Let\'s look at differential expressions for the same function in terms of differ

Question

Let's look at differential expressions for the same function in terms of different variables that may be able to measure and control. We have already worked out the differentials dU for U = U(S, V) and U = U(T, V). Write them down. Next, work out dU for U = U(T, P). Your final answers should only contain the tabulated quantities T, P, V, C_v, C_P, and alpha, kT, and pi T. Box your answer. Step back and look at your answers they show how the same function the internal energy can be expressed with different control variables.

Explanation / Answer

^ U = ^H - P^ V

P^V = ^nRT Hence

^U = ^H - ^nRT

R = Cp - Cv

Hence ^ U = ^ H - ^ n ( Cp - Cv ) T

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