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Consider an adiabatic expansion of an ideal gas that work is done against friction or a piston. Since no heat exchange can occur the gas keep on losing energy and its temperature decreases and the gas molecules getting further and further apart. In principle the temperature can get down to a few degrees Kelvin, close to zero K.

Is it possible that a gas can still be a gas at such a low temperature?

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  • $\begingroup$ Have you heard of Helium (triple point ~2K at standard conditions)? $\endgroup$
    – ACuriousMind
    Jul 8, 2014 at 1:15
  • $\begingroup$ I think I need to make it clear that the temperature is very close to 0K that the molecules can hardly translate. $\endgroup$
    – Kelvin S
    Jul 8, 2014 at 1:53

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Consider the (relatively informal) definitions:

  • Gas: A substance whose molecules fill the space available to it
  • Liquid: A substance whose molecules form a fixed volume but have no fixed shape
  • Solid: A substance whose molecules resist both changes to shape and volume, who do not flow, and do not expand to take the shape or volume of the container.

So based on those definitions, although imprecise as they may be, there is no requirement to be at a particular temperature. In theory, once the molecules reach $0 K$ and they are no longer moving, they will also no longer fill the shape of the container nor will they expand to take up new volume and so they must be a solid. But as soon as it has any temperature and the molecules are once again translating, it could be a solid, a liquid, or a gas.

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  • $\begingroup$ In looking at those loose definitions, I wonder how a plasma fits in. $\endgroup$
    – Kyle Kanos
    Jul 8, 2014 at 1:51
  • $\begingroup$ Thanks. I just wonder can a substance close to 0K be called a solid as there is a lot of space not filled up and it is easy to be compress (i.e. not resistant to both changes to shape and volume) $\endgroup$
    – Kelvin S
    Jul 8, 2014 at 1:51
  • $\begingroup$ @KyleKanos Loosely an ionized gas. When there is sufficient $kT$ around for atomic ionization inter-atomic forces of all types in are real danger of being overwhelmed. I'm quite sure they are completely obliterated in most cases, so now I'm hoping some smart arse will pull up a exceptional case just to confound me. I Double Dog Dare you! $\endgroup$ Jul 8, 2014 at 2:01
  • $\begingroup$ @KyleKanos Per wikipedia, " Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container; unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers." $\endgroup$
    – tpg2114
    Jul 8, 2014 at 2:01
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    $\begingroup$ @KyleKanos It's more like a "pretty awesome gas." And in actuality, I've always kind of objected to considering it an entirely new state of matter. It's really just a slightly different already-existing state of matter. We don't have magnetic solids as a state of matter, why have magnetic gasses? $\endgroup$
    – tpg2114
    Jul 8, 2014 at 2:08

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