Joule-Thomson effect

The Joule-Thomson coefficient is given by

$\mu _{\mathrm {J} T}=\left.{\frac {\partial T}{\partial p}}\right\vert _{H}$

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

In terms of heat capacities one has

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \mu _{\mathrm {J} T}C_{V}=-\left.{\frac {\partial E}{\partial V}}\right\vert _{T}}

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\mathrm JT} C_p = -\left. \frac{\partial H}{\partial p} \right\vert_T }

In terms of the second virial coefficient one has

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)