Question

2. Take the entropy to be a function of the independent variables T and V. For the van der Waals gas, derive an expression for the entropy as a function of volume at a given (fixed) temperature. Hint: You will want to take advantage of Maxwells relations. Your answer will contain an undetermined constant of integration.
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Answer #1

for any gas, entropy change = Cv*dT/T+ (dP/dT)VdV

at constant temperature, entropy change , deltaS= (dP/dT)VdV

(dS/dV)T= (dP/dT)V

but for   Vanderwaal gas P= RT/(V-b)- a/V2

(dP/dT)V= R/(V-b)

(dS/dV)T= R/(V-b)

dS= R/(V-b)dV

when integrated, the equation is deltaS= R*ln(V-b)+C where c is integration constant.

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