# Real Gases: Joule-Thomson Expansion

The Joule-Thomson effect is also known as the Joule-Kelvin effect. This effect is present in non ideal gasses, where a change in temperature occurs upon expansion.

### Introduction

The Joule-Thomson coefficient is given by

\[\mu_{\mathrm JT} = \left. \dfrac{\partial T}{\partial p} \right\vert_H\]

where

*T*is the temperature,*p*is the pressure and*H*is the enthalpy.

In terms of heat capacities one has

\[\mu_{\mathrm JT} C_V = -\left. \dfrac{\partial E}{\partial V} \right \vert_T \]

and

\[\mu_{\mathrm JT} C_p = -\left. \dfrac{\partial H}{\partial p} \right \vert_T \]

In terms of the second virial coefficient at zero pressure one has

\[\mu_{\mathrm JT}\vert_{p=0} = ^0\!\!\phi = B_2(T) -T \dfrac{dB_2(T)}{dT}\]

### References

- Jacques-Olivier Goussard and Bernard Roulet "Free expansion for real gases", American Journal of Physics
**61**pp. 845-848 (1993) - E. Albarran-Zavala, B. A. Espinoza-Elizarraraz, F. Angulo-Br
**3**pp. 17-22 (2009)
own "Joule Inversion Temperatures for Some Simple Real Gases", The Open Thermodynamics Journal - Thomas R. Rybolt "A virial treatment of the Joule and Joule-Thomson coefficients", Journal of Chemical Education
**58**pp. 620-624 (1981)