For a pure substance, if the internal energy is considered to be the function of any two of the independent variables \(P, V\), and \(T\), then show that

(a) \(\left(\frac{\partial U}{\partial V}\right)_{P}=\frac{C_{P}}{V \beta}-P\)

(b) \(\left(\frac{\partial U}{\partial T}\right)_{P}=C_{P}-P V \beta\)