Joule-Thomson effect

The Joule-Thomson coefficient is given by

$\mu_{\mathrm JT} = \left. \frac{\partial T}{\partial p} \right\vert_H$

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

In terms of heat capacities one has

$\mu_{\mathrm JT} C_V = -\left. \frac{\partial E}{\partial V} \right\vert_T$

and

$\mu_{\mathrm JT} C_p = -\left. \frac{\partial H}{\partial p} \right\vert_T$

In terms of the second virial coefficient one has

$\mu_{\mathrm JT} = B_2 -T \frac{dB_2}{dT}$

References

1. Thomas R. Rybolt "A virial treatment of the Joule and Joule-Thomson coefficients", Journal of Chemical Education 58 pp. 620-624 (1981)