Archived Partial Derivatives and Constant Variables in Thermodynamics

AI Thread Summary
The discussion revolves around the equality of partial derivatives in thermodynamics, specifically examining the relationship between entropy (S), volume (V), pressure (P), and temperature (T). The user expresses confusion about which variables remain constant when rearranging the equality. They typically assume all variables except the one being differentiated are constant but seek clarification on this approach. The user also proposes a potential equation involving these variables and asks for confirmation of its correctness. Understanding the proper treatment of constant variables in partial derivatives is crucial for solving thermodynamics problems effectively.
Jalo
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Homework Statement



Consider the following equality:

(\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V

If I rearrange the equality so that I write:

(\frac{∂S}{∂P})? = (\frac{∂V}{∂T})?

What variables will be constant in each side?
I'm having some trouble in a few thermodynamics problems because of this...

Homework Equations





The Attempt at a Solution



I don't know how to do this. Normally I just ignore and assume that every variable except the variable of differentiation is a constant.
If anyone could confirm or correct me I'd be thankful.

Thanks.
 
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I think (T/V)(∂s/∂p)=(∂V/∂T). Is this correct?
 
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