Four years after taking a thermo course and I finally understand what the hell the partial derivative notation in thermodynamics means I think
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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.
When i took thermo we *always* wrote S(E,V), S(E,P), S(T,V) etc..
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That's my point. How do you know which of these functions I am referring to if I just write ∂S/∂E?
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i don't which is why i said "i understand why they do it"
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For the record, that is also an abuse on notation. The function S(•,•) what is being defined and, therefore, T cannot be plugged in where an E was unless they are the same (which is almost but not exactly the case – conversion is required).
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This is related but not entirely on-topic.
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