B Warm air goes up....reason on a microscopic scale?

[Wrichik Basu]

I was wondering about the microscopic reason warm air rises up, while cold air comes down. I am aware of the macroscopic reason - density changes. But what happens microscopically? Decrease in density means that the gas molecules are widely spaced out, but their mass remains the same. Then why does warm air go up?

 

[BvU]

Hi,

Microscopically, it's all collisions, collisions and collisions.
Basically 'hotter gas' means 'higher kinetic energy of molecules'.
Faster molecules go further and redistribute kinetic energy in the 'slower' volume.
Faster molecules exert more 'pressure'

All from the kinetic theory of gases, which google to find something you like to study from

(PS I do hope some real expert like @Chestermiller puts me right if I claim too much )

 

[Wrichik Basu]

Faster molecules go further and redistribute kinetic energy in the 'slower' volume

And the slower molecules just come down when displaced from their position?

 

[BvU]

You can't have read all this stuff in the link yet ? A bit heftier is e.g. this pdf. But a textbook might be more suitable.

'just come down' doesn't describe it in a conceptually responsible manner. It's probably right statistically, though.

Microscopically, gravity is just a puny effect. But for the huge number of molecules involved it only works in one direction: 'down', so macroscopically it sure counts.

 

[Wrichik Basu]

You can't have read all this stuff in the link yet ? A bit heftier is e.g. this pdf. But a textbook might be more suitable.

'just come down' doesn't describe it in a conceptually responsible manner. It's probably right statistically, though.

Microscopically, gravity is just a puny effect. But for the huge number of molecules involved it only works in one direction: 'down', so macroscopically it sure counts.

I know kinetic theory of gases. I know that the molecular speeds and collisions increase with increase in temperature. I just wanted to know why the increased collisions and velocity pushes the molecules up.

 

[BvU]

The density of a hotter gas is lower macroscopically. But you were asking about microscopic effects.

I just wanted to know why the increased collisions and velocity pushes the molecules up.

'They need more room' is unsatisfactory, I suppose ?

 

[Dale]

I was wondering about the microscopic reason warm air rises up, while cold air comes down. I am aware of the macroscopic reason - density changes. But what happens microscopically? Decrease in density means that the gas molecules are widely spaced out, but their mass remains the same. Then why does warm air go up?

The decrease in density is the reason. Temperature is a statistical phenomenon so you need a decent number of molecules. If you have a large enough number of molecules to have a well defined temperature then you also have a well defined density.

 

[Wrichik Basu]

'They need more room' is unsatisfactory, I suppose ?

It's satisfactory.

What happens to the gas which is cool? It needs less room. That's why it comes down?

 

[Wrichik Basu]

The decrease in density is the reason. Temperature is a statistical phenomenon so you need a decent number of molecules. If you have a large enough number of molecules to have a well defined temperature then you also have a well defined density.

So you're saying that kinetic theory of gases explains change in density, and density, in turn, explains the rising of hot gases, right?

 

[Drakkith]

Hmmm. Might if have something to do with the fact that the pressure at the bottom of a mass of air is higher than at the top? Would the warm air molecules be able to better transfer their kinetic energy to the cooler air molecules near the top than the bottom because of this pressure difference? I assume that the warm mass of air that's rising is not composed of the same air molecules as it rises, but is the result of the net transfer of energy to air molecules progressively higher and higher up.

 

[sophiecentaur]

cooler air molecules

You can't really have hot or cold molecules. A mass with molecules that are, on average, faster, will be hot etc.. Hot and Cold are Macroscopic terms.
I feel that the OP is under a bit of a misapprehension that better understanding things necessarily has to involve a microscopic approach. The statistics of a situation are highly relevant to what happens and the behaviour of an individual part of a system may tell you nothing useful.

 

[Drakkith]

You can't really have hot or cold molecules. A mass with molecules that are, on average, faster, will be hot etc.. Hot and Cold are Macroscopic terms.

Sorry, Sophie, but I don't see how my post uses the terms hot and cold (or warmer and cooler) in an incorrect or inaccurate way. I'm still talking about the statistical behavior of large numbers of molecules, a situation where hot and cold apply just fine.

 

[Dale]

So you're saying that kinetic theory of gases explains change in density, and density, in turn, explains the rising of hot gases, right?

I agree with that, but what I was saying is that the concept of temperature only makes sense with a whole bunch of molecules, and once you have enough molecules to have temperature then you also have enough molecules to have density.

 

[rumborak]

Drakkith, I think your intuition about the pressure differential is right. In zero gravity hot air doesn't "move", it only slowly equalizes in temperature.

I suspect the higher average kinetic energy gives the "hot" molecules more opportunity to escape both up and down, whereas the "cold molecules" have less opportunity to do so, feeling gravity more in comparison. This probably results in a sort of "sorting algorithm", where hot molecules slowly percolate up.

 

[sophiecentaur]

Sorry, Sophie, but I don't see how my post uses the terms hot and cold (or warmer and cooler) in an incorrect or inaccurate way. I'm still talking about the statistical behavior of large numbers of molecules, a situation where hot and cold apply just fine.

I don't think I'm being picky to pick on the use of hot or cold as a way to describe a molecule. That was what you appeared to b e doing in your post. Rather than 'hot molecules', you could use "hot gas with mostly faster molecules in it" but it is the gas that's hot and not the molecules
We're in the region of the Maxwell's Demon which is a though experiment in which there is a trap door which let's fast molecules through one way and slow molecules through the other way - thus separating all the 'hot' molecules from all the 'cold' molecules. Thermodynamics doesn't allow that.
I remember a guy describing the three electron beams in an old CRT tube as having red green and blue electrons in them. That was almost allowed into a BBC TV Science programme script until I got agitated about it. Same (not false) dichotomy.

 

[sophiecentaur]

This probably results in a sort of "sorting algorithm", where hot molecules slowly percolate up.

But the molecules are likely rather to transfer their momentum to nearby molecules than to move by themselves. Gas conducts heat faster than diffusion of different gases. And conduction works downwards too. This is why I am not happy with trying to deal with the 'small' in statistical processes.

 

[Drakkith]

I don't think I'm being picky to pick on the use of hot or cold as a way to describe a molecule. That was what you appeared to b e doing in your post.

That's certainly not what I intended.

Rather than 'hot molecules', you could use "hot gas with mostly faster molecules in it" but it is the gas that's hot and not the molecules

Ah, but the gas is composed of a large number of molecules, so saying "hot molecules" should be synonymous with "hot gas" in this case.

I suspect the higher average kinetic energy gives the "hot" molecules more opportunity to escape both up and down, whereas the "cold molecules" have less opportunity to do so, feeling gravity more in comparison. This probably results in a sort of "sorting algorithm", where hot molecules slowly percolate up.

I'm not so sure. I'm thinking along the same vein as sophie, in that individual molecules are mostly randomly moving about and it is their net transfer of energy upwards that leads to the hot mass of rising air, not because the original molecules in the warm air are all moving upwards.

 

[Stephen Tashi]

I was wondering about the microscopic reason warm air rises up, while cold air comes down. I am aware of the macroscopic reason - density changes. But what happens microscopically?

That's an interesting question and to consider it seriously, you would have to model a microscopic situation.

For starters, suppose we have two containers having the same dimensions In one container, we have one slow moving particle and in the other container a fast moving particle. As the particles move and bounce off the walls of the container, does one spend more time near the top of the container than the other? If the container was tall and the slow moving particle was very slow, it might never bounce up near the top of the container.

For another simplistic situation, consider the case when the slow moving particle does have enough energy to hit the top of the container and bounce off of it. Consider particles that are bouncing straight up and down. As time passes, which of the particles spends more time in (say) the top half of the container? I haven't computed the answer , but it amounts to combining the analysis of two elementary physics problems - i.e. "A ball is shot upward from the ground with initial velocity V0 ..." and "A ball is thrown straight down from a height H with an initial velocity -V1..". (The question isn't which particle spends the greater percentage of its "own" time in the top half of the container, the question is which particle has spent more time in the top half of the container after a long time T has elapsed. )

 

[rumborak]

I'm not so sure. I'm thinking along the same vein as sophie, in that individual molecules are mostly randomly moving about and it is their net transfer of energy upwards that leads to the hot mass of rising air, not because the original molecules in the warm air are all moving upwards.

What you are describing is heat conduction. However, air actually being a pretty good insulator, it could not account for the often drastic and fast changes.
Nah, hot air rising is likely to be due to convection instead. Even in the atmosphere, that's how wind comes about after all.

 

[Drakkith]

What you are describing is heat conduction. However, air actually being a pretty good insulator, it could not account for the often drastic and fast changes.

Hmm. Good point.

 

[sophiecentaur]

saying "hot molecules" should be synonymous with "hot gas"

I think this is the nub of our disagreement. You are implying that the word 'molecules' increases the understanding of the phenomenon. We're in the same neck of the woods as when people want to discuss circuit theory in terms of 'electrons', as if that will help them in any way at all. The microscopic has its place but that place is not everywhere. If I throw a brick at you and I describe its trajectory, would it help in any way at all to discuss the molecules of the brick, rather than using macroscopic Newtonian Physics.
Of course, I realize that you know the basics but I always try to look at these questions from the point of view of someone who doesn't. Your approach to this particular problem could serve to promote the mistaken impression that the microscopic is the only really valid approach. But just look at General Relativity. So far, it has not been reconciled with QM, which is the ultimate in microscopic approaches.

 

[Drakkith]

You are implying that the word 'molecules' increases the understanding of the phenomenon.

No, I'm just using "hot molecules" in lieu of "molecules of the hot mass of air".

We're in the same neck of the woods as when people want to discuss circuit theory in terms of 'electrons', as if that will help them in any way at all.

It often does as long as the person asking understands that while you can talk about what the an individual or small number of charges in a wire are doing, the equations and components that are encountered in basic circuit theory are described and formulated in terms of the net behavior of a large number of charges.

Your approach to this particular problem could serve to promote the mistaken impression that the microscopic is the only really valid approach.

This is silly. The OP literally asked what's going on at the molecular level, so I don't know why you're berating me for some imagined slight against scientific education when all I've done is say "cooler air molecules" instead of whatever you personally prefer. I appreciate your dedication to wanting to teach people the correct terms and avoid inaccuracies and pitfalls, but I can't help but feel as if you're twisting what I've said all the way to the breaking point and blowing it well out of proportion.

 

[sophiecentaur]

This is silly. The OP literally asked what's going on at the molecular level, so I don't know why you're berating me

Sorry. I am 'berating' the idea and not the man.
I would say that the correct answer is that there is not a one step answer at the molecular level and I think the OP should have been given that message from the start (or at least a massive caveat). The relationship between PV and T can be derived from a particle model as can the density but, once you've got the macroscopic model, surely you stick with it. When a gas departs from Ideal, due to the effect of Van Der Waal's forces, any PVT calculations can still be done. Where is one supposed to stop in the use of microscopic models? Would every physics calculation have to include lower than statistical treatment in order for it to be 'acceptable'? I guess my Engineering background can be blamed for my being prepared to have my scientific life full of black boxes but the onion approach to learning seems to work very well; you only need to peel away another layer when the one you are at starts to let you down.

 

[Wrichik Basu]

@Drakkith and @sophiecentaur hope that the misunderstanding has been resolved, because it doesn't look good when two esteemed members of PF don't agree over something

From all the discussions, I've come to this conclusion: I should explain change in density using kinetic theory, and then use density for explaining the rest.

Thanks for the explanations. I've once again received a proper explanation at PF, and thanks to all for that

 

[Khashishi]

Consider a bunch of microscopic dots, moving in random directions in a box. Consider an imaginary surface cutting the box into a top and bottom half. The dots in the bottom half move faster than the dots in the top half. So, there are more dots that move across the surface from the bottom half to the top half than vice versa.

But, as more bottom dots start to invade the top half, collisions between the bottom and top dots pushes some more top dots into the bottom half.

 

[Steelwolf]

In a gas, if the particles have differing temperatures this can be represented as 'size' since a hotter particle is moving faster it covers more distance over a given time period, so it ends up being a case of the Brazil Nut question, where the larger items come to rest on the top of the smaller particles since they are able to travel down while the larger particle will be constrained this direction. So the larger particles end up self-sorting in the gravity field to have larger (or hotter) particles (atoms or molecules) coming out on top of the smaller/cooler ones.

 

[Drakkith]

@Drakkith and @sophiecentaur hope that the misunderstanding has been resolved, because it doesn't look good when two esteemed members of PF don't agree over something

Hey, I'll be more worried when Sophie starts agreeing with everything I say. Then I'll know he's finally lost his marbles and I don't have any left to spare.

 

[sophiecentaur]

@Drakkith and @sophiecentaur hope that the misunderstanding has been solved, because it doesn't look good when two esteemed members of PF don't agree over something

From all the discussions, I've come to this conclusion: I should explain change in density using kinetic theory, and then use density for explaining the rest.
Thanks for the explanations. I've once again received a proper explanation at PF, and thanks to all for that

No worries - we always kiss and make up in the end. And we weren't disagreeing about the Physics - just the approach, which is often a matter of preference.

since a hotter particle is moving faster

This idea doesn't allow for collisions and momentum exchange. Which is the "hot" particle after a collision? This just makes my point again, that particles are just fast or slow. Why can they be hot or cold when, if you do your homework, you realize that Temperature is a measure of the Average Kinetic Energy of all the particles?

 

[Demystifier]

Instead of a kinetic approach, I would try with a statistical approach. In general, a particle has a kinetic energy (due to motion) and a potential energy (due to gravitational force acting on the particle). In statistical physics there is an equipartition theorem, which, loosely speaking, says that energy likes to be distributed equally in all forms. So if particle has a lot of kinetic energy (corresponding to high temperature), then it also likes to have a lot of potential energy (and hence likes to go up). The only question is - why do particles like to distribute energy equally? That's because it maximizes entropy. When there is a lot of particles, then there is more phase space available for equidistributed energy than for all energy distributed in one form only.

 

[Demystifier]

Here is a related problem, inspired by ergodic reasoning in the sense that phase-space average (as in the post above) is replaced by a time average. Suppose that you have two elastic balls A and B, both initially at the same height h from the Earth. Suppose also that both have an initial velocity directed towards the Earth, but that the ball A has a larger initial speed than the ball B. Thus they have equal initial potential energies but unequal initial kinetic energies. When the balls hit the Earth, they will elastically recoil and then go up. After a while they will again start to fall down, and so on. So each of the balls will exhibit a periodic motion up and down. However, if you compute the average position of each ball over time, the average height of the faster ball A will be higher than the average height of the slower ball B.

 

[Dr_Zinj]

I was wondering about the microscopic reason warm air rises up, while cold air comes down. I am aware of the macroscopic reason - density changes. But what happens microscopically? Decrease in density means that the gas molecules are widely spaced out, but their mass remains the same. Then why does warm air go up?

Let's try this as a thought experiment. (Mostly because I'm in the middle of two tasks at work.)

Start with a mass of air in an enclosed space at extremely low temperature.

Gravity is going to be exerting a force that pulls the molecules to the bottom of the space.

If you look at collisions as a statistical phenomenon, there is greater number of molecules below (higher density), at the bottom, to run into than there is above, at the top.

As you increase the temperature of the air, the energetic molecules move farther up in the air column due to fewer molecules to collide with. Each molecule travels farther before colliding with another molecule if it goes up than it would if it went down. i.e. the warm air 'rises".

 

[lesaid]

If you have a mass of hot air surrounded by cool air, on earth, the cool air above will have lower density than that below. Which means the molecules are more widely spaced, so that the faster molecules of the hot gas will tend to travel further upwards before they have a collision than if they were traveling into the denser air below. The molecules of the hot gas will tend to diffuse out in all directions, but most quickly in the direction of furthest travel / least density. Also, the temporary drop in density where a fast molecule invades and knocks away a molecule of cool gas will be restored to equilibrium more quickly where there is more pressure - i.e. at the bottom - so the base of the warm air does not move as easily down as the top moves up.

So the mass of hot gas should get more diffuse while tending to rise.

For an intuitive explanation, does that work?

 

[rcgldr]

I think of this as still being a buoyancy issue. For the same reason that a hot air balloon rises, the colder air has higher pressure than the hotter air at the same altitude. In my opinion, the density difference is a factor at the molecular level. Due to the higher density of the colder air, the collisions of molecules between cold and hot air over time involve collisions and energy exchange with a greater number of cold air molecules and fewer number of hot air molecules, so the average effect per molecule is greater for the less dense hot air molecules than the more dense cold air molecules. The end result is a net upwards force that at the macroscopic level is buoyancy.

 

[Demystifier]

It is buoyancy, there is no doubt about that, but I am not convinced that explanation in terms of buoyancy is a fully microscopic explanation.

From my two posts above the following very simple microscopic explanation can be extracted. When particle goes up it increases it's potential energy at the expense of it's kinetic energy. The more kinetic energy particle has, the more of this energy it can spend to increase it's potential energy.

However, to explain the effect, the energy conservation is not enough. In order for all fast particles go up they must all have a momentum directed upwards, which seems incompatible with momentum conservation if initially those particles had momenta in different directions. That's why the environment particles with lower kinetic energy are needed, by moving in the downward direction and thus saving the total momentum conservation. That's how buoyancy emerges from a microscopic point of view, in terms of momentum and energy conservation of particles.

The picture above is particularly compelling in general relativity, where energy and momentum conservation of fluid in the gravitational field are both encoded in a single equation $\nabla_{\mu}T^{\mu\nu}=0$. See e.g. S. Weinberg, Gravitation and Cosmology, Eq. (5.4.5) derived from (5.4.3).

 

[lesaid]

If we assume we're talking about (say) normal ground level air pressure, is the free path of a gas molecule long enough for the argument about potential/kinetic energy to be significant? I would have thought an upward moving fast gas molecule would collide with another molecule long before there would be any significant gain in potential energy? I know it is from Wikipedia, but here (https://en.wikipedia.org/wiki/Mean_free_path) it suggests a mean free path in the tens of nanometres.

Does that explanation about potential/kinetic energy exchange really account for rising warm air? Does the huge number of molecules involved mean that even this tiny effect becomes significant? I guess it needs some maths?

Edit : Apologies - Only the first two paragraphs of the previous post showed on my browser at first - I have since seen the whole of that post, and see that my comments were not so relevant !

 

[GTrax]

On a practical level, I think Wrichik has a point. Please allow that I cannot manage a theoretical approach at the level of most in this company.

I was wondering about the microscopic reason warm air rises up, while cold air comes down. I am aware of the macroscopic reason - density changes. But what happens microscopically? Decrease in density means that the gas molecules are widely spaced out, but their mass remains the same. Then why does warm air go up?

The curious near equivalent is lower density gas, but not by reason of being warmer.
For me, I was impressed by the direct experience with Helium used in a vacuum furnace leak detection where a turbo-molecular pump feeding a mass spectrometer device used at the at a vacuum port when all is well pumped down. A small amount of helium is leaked from a wand probe into the air surrounding the vacuum chamber, and if there is even the smallest leak, the instrument squeals and displays the order of the leak.

Of course, if Helium is confined to a balloon, it readily displaces enough air for it to go straight on upwards by buoyancy. The situation seems completely different for letting the gas loose into the air. The amount was tiny, not even enough to partly inflate a party balloon, about 2 seconds of tiny puff through 3mm pipe into the room. I was struck by the speed the helium found it's way through the leak. Seemingly less than half a second to mix with the room air, through the leak several metres away, and into the instrument which howled immediately!

Getting curious, I then found that releasing a little Helium in the next door industrial unit (with connecting aperture) was similarly speedy.
After 4 short-lived "experiments", we found the unit would no longer properly detect leaks because of all the Helium hanging around, and that our helium releases had contaminated most of the space right out to beyond the car park outside. It took more than 20 minutes to disperse! Clearly it does quickly not "go upward" as like in a balloon, so maybe amid the mean free path movement, all there is to have it make it's way upward is the gravity effect of the heavier molecules around it going the other way. One wonders if a mix of Hydrogen and Helium in a tall jar would have Hydrogen end up at the top?

I get it that Wrichik was not talking about Helium, but instead warm air. The significant thing is that the warm air is only different from the other air by the fact it's molecules are moving faster. It still does all the mean free path mixing action. Does warm air "hang together" in some way to gain buoyancy from lower density, sort of like if it was in a ill-defined balloon? Here is where I lose it. I don't yet really see the real mechanism of an air convection current. I know it happens, because I have experienced how three quarters of a ton of sailplane can be strongly shoved upwards from a heat source (combine harvester) hundreds of feet below. In passing, I would just love to have some gadget capable of displaying such a rising air current!

 

[sophiecentaur]

Does warm air "hang together" in some way

The only way it can 'get away' is by diffusion. That is a much longer term effect than the macroscopic buoyancy effect, which is why clouds and thermals happen. Conduction in gases (the spreading of the heat) must be due to a combination diffusion of actual molecules and momentum transfer at the hot/cold boundary. The momentum would transfer faster than individual molecules. I wouldn't mind betting that experiments with isotopes or gases with similar molecular masses have been done to compare the two effects.

 

[Demystifier]

One additional remark. Once the less dense object (be it helium balloon or hot gas) goes up, it doesn't later fall down. Therefore the process is irreversible. On the other hand, the microscopic laws are reversible. This implies that the irreversible statistical law of entropy increase (which is valid only when a large number of degrees of freedom plays an important role) must take place in some form.

 

[sophiecentaur]

One additional remark. Once the less dense object (be it helium balloon or hot gas) goes up, it doesn't later fall down. Therefore the process is irreversible. On the other hand, the microscopic laws are reversible. This implies that the irreversible statistical law of entropy increase (which is valid only when a large number of degrees of freedom plays an important role) must take place in some form.

This has been my point. Diffusion will always be at work and, given time, the helium in a room would spread all round the volume. This process is a lot slower than the thermal conduction / convection process (hours or days). I think the Dalton Law of partial pressures would apply and you will arrive at a different pressure distribution for all the gases. The proportion of He molecules at the top would be greater than the proportion at the bottom. The ideal condition would require still air and no temperature gradients.

 

[Demystifier]

A new attempt, inspired by my remark above. In general, objects like to minimize their potential energy. Why? Contrary to a widespread opinion, this is not because force ${\bf F}=-\nabla V$ acts in the direction in which potential energy decreases. The Newton law $m\ddot{\bf x}={\bf F}$ is a reversible law, so by Newton law alone the potential energy may decrease as well as increase. The true reason why objects like to minimize their potential energy is dissipation. Objects like to give all its energy (both kinetic and potential) to the environment because environment has more degrees of freedom than the object, so if the initial energy of the object gets distributed among the environment degrees, then the total entropy gets larger.

Now consider a vessel containing two gases, one with a lower density than the other. As we said above, the system wants to minimize its potential energy. Clearly, the configuration in which the gas with a lower density is up and gas with a larger density is down has a lower potential energy than the opposite configuration. But how does entropy increase in this process? The entropy increases due to interaction between the two gasses (for simplicity, we assume that the gasses do not mix), which takes place at the contact surface where the two gasses touch each other. And where does the initial potential energy go? It transforms into a heat, that is into an increase of temperature of both gasses due to a friction at the contact surface.

Finally, what if we have superfluids which do not have any friction? My theory above has an interesting testable prediction. If the theory is correct, then a superfluid with lower density immersed in a superfluid with larger density should be able to move both up and down. We can have a circulation of two fluids which never slows down. Can some experimentalist verify this prediction?

 

[DrDu]

You can't really have hot or cold molecules.

I do not quite agree on this.
Statistical mechanics is applicable to finite systems and you don't need large sample asymptotics to justify properties like temperature.
Hence I would assign the temperature of a container wherein the molecule is moving an with which it is in equilibrium to be a property also of the molecule.

 

[jbriggs444]

I do not quite agree on this.
Statistical mechanics is applicable to finite systems and you don't need large sample asymptotics to justify properties like temperature.
Hence I would assign the temperature of a container wherein the molecule is moving an with which it is in equilibrium to be a property also of the molecule.

"Equilibrium" with the container would indicate that the molecule within the container has a constant relationship with the container. The only way that can happen is if the molecule is at rest with respect to the container. This would lead to the conclusion that only molecules at rest with respect to the container can have a temperature and that their temperature is always zero. Surely this is not what you had in mind?

 

[DrDu]

"Equilibrium" with the container would indicate that the molecule within the container has a constant relationship with the container. The only way that can happen is if the molecule is at rest with respect to the container. This would lead to the conclusion that only molecules at rest with respect to the container can have a temperature and that their temperature is always zero. Surely this is not what you had in mind?

I don't mean mechanical but thermodynamical equilibrium.

 

[jbriggs444]

I don't mean mechanical but thermodynamical equilibrium.

Does that not beg the question? What do you mean by thermodynamic equilibrium for a single molecule within a container?

If one has a container at 100K and a molecule with a kinetic energy equivalent to 200K, is that molecule in thermodynamic equilibrium with the container? Is there enough information to tell?

 

[sophiecentaur]

As we said above, the system wants to minimize its potential energy.

That just means the lighter gas will end up in more concentration near the top and less at the bottom. But thermodynamics will ensure that the gases mix and have the same average KE in all locations, eventually.
Superfluids don't seem to follow the rules because it's a quantum effect. There are plenty of apparent examples of perpetual motion - fountains etc. so your suggestion would probably be reasonable. But it is not really relevant to the OP and subsequent discussion.

 

[Paul C]

As an atom of air (more energetic, i.e., warmer than its neighbors) rises it gives up energy as heat and over time stabilizes at an dynamic equilibrium. Atomic vibration is in and of itself not a qualification for motion in any particular direction, inasmuch as "rebounding" from more concentrated, to wit, "cooler" surroundings acts to increase the movement of atoms relative to one another. BTW, marvelous explanation https://www.physicsforums.com/threa...-microscopic-scale.937606/page-2#post-5927266 by Demystifier of a statistical rationale.

 

[MRBlizzard]

Try this:
1. What is the mean time between scattering / collisions for slightly warmer or cooler atoms?
2. How much is the difference between the height fallen (between collisions) between slightly warmer or cooler atoms?

How many times a second does the cooler atom drop a little bit. Multiply by the answer to #2.

Of course, there is a lot of scattering up and down. But conceptually, this is why cold atoms gather at the bottom, and warm atoms are at the top.

 

[DrDu]

Does that not beg the question? What do you mean by thermodynamic equilibrium for a single molecule within a container?

If one has a container at 100K and a molecule with a kinetic energy equivalent to 200K, is that molecule in thermodynamic equilibrium with the container? Is there enough information to tell?

For a single atom in a container of a given temperature, if we repeat this experiment many times, we would find a certain distribution of the energy of the atoms. I.e., our information about the atom will be described by a canonical density matrix with a certain temperature.

 

[256bits]

canonical density matrix

Isn't that what a thermometer measures with just one experiment using many atoms as a continuum.
An doing the whole calculation in one shot.

 

[DrDu]

Isn't that what a thermometer measures with just one experiment using many atoms as a continuum.
An doing the whole calculation in one shot.

Of course, but the question was whether it is admissible to use the concept of temperature also for a single atom.