What about with heavy gases and light ones like helium? Do they eventually mix completely in large atmospheres under a big gravity gradient?

I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, releasing photons from the heat which increases total entropy, but in a closed system where the photons are reflected back it would hit some equilibrium with heavier stuff at the bottom, but more kinectic and photonic energy which maybe both together give more degrees of freedom than a more evenly mixed mixture with less kinetic energy and higher gravitational potential energy.

> I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom,

But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere.

> I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom,

But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere.

Edit: Maybe you know this already, but in equilibrium the mixture does indeed have more kinetic energy (per unit of volume) as you go down because even though the temperature remains constant the pressure increases.

This is not the enclosed system case, but light gases do escape easier and heavier gases do accumulate more predominately towards the ground:

https://en.m.wikipedia.org/wiki/Atmosphere_of_Earth#Stratifi...

At extreme elevations you find much higher concentrations of H and He.

It doesn’t fully separate like you might see with liquids, but there are tendencies.

You’re right, the atmosphere is much more complex and dynamic than in these idealized models. But assuming the system is closed and in thermal equilibrium and that these are ideal non-reacting gases then gravity has an effect on the density and pressure but not on the composition.

I disagree. Assume it is a closed box reflecting all photons back inwards and perfectly bouncing the gas particles. Now assume here are only two gas particles in the box, a heavy atom and a light one. Assume the box is tall enough that in the presence of gravity there is not enough total energy in the system for either particle to reach the top of the box.

The light one will move faster than the heavier one on average when they come into contact, and in the presence of gravity it will have a higher average height. The same will hold as you add more particles, but there is a curve to it.

It is true hat the atmosphere is more complex, and has things like ozone layer causing temperature inversion due to different absorption characteristics, etc., but the general reasons that H and He are so much more prevalent in the upper layers is largely due to this kind of explanation using gravity.

It’s true, I don’t know what I was thinking. The barometric formula that gives the density gradient for each (ideal) gas depends on the molecular mass so the profile will be different and the composition of the mixture will vary with height.

I would assume Dalton's law of partial pressures would apply.

I think this example is not fair, because it doesn’t compare the entropy of two states in thermodynamic equilibrium. The emulsion state is clearly not an equilibrium state.

In this situation I think of entropy as “lowest energy state”.

The oil and water have different densities, and are under the same force of gravity.

Any higher-density substance above a lower-density substance will have potential energy, that eventually must dissipate into thermal energy as the higher-density molecules descend and perturb other molecules.

Why don’t the higher density molecules of water descend in a bottle of wine? You don’t have the molecules of ethanol floating on top, do you?

(Hint: “higher-density molecules” doesn't mean anything.)