Starting with the internal energy U(S,V) for single component system with constant number of moles N, obeying, dU = TDS - POV (1) go through the steps of performing the Legendre transformations to F(T,V), H(S,P) and G(T,P). Goal: Find the complete differenti als dF, dH and dG. Recall: (a) In general, the Legendre transform can be expressed as -() ( axk XR+U. (2) (b) T = (35)and - P = (*)s au as v