The rate of change of temperature $\begin{array}{l}{\displaystyle T}\end{array}$ with respect to pressure $\begin{array}{l}{\displaystyle P}\end{array}$ in a throttling process:

(1)	$\begin{array}{l}\displaystyle \epsilon_{JT} = \left( \frac{\partial T}{\partial P} \right)_{H} = \frac{\alpha_V \cdot T - 1}{c_{vp}}\end{array}$

where

$\begin{array}{l}T\end{array}$	Temperature
$\begin{array}{l}\alpha_V\end{array}$	Thermal expansion coefficient
$\begin{array}{l}c_{vp}\end{array}$	Isobaric volumetric heat capacity

For the Ideal Gas: $\begin{array}{l}\alpha_V = \frac{1}{T}\end{array}$ and Joule–Thomson coefficient is strictly zero: $\begin{array}{l}\mathrm{\epsilon_{JT}\,= 0}\end{array}$ .

In case of general Fluid: $\begin{array}{l}\alpha_V = \alpha_V (T)\end{array}$ and the temperature $\begin{array}{l}T_{\rm inv}\end{array}$ where $\begin{array}{l}T_{\rm inv} \cdot \alpha_V(T_{\rm inv}) = 1\end{array}$ is called Inversion Temperature.

The Fluid above Inversion Temperature $\begin{array}{l}T > T_{\rm inv}\end{array}$ has negative Joule–Thomson coefficient $\begin{array}{l}\epsilon_{JT} < 0\end{array}$ and hence will be cooling under expansion ( $\begin{array}{l}\delta P > 0\end{array}$ ).

The Fluid below Inversion Temperature $\begin{array}{l}T < T_{\rm inv}\end{array}$ has positive Joule–Thomson coefficient $\begin{array}{l}\epsilon_{JT} >0\end{array}$ and hence will be warming under expansion ( $\begin{array}{l}\delta P > 0\end{array}$ ).

Page tree

See also