4.12. From the van der Waals equation a p= RT V - b 02 and assuming that the molar heat capacity is a constant, C, =c, obtain the funda- mental relation of a van der Waals fluid in the Helmholtz free energy representation. Show that u = cT a/v. 4.13. From the fundamental relation of a van der Waals fluid in the entropy representation, obtain the fundamental relation in the energy representation. From this relation determine the fundamental relation in the Helmholtz free energy representation by a Legendre transformation