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Can any gas be liquidified by lowering the temperature? What happens with gases at absolute zero? Are there gases that remain gases at absolute zero? Do their molecules move at these temperatures? Does the gas acquire a crystallic structure at these temperatures while still remaining gaseous?

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As we decrease the temperature, the vibration decreases and decreases until, at absolute zero, there is a minimum amount of vibration that the atoms can have, but not zero. This minimum amount of motion that atoms can have is not enough to melt a substance, with one exception: helium. Helium merely decreases the atomic motions as much as it can, but even at absolute zero there is still enough motion to keep it from freezing. Helium, even at absolute zero, does not freeze, unless the pressure is made so great as to make the atoms squash together. If we increase the pressure, we can make it solidify.$_1$

So, to your questions, gases can be liquified by lowering the temperature. Liquids may solidify or liquify at absolute zero. Molecules or atoms do have minimum vibration at absolute zero.

Credits: $_1$ Feynman-lectures on Physics-Volume1-Page NO.1-6 Data is subjected to modification and page no.s may change depending on editions.

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Is it conceivable that a certain gas (electron gas, neutron gas) does not liquidify at zero temperature? – Anixx Jun 14 '14 at 14:52
@Anixx Density matters. In experiments with ultra-cold neutrons (energy below $100\,\mathrm{neV} \approx k\cdot 1.2\,\mathrm{nK}$) the world record density is around 10$^4$ neutrons per cubic centimeter, and they behave like noninteracting particles in a gas. – rob Jun 14 '14 at 15:32

A Bose-Einstein condensate can made by cooling a (very) dilute gas, and once the condensate has formed it can be cooled arbitrarily close to absolute zero without forming a liquid or a solid phase. The atom energies approach zero, but the atoms don't crystallise because they become delocalised instead.

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So what about Fermions? Cose -Einstein is applied just for Bosons. – Abolfazl Jun 14 '14 at 19:07
@Abolfazl Paired fermions may also condense, in their way, e.g. the Cooper pairs of electrons in a superconductor. – rob Jun 14 '14 at 23:24
@Abolfazl: see the Wikipedia article on fermionic condensates. As Rob says, the fermions pair up and the pairs then form a condensate. This has been done with potassium atoms. – John Rennie Jun 15 '14 at 6:47

Carbon dioxide at standard atmospheric pressure does not liquify as it is cooled. It directly desublimates from gas to solid.

Phase changes are typically associated with a large inflow or outflow of heat. We are usually familiar that heat has to be put into ice to melt it, heat has to be put into a pot of water to boil it. This motion of energy is strongly associated with a change of phase of material. If under cooling or pressure (or both) the pressure, volume, and temperature of a gas smoothly change, then stop changing while energy flows in or out of the gas, then the pressure, volume, and/or temperature suddenly change to a new value and then continue changing smoothly, we say that the gas has changed state. (Typical examples for gasses are condensing into a liquid or ionizing into a plasma.)

The temperature "absolute zero" is a theoretical construct. No physical process can reduce the temperature of any object to absolute zero. Any assertion of a property of a material "at absolute zero" is an inference from its trend of behaviour as the temperature is lowered to temperatures closer and closer to absolute zero.

At very low temperatures, we observe electrons, atoms, molecules and other constituents of matter to possess "zero-point energy", which is a form of energy inherent to quantum mechanical constraints on the certainties of position and momentum (similar to temperature) of particles. At large temperatures, the zero-point energy is completely hidden, swamped by thermal processes. At very low temperatures, the thermal energy becomes a minor component and the zero-point energy is more directly observable. Inferring from the trend of observations as the temperature is lowered closer and closer to absolute zero, we can say that particles at the theoretical temperature of absolute zero would still possess zero-point energy and would still be in motion.

Certain forms of matter: plasmas, electron gasses (Fermi gasses), Bose gasses, et al. have properties that are not as familiar as normal materials. Plasmas are charged. If a plasma is cooled to lower and lower temperatures (without some means to neutralize its charge, which happens in, for instance, the Sun's corona), unless there is pressure applied, the electrostatic repulsion will cause the plasma particles to fly apart. If pressure is applied, the particles continue moving (at least with zero-point energy) and their density increases, but they remain separated. The state of matter may be described as a fluid (a term encompassing both gasses and liquids), but there is not the large change of internal energy associated with a phase change, so would not normally be called a liquid. The description for electron gasses is similar to that for plasmas although some of the underlying physics are different. In particular a Fermions (electrons and some other particles) cannot occupy identical quantum states, so cannot behave similarly to Bose-Einstein condensates (next). As a Bose gas (photons, Helium-4 atoms, et al.) is cooled, there is a phase change where the particles go from having different states to having identical states. The condensed form of this is called a Bose-Einstein condensate. This condensate still has zero-point energy, so at the theoretical temperature of absolute zero, this condensate would still be in motion.

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