# Gas at zero K

Sunfire
Hello All,

Can matter exist in a gaseous form at zero K? I am asking because common gasses (e.g. air) would liquify at cryogenic temperatures...

Many thanks

Just guessing: If the density was low enough and there was no force (like gravity) to make the molecules come together.

Darwin123
Hello All,

Can matter exist in a gaseous form at zero K? I am asking because common gasses (e.g. air) would liquify at cryogenic temperatures...

Many thanks
I don't think the phase of a system can be determined in the limit of zero pressure and zero absolute temperature.
I suspect that all materials would be gaseous in the limit of finite temperature, zero pressure and infinite time. If the atoms of a material are spaced far enough from other materials, the forces that hold them together would be effectively zero. So if there was absolutely nothing else in the universe except a solid piece of iron with finite mass, and if the absolute temperature was more than zero, then I think that that piece of iron would eventually sublimate into an iron gas. This is a zero pressure system which never reaches equilibrium. Real systems have a finite pressure and eventually reach thermal equilibrium.
Given a finite pressure, I think that all gases would condense to some other phase at zero absolute temperature. I say that because of the third law of thermodynamics (weak form). The third law of thermodynamics says that the specific heat of a material approaches zero in the limit of absolute temperature approaching zero.
Ideal gases have a finite specific heat proportional to the universal gas constant. This contradicts the third law of thermodynamics. Therefore, gases at finite pressure have to equilibrate at zero absolute temperature to some other phase.
Note that this phase does not have to be a solid. Helium at q atmosphere condenses to a superfluid at temperatures below 4 °K. Other materials equilibrate to Bose-Einstein condensates at millidegree absolute temperatures. However, these materials are not considered true gases. At least these states are very far from ideal gases.
There are some other discussion threads around here that involve the third law of thermodynamics. You may be interested in some of those threads.
Also note that near absolute zero temperature, the quantum nature of materials starts to become important. At millikelvin temperatures, atoms start to behave more like waves than particles. At very low temperatures, the wavelength of an atom can be bigger than the distance to other atoms. So materials act real weird at microKelvin temperatures. There are some very strange phases that are outside the paradigm of gas, liquid and solid.
If one are interested in very cold temperatures, then one should know a little about quantum mechanics and the third law of thermodynamics. I think that you may find the third law of thermodynamics particularly interesting.

Sunfire
I agree, the 0K is more of an asymptotic limit, rather than a temperature of a real material. Isn't there a principle of 0K being unreachable?

Than at least for the purposes of my current study, I need to look at the behavior of an (ideal) gas when T-->0. I need this expression for say c_p = f(T) @ T -->0