Show that (left(frac{partial C_{P}}{partial P} ight)_{T}=frac{6 B}{T^{3}}) for a gas obeying the equation of state (V=frac{R T}{P}+A-frac{B}{T^{2}}).

Show that \(\left(\frac{\partial C_{P}}{\partial P}\right)_{T}=\frac{6 B}{T^{3}}\) for a gas obeying the equation of state \(V=\frac{R T}{P}+A-\frac{B}{T^{2}}\). [Hint: We know that \(\left(\frac{\partial C_{P}}{\partial P}\right)_{T}=-T\left(\frac{\partial^{2} V}{\partial T^{2}}\right)_{P}\). Find out \(\left(\frac{\partial V}{\partial T}\right)_{P}\) and \(\left(\frac{\partial^{2} V}{\partial T^{2}}\right)_{P}\), and substitute.]