For a gas which obeys the equation of state (left(P+frac{a}{V^{2}} ight) V=R T), prove that the JouleThomson

For a gas which obeys the equation of state \(\left(P+\frac{a}{V^{2}}\right) V=R T\), prove that the JouleThomson coefficient is

\[ \mu_{\mathrm{JT}}=\frac{2 a R T}{C_{P} V^{2}\left(P^{2}-\frac{a^{2}}{v^{4}}\right)} \]