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

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

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