Inversion temperature

The inversion temperature in thermodynamics and cryogenics is the critical temperature below which a non-ideal gas (all gases in reality) that is expanding at constant enthalpy will experience a temperature decrease, and above which will experience a temperature increase. This temperature change is known as the Joule-Thomson effect, and is exploited in the liquefaction of gases.Inversion temperature depends on the nature of gas.

The Joule-Thomson effect cannot be described in the theory of ideal gases, in which interactions between particles are ignored. Instead, one must use a theory that accounts for the Van der Waals force between interacting particles that becomes much stronger as a gas becomes a liquid.

For a van der Waals gas we can calculate the enthalpy H using statistical mechanics as

where ${\displaystyle N}$ is the number of molecules, ${\displaystyle V}$ is volume, ${\displaystyle T}$ is temperature (in the Kelvin scale), ${\displaystyle k_{B}}$ is Boltzmann's constant, and ${\displaystyle a}$ and ${\displaystyle b}$ are constants depending on intermolecular forces and molecular volume, respectively.

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