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.
Theory
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
From this equation, we note that if we keep enthalpy constant and increase volume, temperature must change depending on the sign of
where