10) [20 pts]-Develop two expressions for the entropy change of a system in terms of pressure,
temperature, volume.
Case 1:
$S = S(T,V)$
Case 2:
$S = S(T,P)$
Start with a total derivative of S in each case, make use of Maxwell relations. Select the most
convenient expression to use with the R-K EOS, then set up an expression to calculate the entropy
change for n-C$_4$ undergoing compression from 80°C and 10 bar to 125°C and 20 bar. For Full Credit:
Set up your expression, including integration limits. Do not evaluate. Leave 'a' and 'b' parameters
as a/b, include appropriate temperatures/pressures in your expression.