[QUE/TH-02008] TH-PROBLEM

An approximate equation of state of a real gas at moderate
pressures, devised to take into account of the finite size of the
molecules, is $P(v-b)=R\theta$, where $R$ and $b$ are constants.
Show that

\begin{equation*}
\beta = {1/\theta\over 1+bP/(R\theta)}~~,~~~~\chi =
{1/P\over1+bP/(R\theta)}
\end{equation*}