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Chemistry LibreTexts

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.


The Joule-Thomson coefficient is given by

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


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

In terms of heat capacities one has

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


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

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

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


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