# For a certain system, the thermodynamic energy U is given as a function of S,V,and n by U = U(S,V,n)

## Question:

For a certain system, the thermodynamic energy U is given as a function of S,V,and n by

U = U(S,V,n) = Kn^{5/3}V^{−2/3}e^{2S/3nR},

where S is the entropy, V is the volume, n is the number of moles, K is a constant, and R is the gas constant.

(a) According to thermodynamic theory, T = (∂U/∂S)_{V ,n}. Find an expression for (∂U/∂S)_{V ,n}.

(b) According to thermodynamic theory, the pressure P = − (∂U/∂V )_{S,n}. Find an expression for (∂U/∂V )_{S,}n.

(c) Find an expression for (∂U/∂n)_{S,V}.

(d) Find dU in terms of dS,dV, and dn.

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