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@wikipedia
critical temperature below which a fluid that is expanding at constant enthalpy will experience a temperature decrease, and above which will experience a temperature increase


Fluid temperature 

LaTeX Math Inline
body--uriencoded--T_%7B\rm inv%7D
  satisfying the following condition: 

LaTeX Math Block
alignmentleft
T_{\rm inv} \cdot \alpha_V(T_{\rm inv}) = 1

 where

LaTeX Math Inline
body\alpha_V

Thermal expansion coefficient


The Fluid above Inversion Temperature 

LaTeX Math Inline
body--uriencoded--T > T_%7B\rm inv%7D
 has negative Joule–Thomson coefficient  
LaTeX Math Inline
body--uriencoded--\epsilon_%7BJT%7D <0
 and hence will be cooling under expansion (
LaTeX Math Inline
body\delta P > 0
)
.

The Fluid below Inversion Temperature 

LaTeX Math Inline
body--uriencoded--T < T_%7B\rm inv%7D
 has positive Joule–Thomson coefficient  
LaTeX Math Inline
body--uriencoded--\epsilon_%7BJT%7D >0
 and hence will be warming under expansion (
LaTeX Math Inline
body\delta P > 0
)
.

See also

...

Physics / Thermodynamics / Thermodynamic process Adiabatic Process / Throttling process

Joule–Thomson coefficient ]