era of recombination-- but also small). Another common way to enforce isotropy is to have particles interacting with randomly varying fields, as often happens in collisionless plasmas. A final application where isotropy is maintained noncollisionally is when you have spherical symmetry in a static distribution maintained by self-gravity, such as a slowly evolving nearly spherical galaxy of stars. Arms in spiral galaxies is also a common application of collisionless gas dynamics, though I don't know if the anisotropic complexities there require a tensor pressure treatment.

LaurieAG
2018-Dec-30, 10:08 AM
This sounds unnecessarily complicated-- can we not simply say that that concept of volume exists independently of the concept of containers, and be done with it?

I have just presented the caveats, that your explanations omitted, to highlight the pitfalls associated with regarding 'special' cases (with redefined hidden variables) as 'general' cases, which was directly implied due to those omissions.

In the 'general' case the concept of volume does not exist 'independently of the concept of containers' so you need to provide a method/mechanism (different to mine) to prove that your statement in the 'special' case is truly 'independent of the concept of containers' in the 'general' case.

The end result is a draw, no side is completely right or completely wrong, a quantum conundrum if you like.

Ken G
2018-Dec-30, 10:51 AM
I have just presented the caveats, that your explanations omitted, to highlight the pitfalls associated with regarding 'special' cases (with redefined hidden variables) as 'general' cases, which was directly implied due to those omissions.
Unfortunately, this sentence does not make much sense to me.


In the 'general' case the concept of volume does not exist 'independently of the concept of containers' so you need to provide a method/mechanism (different to mine) to prove that your statement in the 'special' case is truly 'independent of the concept of containers' in the 'general' case. That one, even less.
I would quite confidently state that the general concept of volume requires no input from the concept of containers, as a universe devoid of containers (say, our universe after the era of recombination) could still find use for the concept of volume and its crucially related notion of density. Hence the concept of volume does not rely on containers, but rather, volume is an attribute of a container. It is also an attribute of a region of empty space. Indeed, the concept of the volume of a container can be regarded as an attribute the container inherits from the empty space that it encloses.

The end result is a draw, no side is completely right or completely wrong, a quantum conundrum if you like.It's not a competition, but what's clear is that one "side" understands gases, and the other does not, leading to a host of misconstrued claims about fluids, the ideal gas law, buoyancy, kinetic theory, and so on. This is the purpose, and it's up to the individual-- all victories are personal victories of achieving, or not achieving, insight.

slang
2018-Dec-30, 11:43 AM
This thread was supposed to be about gas behavior, and not forum member behavior. If a bunch of adult people cannot discuss such a topic without bickering about each other like little kids, we'll just close it.

For the any next threads: please learn to ignore baiting, and re-read every one of your posts before submitting, to check if you're talking about attributes of an idea, or of a person. And if you find that it is about a person, or not specifically about the topic, simply don't post. It's really not that hard. You don't lose anything by not posting a bunch of already typed words, and gain a lesson in thinking before posting. How's that for a new years resolution?