1. The problem statement, all variables and given/known data The question is attached along with its solution. 2. Relevant equations Partial differentiation and the implicit function theorem. 3. The attempt at a solution My work is attached. I feel it's correct but is it incomplete? I have the following questions/confusions.: 1) What's the purpose of the solution showing that T=T(P,V) and then F( P,V,T(P,V) )? Couldn't I just as easily have said V=V(P,T) or P=P(V,T) and modified F accordingly? 2) Prior to making this forum thread, I was completely confused as to what the 0 = stuff meant before the implication arrow however, I know see that it is the implicit function theorem written in one line. Is this important? Why is it being done in the solution? Any input would be appreciated! Thanks in advance!