Joule-Thomson inversion curve (${\mu }_{\mathrm{JT}}(T,p)=0$)

The Joule-Thomson inversion curve is the set of equilibrium temperature–pressure states where the Joule-Thomson coefficient vanishes. For positive heat capacity at constant pressure, its condition is $T\alpha =1$, with $\alpha$ the coefficient of thermal expansion. The curve separates locally cooling and warming throttle regions. A finite isenthalpic process can cross it, so the inlet sign alone does not fix the total temperature change. An ideal gas has zero coefficient everywhere, rather than an isolated dividing curve.

A Joule-Thomson inversion temperature is a temperature at which the Joule-Thomson coefficient is zero at a specified pressure. There can be more than one such temperature at that pressure; distinguish the upper and lower branches from a maximum or a dilute-gas limiting value.