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

$\mu _{\mathrm {J} T}C_{V}=-\left.{\frac {\partial E}{\partial V}}\right\vert _{T}$

and

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

In terms of the second virial coefficient one has

$\mu _{\mathrm {J} T}=B_{2}-T{\frac {dB_{2}}{dT}}$

References

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