Prove that (a) (left(frac{partial C_{P}}{partial P} ight)_{T}=-Tleft(frac{partial^{2} V}{partial T^{2}} ight)_{P}) (b) (left(frac{partial C_{V}}{partial V} ight)_{T}=Tleft(frac{partial^{2} P}{partial T^{2}}

Prove that

(a) \(\left(\frac{\partial C_{P}}{\partial P}\right)_{T}=-T\left(\frac{\partial^{2} V}{\partial T^{2}}\right)_{P}\)

(b) \(\left(\frac{\partial C_{V}}{\partial V}\right)_{T}=T\left(\frac{\partial^{2} P}{\partial T^{2}}\right)_{V}\)