Partial Derivatives and Constant Variables in Thermodynamics

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SUMMARY

The discussion centers on the relationship between partial derivatives in thermodynamics, specifically the equality (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V. The user seeks clarification on rearranging this equation to (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? and identifying the constant variables on each side. The consensus is that typically, all variables except the one being differentiated are treated as constants, which is a standard approach in thermodynamic analysis.

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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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