[QUE/TH-02003] TH-PROBLEM

An approximate equation of state of a real gas at moderate pressures is given by $$ P_v = R\theta\left(1+{B\over v}\right) $$ where $R$ is a constant and $B$ is a function of $\theta$ only.  Show that

• [(a)] $\beta=\dfrac{1}{\theta}\left(v+B+\theta~\dfrac{dB}{d\theta}\right)\biggl/(v+2B)$
• [(b)] $\kappa = \dfrac{1} {P} ~\dfrac{1}{(1+BR\theta/Pv^2)}$ \hfill{[7]}