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Nonkers
2006-Aug-13, 08:50 PM
If the Sun was suddenly totally extinguished, what would be the surface temperature of the Earth after 1 day, 1 week, 1 year and 10,000 years (ignoring gravitational effects)?

Ken G
2006-Aug-13, 09:10 PM
It's not an easy question, but you can get some hint by looking at the Moon. It only takes one night for the surface of the Moon to get quite cold, and that's not much different from what would happen to the Earth in 1 day (probably a bit longer, as water holds a lot of heat). Then, more of the same the second day, and you get the idea. In 1 week, it'd be extremely cold, and in a year, it would probably start asyptotically approaching the coldest it will get (which it reaches once the rate the Earth radiates balances the heat flux from the core.) I don't know what the core flux is, but I think it might be somewhere in the ballpark of 1% of what the Earth radiates now. If so, that means the final temperature after a year or maybe a few will be about 100 Kelvin.

neilzero
2006-Aug-13, 09:23 PM
I'll take a wild guess. Present average surface temperature is about 285 k. in 24 hours it would cool to 280k
7 th day 250 k if linear, but I'll guess 270 as the oceans would not freeze except near the poles
30 th day 135 if linear, but I'll guess 150k
365 th day 20k all the volitiles (except the neglible quantities of helium and hydrogen) would be frozen on the surface, but the temperature a mile below the ice and snow would be a bit warmer than before, as the frozen volitiles would slow the heat loss at the surface. Volcanoes would become more active after a few years. It might take 10,000 years for the average surface temperature to cool to 15 degrees k. Neil

Nonkers
2006-Aug-13, 09:24 PM
At what temperature does air become liquid?

Would those right next to geysers and volcanic magma be able to survive some time (assuming they had food and artificial illumination)?

Van Rijn
2006-Aug-14, 12:58 AM
A long time ago I posted a breakdown from Fogg's "Terraforming" on what would happen if Venus was screened from sunlight, but I can't seem to find it. Anyway, in the case of Venus, with a thick hot atmosphere, it would take about two centuries for most of the atmosphere to freeze out. First there would be period of cooling, then as CO2 rained out, there would be a period where the pressure dropped but the temperature remained the same. Then the CO2 would start freezing and there would be another period where the temperature remained the same.

The earth has a much thinner atmosphere, but the water in the oceans have a large energy content. Temperatures would drop and the oceans would start freezing. For awhile that would stabilize temperatures. As the surface became solid, heat transfer would slow, but there would still be some transfer. The bottom of the oceans would probably be the last to go far below freezing temperatures. Air temperatures would drop, the little CO2 that is there would freeze out. Eventually, oxygen would start raining out, and the temperature would stabilize for a time, then nitrogen would rain out. Then eventually it would freeze and temperatures would stabilize again. Finally, things would get down to background temperature.

PhantomWolf
2006-Aug-14, 01:15 AM
I think that Van Rijn is onto something here that most people don't think about. Certain state transistions require energy, and while they are happening they steal, or put back energy into the system. In Chemistry we do fractional distillation. If you mix Ethanol and Water and then boil the resulting liquid, it will boil at 78.15°C, not 100°C, and that liquid will be 95% Ethanol. The Temperature will then not rise until all the Ethanol is gone.

In the Atmosphere we have the same deal. As each volitile condenses and then freezes, there will be a period where the temperature will not drop. We see this already in our weather, when the ground temp gets to a Dew Point, where the water condenses, it will not get colder until enough water has been removed from the air to allow the dew point temperature to continue dropping. (when this hits zero you get a frost.) As a result you'd see the atmosphere go through a number of "rains" and "snows" where the temperature of the planet would not change a great deal, followed by the next period of cooling.

Ken G
2006-Aug-14, 02:51 AM
It's true that you'll freeze the water, but I doubt you'll freeze or condense anything else of significance, for the reasons I gave above.

publius
2006-Aug-14, 03:52 AM
I'll bet if you went underground, or underwater, you could last a long time, provided you had some energy source to make electricity to keep the air purified, make light to grow plants you brought you down, etc.

About the oceans freezing. Salt water will behave differently that fresh water, and I wonder just how long it would take for the tops of the oceans to freeze, and at what temperature. I imagine it would remain liquid below the surface layer for a long time. Currents and variations in salt concentration and overall density would probably make this fairly complex.

For example, if you have a temperature probe, get some ice out of the freezer and put in a fairly insulated container, like a mug. Then pour some table salt on the ice and stick your temp probe in it. You'll see the ice melt and the temperature of the mixture drop. This is how your grandmother used to make ice cream, and why they salt bridges and overpasses during ice and snow storms. :)

-Richard

TriangleMan
2006-Aug-14, 04:34 AM
About the oceans freezing. Salt water will behave differently that fresh water, and I wonder just how long it would take for the tops of the oceans to freeze, and at what temperature.
The tops of the oceans freeze during the winter in Northern latitudes (and vice versa during the southern winter) so it would not take long for the top part of the oceans to freeze. I'd imagine that if the sun stopped shining the Earth would become pretty inhospitable in less than a week, and most life would be gone within a month, except for maybe deep-water animals and cave dwellers.

WaxRubiks
2006-Aug-14, 04:36 AM
I read a story once about how a rouge star came into the solar system and took the Earth with it. There was a man who survived by keeping a fire going fueled by frozen methane and frozen oxygen, and by warming up frozen oxygen he could keep breathing. I cant remember what he did for food.

crosscountry
2006-Aug-14, 04:42 AM
It's true that you'll freeze the water, but I doubt you'll freeze or condense anything else of significance, for the reasons I gave above.

and even that would be well below 0C wouldn't it? At what temp does salt water freeze?

TriangleMan
2006-Aug-14, 04:53 AM
At what temp does salt water freeze?
It depends on the salinity of the water but generally ice can form on the surface of an ocean at around -2C. Wave action makes it more difficult to freeze over so the temperature has to be less for a length of time before a solid layer of ice forms.

Goblin
2006-Aug-14, 05:02 AM
It's not an easy question, but you can get some hint by looking at the Moon. It only takes one night for the surface of the Moon to get quite cold, and that's not much different from what would happen to the Earth in 1 day (probably a bit longer, as water holds a lot of heat). Then, more of the same the second day, and you get the idea. In 1 week, it'd be extremely cold, and in a year, it would probably start asyptotically approaching the coldest it will get (which it reaches once the rate the Earth radiates balances the heat flux from the core.) I don't know what the core flux is, but I think it might be somewhere in the ballpark of 1% of what the Earth radiates now. If so, that means the final temperature after a year or maybe a few will be about 100 Kelvin.

Why use the moon which has no atmosphere? Use the earth at night for your example.

Van Rijn
2006-Aug-14, 08:16 AM
It's true that you'll freeze the water, but I doubt you'll freeze or condense anything else of significance, for the reasons I gave above.

Just to make that clear: It would depend on earth's own radioactively generated heat, which you believe might keep temperatures above what it would take to liquify oxygen and nitrogen.

Ken G
2006-Aug-14, 11:10 AM
I read a story once about how a rouge star came into the solar system and took the Earth with it. There was a man who survived by keeping a fire going fueled by frozen methane and frozen oxygen, and by warming up frozen oxygen he could keep breathing.

Yeah, but that isn't right. The oxygen would never freeze, the Earth would not get that cold.

Ken G
2006-Aug-14, 11:15 AM
Why use the moon which has no atmosphere? Use the earth at night for your example.

I didn't want to use the Earth at night because the atmosphere shares warmth from the day side to the night side. Also, the amount of heat stored in Earth's atmosphere must be a lot less than is stored in the ground, relative to the no-Sun temperature. The ocean has been mentioned, that's kind of a wild card, but I still think lunar rock and Earth's ocean will behave somewhat similarly, at least more so than bringing in the insignificant heat capacity of the atmosphere.

Ken G
2006-Aug-14, 11:17 AM
It would depend on earth's own radioactively generated heat, which you believe might keep temperatures above what it would take to liquify oxygen and nitrogen.

Yes, that's the point, and I'm quite certain it would not freeze oxygen and nitrogen. You won't liquify them either-- not only does that take cold, it takes high pressure, and you won't have it.

cjbirch
2006-Aug-14, 12:21 PM
It depends on the salinity of the water but generally ice can form on the surface of an ocean at around -2C. Wave action makes it more difficult to freeze over so the temperature has to be less for a length of time before a solid layer of ice forms.



Surely water would freeze quicker than you are proposing, no radiated energy source would be sufficient for the movement of air and water as we know. Happy to be told otherwise!

CJ

pghnative
2006-Aug-14, 02:13 PM
Yes, that's the point, and I'm quite certain it would not freeze oxygen and nitrogen. You won't liquify them either-- not only does that take cold, it takes high pressure, and you won't have it.
Unless I'm doing my cipherin' and my gusintas wrong, your guess is a little off.

From (caveat) wikipedia, the Earth's core generates 3.7 E13 watts.
Using 5.1E14 m2 as Earth surface area, the equilibrium blackbody temperature of earth is about 33K. Plenty cool to both liquify nitrogen and oxygen*, and eventually freeze both.

Conversely, I think it'd take longer to cool than you estimate. The big difference between the Earth cooling and the moon cooling, is that the moon's surface is stagnant. On earth, as the ocean surface surrenders heat, the water becomes denser and sinks, allowing warm water to surface.

Maybe later I'll put pen to paper and figure out how much energy is in the ocean compared to how much earth radiates and current temps. I'll need to estimate average water temp (10C???) and average earth temp (25C???)

*Not sure if the oxygen will liquify first. Since it is only 20% of the atmosphere, it'll liquify on Earth at a lower temperature than its stated boiling point of ~90K. Whether that temperature is above the freeze point, I don't know.

crosscountry
2006-Aug-14, 03:05 PM
From (caveat) wikipedia, the Earth's core generates 3.7 E13 watts.
Using 5.1E14 m2 as Earth surface area, the equilibrium blackbody temperature of earth is about 33K. Plenty cool to both liquify nitrogen and oxygen*, and eventually freeze both.

Conversely, I think it'd take longer to cool than you estimate. The big difference between the Earth cooling and the moon cooling, is that the moon's surface is stagnant. On earth, as the ocean surface surrenders heat, the water becomes denser and sinks, allowing warm water to surface.


Hmmm... I thought lakes froze on top because after a certain point of cooling water actually becomes less dense and rises. The ice then blocks the warm water from reaching the surface. If that weren't the case marine animals wouldn't be able to live out the winter.



Maybe later I'll put pen to paper and figure out how much energy is in the ocean compared to how much earth radiates and current temps. I'll need to estimate average water temp (10C???) and average earth temp (25C???)

*Not sure if the oxygen will liquify first. Since it is only 20% of the atmosphere, it'll liquify on Earth at a lower temperature than its stated boiling point of ~90K. Whether that temperature is above the freeze point, I don't know.

I'm not sure composition makes a difference. Oxygen liquefies at the same temp (pressures being equal) whether mixed or not.

Charles Law.


I didn't want to use the Earth at night because the atmosphere shares warmth from the day side to the night side. Also, the amount of heat stored in Earth's atmosphere must be a lot less than is stored in the ground, relative to the no-Sun temperature. The ocean has been mentioned, that's kind of a wild card, but I still think lunar rock and Earth's ocean will behave somewhat similarly, at least more so than bringing in the insignificant heat capacity of the atmosphere.


You're right that the atmosphere holds lots less energy. But I think the oceans hold quite a bit making it less than a wild card. It's also very well known the heat index of water. The volume is known fairly well I suspect to figure total energy of the ocean.




I think the easiest way to solve this problem would be to known the total input of solar heat at all wavelengths, and estimate the heat loss from the atmosphere. Now, that would change after time and probably not be linear. Of course phase transitions would make be very important.

neilzero
2006-Aug-14, 03:17 PM
Hi cj: You must be thinking -2 f, not 29 degrees f = -2 degrees c. I would have guessed about -10 degrees c to get ice on the ocean surface.
Both fresh water and ocean water have a peculier property of maximum density at about 4 degrees c = 39 degrees f. When the surface water cools to that temperature, it starts to sink to the bottom, exposing warmer water. Only a thin layer of ice is possible until all the water has cooled to 4 degrees c. Neil

cjbirch
2006-Aug-14, 03:29 PM
Hi cj: You must be thinking -2 f, not 29 degrees f = -2 degrees c. I would have guessed about -10 degrees c to get ice on the ocean surface.
Both fresh water and ocean water have a peculier property of maximum density at about 4 degrees c = 39 degrees f. When the surface water cools to that temperature, it starts to sink to the bottom, exposing warmer water. Only a thin layer of ice is possible until all the water has cooled to 4 degrees c. Neil

Yep schoolboy error!

pghnative
2006-Aug-14, 03:34 PM
Hmmm... I thought lakes froze on top because after a certain point of cooling water actually becomes less dense and rises. Correct-- the break point is ~ 4C. So until the ocean becomes uniformly 4C, there will be a top to bottom circulation as the top cools. This would slow down the cooling of the Earth (as compared to how quickly the moon cools down.). You're right, we'd need to do some calculations of the current radiation rate compared to the total heat energy of the oceans. By the way, freezing gives off a tremendous amount of heat energy, so as the oceans froze, much of earth solid surface would remain at 0C.

I'm not sure composition makes a difference. Oxygen liquefies at the same temp (pressures being equal) whether mixed or not.
Nope -- composition makes a big difference. Water will liquify out of the atmosphere (ie, dew) at a higher temperature when the relative humidity is higher. Meteorologists routinely talk of "dew point" as an indication of how humid the air is.

You're confusing total pressure with what chemists call "partial pressure". Partial pressure is simply total pressure multiplied by the fraction* of the individual component. So the partial pressure of oxygen at sea level is approximately 3 psi (20% x ~15 psi).

The boiling point of O2 at sea level is 90K. This means that the vapor pressure of liquid oxygen at 90K = ~15 psi. At lower temperatures, the vapor pressure of liquid oxygen will be less than 15 psi. So if you want to determine the temperature at which O2 will start to rain, you need to know the temperature at which liquid O2 has a vapor pressure of about 3 psi. (all of this assumes that the total atmospheric pressure stays the same -- I think it essentially would, but I'm not sure). This temperature is a lot less than 90K.

The same caveat applies to nitrogen -- but since it's fraction in the air is 80%, it's "dew point" likely isn't much lower than its boiling point.

*It's actually mole fraction, not mass fraction, but this fraction is about the same for O2/N2 mixtures

neilzero
2006-Aug-14, 03:38 PM
Hi ken: "never" is a very long time. After about 100 trillion years, nearly all the isotopes would have decayed to negligible and Earth would be about 1 degree k all the way to the center, and everything would be frozen except a trace of helium.
A mini black hole (if any) at the center of Earth might keep the average temperature at several degrees k, but even a mini black hole would eventually injest all the mass of Earth after which the only heat source would be evaporation of the black hole. Neil

crosscountry
2006-Aug-14, 03:41 PM
you're talking really low temperatures. I've seen liquid nitrogen :/


I do think the atmosphere would condense as it cools. Just Charles Law in effect.



Dew point is lower than the boiling point of water true. So it all makes sense. Been a long time sine studying pressure temperature diagrams.

pghnative
2006-Aug-14, 04:03 PM
you're talking really low temperatures. I've seen liquid nitrogen :/~30 - 35K if my calculation is correct.


I do think the atmosphere would condense as it cools. Just Charles Law in effect.
Not sure what Charles Law is -- but I think the data shows that N2 would rain, and later freeze, while O2 would almost certainly go directly from vapor to solid (much like the CO2 would).

Squashed
2006-Aug-14, 05:12 PM
Correct-- the break point is ~ 4C. So until the ocean becomes uniformly 4C, there will be a top to bottom circulation as the top cools. This would slow down the cooling of the Earth (as compared to how quickly the moon cools down.). You're right, we'd need to do some calculations of the current radiation rate compared to the total heat energy of the oceans. By the way, freezing gives off a tremendous amount of heat energy, so as the oceans froze, much of earth solid surface would remain at 0C.

True much of the oceans' surface would be at zero celsius but the air temperature would plummet quite low as has been seen in the polar regions regularly. So to stay "warm" one would have to tunnel down to the ocean ice and lay on it with a blanket on top.

Weather would be quite violent during the transition as the cold from the land masses mixed with the warm damp air of the oceans.

I would predict that most of multicellular life, outside the oceans, would be dead within a week as subzero temperatures caught the world by surprise.

The comforts of humanity would disappear overnight due to the increased energy requirements of heating/lighting overburdening the electrical infrastructure (that and violent weather downing powerlines).

Gas furnaces and petro heating systems would fail as each supply was exhausted or as breaks in piping occurred due to the stress of the lower temperatures.

Violence would erupt as competition for heat sources increased which would quicken the pace of extinction.

Life as we know it will all end quite quickly, without the sun.

In such a scenario being on a nuclear submarine would prolong your life the longest but eventually cannibalism and/or barbarism would kill you.

neilzero
2006-Aug-14, 06:05 PM
pghnative @10:13 am August 14, 2006: Several decades ago the average temperature of Earth was 55 f. Figure 56 f due to global warming. Neil

Ken G
2006-Aug-14, 06:20 PM
Hi ken: "never" is a very long time.

That is true, I only meant in the longest time frame mentioned in the OP. Never say never!

Ken G
2006-Aug-14, 07:38 PM
From (caveat) wikipedia, the Earth's core generates 3.7 E13 watts.
Using 5.1E14 m2 as Earth surface area, the equilibrium blackbody temperature of earth is about 33K.
I'll have to find the info Grant Hutchison sent me, but for 30 K to be right, the heat flux coming up through Earth would have to be a factor 10,000 less than the radiation from the Sun, and that sounds way too small to me.


Plenty cool to both liquify nitrogen and oxygen*, and eventually freeze both.
Why would they freeze?

pghnative
2006-Aug-14, 07:51 PM
OK, a little more math with some surprising results.

First, assuming average earth temperature of 13C (286K), then earth is radiating ~ 2E17 watts, (Joules/sec).

The total water in earth's oceans, seas, etc seems to be about 1 E 24 grams. Let's assume the average water temperature is 9C.

To cool all of earth's water from 9C to 4C, which I think we agree would happen before the oceans iced over, therefore requires over 2 E25 Joules. At the current radiative rate, this would require over 3 years.

The biggest flaw in the above analysis is that I used an average temperature, instead of a weighted average temperature. The weighting needs to by a factor of temperature to the fourth power --- nevertheless, the hot areas would quickly cool down to ~ 13C, so the flaw isn't too big.

The two big unknowns are:
a) would the kinetics of cooling/freezing overwhelm the kinetics of upwelling. It takes a while for "warm" water a mile deep to rise to the surface due to density effects. Would the surfaces freeze before the ocean as a whole reached maximum density?

b) to what extent is the "warmth" of the ocean distributed to the land? In other words, would the oceans radiate heat directly to space, or would some of that warmth be distributed throughout the landed areas. Certainly small islands would stay above freezing for quite some time.

Pockets of humanity (the ones that didn't kill themselves through wars) would hold out for at least several months, burning whatever fuel they had left for warmth, and consuming whatever dead animals/plants they were able to preserve.

pghnative
2006-Aug-14, 08:06 PM
Why would they freeze? Well, assuming my numbers are correct and the equilibrium earth temp is 30K, then both would solidify. N2 does this at 63K, O2 at 54K.


I'll have to find the info Grant Hutchison sent me, but for 30 K to be right, the heat flux coming up through Earth would have to be a factor 10,000 less than the radiation from the Sun, and that sounds way too small to me.
The best info I could find is this story here (http://www.earthinstitute.columbia.edu/news/2004/story05-14-04.html). Ignoring the point of the article, they do show data that indicates that 1% of solar irradiance = 3 watts/m2.

Again using 5 E 14 m2 for earth area, this gives an irradiance of 1.5 E17 watts, which is 4 orders of magnitude higher than the core energy that I referenced.

Edited to remove caveat about Wikipedia data. According to here (http://www.mantleplumes.org/Energetics.html) and here (http://www.nature.com/nature/journal/v436/n7050/full/436467a.html;jsessionid=0CA0EA44B315927307E6BC8CA0 3788C3), earth heat output is indeed on the order of 10E13 watts. So unless I plugged the numbers incorrectly, the 30K value is correct.

PhantomWolf
2006-Aug-14, 09:03 PM
you're talking really low temperatures. I've seen liquid nitrogen :/

Bleah! I've played with the stuff, even poured it all over my hand*.







*If trying this at home, don't do it palm up. This could lead to pooling and severe cold burns.

Jim
2006-Aug-14, 09:19 PM
I read a story once about how a rouge star came into the solar system and took the Earth with it. There was a man who survived by keeping a fire going fueled by frozen methane and frozen oxygen, and by warming up frozen oxygen he could keep breathing. I cant remember what he did for food.

"A Pail of Air" by Fritz Leiber.

Alfred and Effie live on an Earth that has been knocked off it's orbit and is drifting without the warmth and light of the Sun. ... They survive in an apartment building, slowly burning what coal they can find to keep warm and keep the air from freezing. Then one day when Bud went to get a pail of frozen air, he saw a light moving through the building across the way.

In Leiber's story, the earth's atmosphere has frozen in layers. Bud is looking for the oxygen layer, which they will heat over the coal fire.

Leiber researched the premise very well and the story is scientifically accurate. The freezing process took long enough for Alfred to build a safe room for them to survive.

Van Rijn
2006-Aug-14, 09:44 PM
And here is a link to the story, A Pail of Air. (http://www.webscription.net/chapters/0743498747/0743498747___6.htm)

Ken G
2006-Aug-14, 11:43 PM
Well, assuming my numbers are correct and the equilibrium earth temp is 30K, then both would solidify. N2 does this at 63K, O2 at 54K.
Then it's important to get the numbers right. I wish I could find what Grant posted.


Again using 5 E 14 m2 for earth area, this gives an irradiance of 1.5 E17 watts, which is 4 orders of magnitude higher than the core energy that I referenced.
I can't find any contrary numbers at this point, so I'll have to concede the point.

Goblin
2006-Aug-15, 03:45 AM
I remember reading that while space is very cold it can't cool things as fast as say cold air can. Ie. Something that is 100c would get to 0c faster at the north pole vs being in space. In space it would eventually catch up and get colder but the race to 0c would be lost. It had to do with cold air molecules being able to remove heat faster than a cold vacumme.

I have not looked into so don't know if it really correct.

ZaphodBeeblebrox
2006-Aug-15, 03:53 AM
I remember reading that while space is very cold it can't cool things as fast as say cold air can. Ie. Something that is 100c would get to 0c faster at the north pole vs being in space. In space it would eventually catch up and get colder but the race to 0c would be lost. It had to do with cold air molecules being able to remove heat faster than a cold vacumme.

I have not looked into so don't know if it really correct.
Actually, you're Quiite Riight ...

Heat Transfers Via 3 Methods:

Conduction, Being in Direct Contact
Convection, Movement of a Surrounding Fluid
Radiation, Direct Removal of Energy Via PhotonsIn a Vacuum, ONLY The Laast One Functions, Outside of Random Particle Collisions, Ergo Things Lose Heat and Thereby Cool Down, Faster!!!

Jim
2006-Aug-15, 12:34 PM
Ah, yes, the science behind the Thermos bottle.

However, I don't think anyone has ever explained how a Thermos knows to keep hot things hot and cold things cold. (Sorry, old joke, but I couldn't resist.)