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In crystalline solids, the constituent atoms sit close to each other in their equilibrium positions. The solid is not compressible because as the pressure is increased, the atomic orbitals tend to overlap and due to Pauli exclusion principle a large repulsive force comes into play.

Let's come to gases. Gases are easily compressible than liquids or solids. This is because the molecules of a gas are far apart and there is no significant overlap between the orbitals. It is also easier to compress it because there is a long-range Van der Waal attraction (the attractive part of the Lennard-Jones potential).

  1. However, if we keep increasing the pressure on a gas, keeping the temperature fixed, there comes a time when a huge pressure needs to be applied to the gas to convert it to a liquid. Is it the same Pauli exclusion principle (PEP) that opposes compression during gas to liquid transition?

  2. Do liquids resist compression due to the same reason i.e., Pauli exclusion principle (PEP) like solids?

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    $\begingroup$ "If liquids resist compression due to the same reason i.e., Pauli exclusion principle (PEP) like solids, why are liquids still compressible while solids are not?" Where did you hear that? Liquids and solids actually generally describe compressibility in the same way. $\endgroup$ – JMac Jul 10 '17 at 16:31
  • $\begingroup$ You asked why liquids are compressible whiles solids are not. The question does not make sense because solids are compressible in the same way liquids are. $\endgroup$ – JMac Jul 10 '17 at 16:35
  • $\begingroup$ Depends completely on the substances. $\endgroup$ – JMac Jul 10 '17 at 16:37
  • $\begingroup$ I'm not sure if that's true for all substances. Water for example may be less compressible than ice due to density changes. $\endgroup$ – JMac Jul 10 '17 at 16:44
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Pauli exclusion principle does not preclude atomic orbitals to deform under pressure. For example, the classic tetrahedral angles that C-C form in diamond can bend a bit as the result of an applied pressure, resulting in a compression at the macroscopic level.

What opposes compression of a gas is thermal pressure. The molecule in the gas randomly move in all direction with a mean speed of $\sqrt{8kT/\pi m}$ ($m$ is the mass of the molecules), that is to say of the order of 100 m/s at room temperature. As they hit the piston used to compress the gas, they push it back: the change of momentum of the piston per unit of area is the thermal pressure. As the gas is compressed, its density increases and the number of hits increases, thus increasing that pressure. So most of the work one has to provide to liquefy a gas only by applying an external pressure, where by external, I mean as opposed to the gas thermal pressure, comes from overcoming the latter all the way to densities high enough for intermolecular forces to take over.

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