1. The problem statement, all variables and given/known data We are working on some problems for class and we are given statements which I accept as valid but don't know how to prove they are valid. I believe I have to utilize the maxwell relations but the terms seem unfamiliar to me. 2. Relevant equations (1) Partial (d^2f / ds^2)_T = T / Kv (2) Partial (d^2h / ds^2)_P = T / C_p (3) Partial (d^2u / ds^2)_v = T / C_v 3. The attempt at a solution For the first equation, I know that the isothermal compressibiity K = -1/v partial(dv/dP)_T For the second equation I also know that C_p/T = partial(ds/dT)_P = 1/T * partial(dh/dT)_P and i need to take this knowledge to combine the equations but I don't see how I would be getting the square on the ds out of this. Obviously I'm missing something. C_v/T should be the same proof with u in place of h holding v constant. Thanks for any help.