〈 Berger | Dillon 〉

Four years after taking a thermo course and I finally understand what the hell the partial derivative notation in thermodynamics means I think

i asked early on .. it just means to hold the subscripts constant .. but isn't that what a partial derivative means anyways? it's kind of an over-clarification that makes it somewhat confusing tho i understand why they do it

The notation for partial derivatives is actually ambiguous. Yes, it implies that all the other variables are held constant, but what ARE the other variables? Consider f(x,y)=(x+y)²; what is ∂f/∂x? It depends, are you holding y constant or z=x+y constant?

why would you hold x+y constant? once you define f(x,y) then ∂f/∂x is unambiguous

But this is exactly what we DON'T do in thermodynamics! Do you distinguish between S(E,V), S(E,P), S(T,V)...? It's just S.