Okay, you probably won’t know the answer to this, but…
You know when you release the pressure from something, like a can of butane or a CO2 cartridge, it gets cold. Well, what if you got that can to 0 degrees Kelvin (absolute zero), and kept pumping either the Co2 or butane into it so it remained pressurized, and then released the pressure, what would happen? It can’t get any colder, as it contains no heat already. And please don’t tell me that the can would shatter, of course it would. My question is about what happens to the temperature of the can. Can you please explain?
If you were able to have a can at absolute zero, and an infinitely powerful heat pump (conveniently available in gedankenexperiments everywhere) to maintain the can at absolute zero as you added gas, you could keep adding gas, but there would be no pressure to release. At absolute zero, the gas molecules have no kinetic energy (that is, they are not moving), so there are no collisions with the container wall and, therefore, no pressure.
As it’s easier to deal with the Ideal Gas Law than with the statistical physics directly, consider that the Ideal Gas Law can be rearranged algebraically to determine pressure from the other factors:
P = nRT/V
Where:
P is the pressure,
n is the number of gas molecules in the container,
R is a constant,
T is the absolute temperature, and
V is the volume of the container.
This shows that, as long as V is not zero, you can add as many molecules as you’d like at T = 0 and P will always be zero. (If V is zero, then you don’t have a can to which to add gas.)
Put another way: At absolute zero, there would be, as you said “no heat already”. As there would be no heat, there would be no energy to release, so you couldn’t decrease the energy of the can’s contents, so the temperature would stay at absolute zero.
That’s assuming that the gas is an ideal gas, which it would not be at 0 Kelvins. An ideal gas assumes that their are no intermolecular forces, but without any kinetic energy, intermolecular forces will be much more pronounced than when the gas is flying around randomly at higher temperatures.
Also, you would need to worry about the gas changing state.
