1. The problem statement, all variables and given/known data Show that if a single-component system is such that PVk is constant in an adiabatic process (k is a positive constant) the energy is U = [1/(k-1)]PV + Nf(PVk/Nk) where f is an arbitrary function. 2. Relevant equations Fundamental relation: U = [1/(k-1)]PV + Nf(PVk/Nk). State equations: T = δU/δS, P = - δU/δV, μ = δU/δN. 3. The attempt at a solution PVk has to be a function of S, so that (δU/δV)S = g(S) x V-k, where g(S) is an unspecified function, and V-k is Vk inverse. I think I'm going to end up finding dU first, and integrating to find U, but pretty much, I'm stuck here. Any help at all would be greatly appreciated.