How cool do you want to go? The energy of individual gas molecules decreases linearly with temperature, but their speed with the square root of the energy. Low mass molecules - even nitrogen and oxygen are in that class - have high speeds at STP. Dropping from 298 K to just 29.8 K only decreases the average molecular speed to "merely" 163 m/s in the case of N
2... or it does if it doesn't freeze. Hydrogen is still moving at 600 m/s and helium is doing 430 m/s.
Problem with going really cold is that intermolecular forces begin to dominate and the molecules become "sticky" with each other, forming liquids or ices.
This happens even if i arrange the apparatus so that the vacuum chamber is above the gas and it's all inline with the direction of gravity.
So, why does the gas quickly fill the vacuum down here at earth? why does the gas not stay in the bottom chamber due to gravity? Does it have anything to do with the volume of the evacuated chamber?
How high do you want the chamber? Consider N
2 again. At 29.8 K its molecules are doing 163 m/s. How many metres of fall at 1 gee (9.80665 m/s
2) is that equal to? Easy computation g.h = 1/2.v
2 ...which means the required h is 1,355 metres. This is known as the
scale height, and because the temperature is a measure of
average energy, that means a gas thins out 1/e for each scale height the gas rises against gravity, at constant temperature.
However there is a complication. If a gas suddenly goes from one small volume to a larger one, then it undergoes what's called
adiabatic cooling
because it expends internal energy by expanding. This cooling can be quite significant and can even cause a gas to change phase.
If i increase the volume of the evacuated chamber by a very large amount will the gas reach a "volume of equilibrium" whereby the volume of the gas does not change much?
If you expand the volume quickly and the amount of gas remains constant, then it will get colder and colder. But it will still move to try to fill the volume - so long as it doesn't freeze.