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**1. Homework Statement**

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. Homework 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.