The rate of change of temperature {\displaystyle T} with respect to pressure {\displaystyle P} in a throttling process:
(1) | \epsilon_{JT} = \left( \frac{\partial T}{\partial P} \right)_{H} = \frac{\alpha_V \cdot T - 1}{c_{vp}} |
where
For the Ideal Gas: \alpha_V = \frac{1}{T} and Joule–Thomson coefficient is strictly zero: \epsilon_{JT} = 0.
In case of general Fluid: \alpha_V = \alpha_V (T) and the temperature T_{\rm inv} where T_{\rm inv} \cdot \alpha_V(T_{\rm inv}) = 1 is called Inversion Temperature.
The Fluid above Inversion Temperature T > T_{\rm inv} has negative Joule–Thomson coefficient \epsilon_{JT} <0 and hence will be cooling under expansion ( \delta P > 0).
The Fluid below Inversion Temperature T < T_{\rm inv} has positive Joule–Thomson coefficient \epsilon_{JT} >0 and hence will be warming under expansion ( \delta P > 0).
See also
Physics / Thermodynamics / Thermodynamic process / Throttling Temperature Effect