Problem 2 (of 5): [Total: 15 pts] For systems in diffusive equilibrium none of the thermodynamic potentials we have discussed are particularly useful. By subtracting the quantity uNfrom the internal energy U, we can define a new thermodynamic potential which we will call U. a) Determine the thermodynamic identity for U and its natural variables. b) Using your answer to part a), determine formulas relating appropriate partial derivatives of U to other thermodynamic quantities (e.g., by thermodynamic quantities we mean things like S, P, V, µ, etc.). You should end up with three separate partial derivative relationships. c) Using your expressions in part b), produce two separate Maxwell's Relations involving the number of particles, N.

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