A chemical process is being evaluated and measurable property data is available for P, V, T, CP, and CV, and there is sufficient data to calculate their derivatives. Data is also available to calculate the value of entropy (S). However there is not sufficient data to calculate derivatives involving S where S is in the derivative or S is held fixed for a derivative. In the process evaluation, it is necessary to calculate values for various conceptual properties. Your task as an engineer is to develop expressions that will relate the following partial derivatives to P, V, T, CP, and CV and their derivatives. The expressions can also use the absolute value of S, but S cannot be used within a derivative or as a constraint.
a. (? G /? P) T
b. (? P/? A ) V
c. (? T/ ? P) S
d. (? A /? S ) P