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I'm looking for a better discussion than I've found regarding thermodynamic functions. In particular, in reading various treatments, it would appear that E = E(S,V) and E = E(V,T) are valid, but E = E(S,T) is not.
I was thinking originally that there was some rule about mixing intensive and extensive variables, but the 2nd of the above 3 functional forms seems to kill that idea.
But why can't I use the 3rd functional form, E(S,T)?
It would seem no more or less valid than E(V,T) from an intensive/extensive standpoint, but I'd get
dE = (dE/dS)dS + (dE/dT)dT = TdS + CvdT
which is clearly at odds with the above.
 Interpret the parenthetical quantities as garden variety partial derivatives with the appropriate variable held constant.
I'm looking for a better discussion