Statistical Mechanics · Problem 9.5

Statistical Mechanics of Interacting Systems: The Method of Quantized Fields — R. K. Pathria

Physics — Statistical Mechanics · joule-thomson-coefficient

Problem

Show that the first-order Joule–Thomson coefficient of a gas is given by the formula

\left(\frac{\partial T}{\partial P}\right)_H = \frac{N}{C_P}\left(T\frac{\partial(a_2\lambda^3)}{\partial T} - a_2\lambda^3\right),

where

a_2(T)

is the second virial coefficient of the gas and

H

its enthalpy; see eqn. (9.2.1). Derive an explicit expression for the Joule–Thomson coefficient in the case of a gas with interparticle interaction

u(r) = \begin{cases} +\infty & \text{for} \quad 0 < r < r_0, \\ -u_0 & \text{for} \quad r_0 < r < r_1, \\ 0 & \text{for} \quad r_1 < r < \infty, \end{cases}

and discuss the temperature dependence of this coefficient.