# Thread: <Gas behavior>

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## <Gas behavior>

Originally Posted by Presocratics
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.
Last edited by Ken G; 2018-Dec-20 at 03:45 PM.

2. Originally Posted by Ken G
... 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?
Last edited by Selfsim; 2018-Dec-21 at 03:14 AM.

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Originally Posted by Selfsim
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.
Last edited by Ken G; 2018-Dec-21 at 05:49 AM.

4. 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?

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Originally Posted by Selfsim
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.
Last edited by Ken G; 2018-Dec-21 at 05:57 AM.

6. 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?

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Originally Posted by Selfsim
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.
Last edited by Ken G; 2018-Dec-21 at 09:54 PM.

8. 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):
Originally Posted by Ken G
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).

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 10˛ł 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?

9. Originally Posted by Ken G
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.
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)?

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Originally Posted by Selfsim
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).
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.
Last edited by Ken G; 2018-Dec-22 at 09:46 PM.

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Originally Posted by Selfsim

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.
Last edited by Ken G; 2018-Dec-22 at 09:50 PM.

12. 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:
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:
Originally Posted by Ken G
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(0.5˛) = 0.5Mű˛ where M is the molar mass of the gas.

Combining the two equations gives:
ű˛ = 3RT/M
√ű˛ = √3RT/M
√ű˛ 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)
Originally Posted by Ken G
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
Last edited by Selfsim; 2018-Dec-23 at 07:54 AM. Reason: ű˛ is speed .. and not a 'mu', wrong link

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Originally Posted by Selfsim
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:
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(0.5˛) = 0.5Mű˛ 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:
ű˛ = 3RT/M
√ű˛ = √3RT/M
√ű˛ 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.
Last edited by Ken G; 2018-Dec-23 at 08:50 AM.

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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.

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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?

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Originally Posted by chornedsnorkack
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).
Last edited by Ken G; 2018-Dec-23 at 09:59 AM.

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Originally Posted by Ken G
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?

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Originally Posted by chornedsnorkack
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).
Last edited by Ken G; 2018-Dec-23 at 04:54 PM.

19. 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'):

Originally Posted by Ken G
.. 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.

Originally Posted by Ken G
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).

Originally Posted by Ken G
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.

Originally Posted by Ken G
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_...EN_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

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Originally Posted by Selfsim
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.
Last edited by Ken G; 2018-Dec-24 at 02:45 AM.

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Originally Posted by Ken G
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.

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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?
Last edited by Ken G; 2018-Dec-24 at 07:37 AM.

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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.

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Originally Posted by chornedsnorkack
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.
Last edited by Ken G; 2018-Dec-24 at 04:43 PM.

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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.
Last edited by Ken G; 2018-Dec-24 at 06:24 PM.

26. 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'.

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'.

Originally Posted by Ken G
Originally Posted by SelfSim
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.

Originally Posted by Ken G
Originally Posted by SelfSim
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 based on the assumptions posited by the kinetic theory of gases.

Originally Posted by Ken G
Originally Posted by SelfSim
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(?)

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Originally Posted by Selfsim
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 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.
Last edited by Ken G; 2018-Dec-26 at 01:53 AM.

28. This derailment/side discussion about gas behavior has been split off from this thread.

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

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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.
Last edited by Ken G; 2018-Dec-26 at 06:37 AM.

30. 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) ..
T
here 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= P(exp(-zg/RT)), where P 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.
Last edited by Selfsim; 2018-Dec-26 at 11:15 AM.

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