4. A pure substance is described by the following thermodynamic equation: where

Question

4. A pure substance is described by the following thermodynamic equation: where bar U, bar S, and bar V are the molar energy, entropy, and volume, R is the gas constant, and T0 and V0 are constants. a) Obtain an explicit expression for the pressure as a function of temperature and molar volume, P = P(T, bar V) for this system. Your expression may contain the constants T0 and V0 but not bar U or bar S. b) Find the functional form of adiabats (constant-entropy lines) in the P - bar V plane, i.e. an expression analogous to P bar V^gamma=constant for an ideal gas.

Explanation / Answer

A) Remember U = function of Temperature

U is function of T when V is constant -> dU/Dt = Cv or dU = CvdT

U = Cv

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