From classical thermodynamics we are familiar with the so-called Gibbs and Helmholtz equations, which link different thermodynamic energy functions. This is especially true for the internal energy and the Helmholtz function U= 35 . U=. Show that this equation is indeed valid between the internal energy and the F : k3T1nZ, Helmholtz function: Tip: changing the derivative taken with respect to temperature into a derivative taken with respect to I3 both makes the calculation easier