Partial derivative in thermodynamics

AI Thread Summary
The discussion centers on the use of partial derivatives in calculus, specifically regarding the expression (∂Cv/∂V)T=0. The user is struggling to understand a proof that involves switching the order of differentiation in partial derivatives, leading to the expression [(∂/∂T)(∂U/∂V)T]V. This switching is permissible due to Schwarz's theorem, which applies to functions that meet certain conditions, allowing for the interchange of the order of differentiation. The user seeks clarification on this rule and its name for further study, indicating a gap in their understanding of partial derivatives.
orgohell
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So I have a proof and I can't follow the process, I think its because I haven't learned how to do partial derivatives or I've forgotten, anyways can someone tell me if this is a rule in calculus

(∂Cv/∂V)T=0

I've gotten to
[(∂/∂V)(∂U/∂T)V]T

and the proof I have goes to
[(∂/∂T)(∂U/∂V)T]V
-is this a rule? they were able to switch the denominators of the derivatives which is can see but then they switched the constants as well If so what is the name so I can read up on it, I can't seem to find it with google
 
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orgohell said:
So I have a proof and I can't follow the process, I think its because I haven't learned how to do partial derivatives or I've forgotten, anyways can someone tell me if this is a rule in calculus

(∂Cv/∂V)T=0

I've gotten to
[(∂/∂V)(∂U/∂T)V]T

and the proof I have goes to
[(∂/∂T)(∂U/∂V)T]V
-is this a rule? they were able to switch the denominators of the derivatives which is can see but then they switched the constants as well If so what is the name so I can read up on it, I can't seem to find it with google

That's allowed because U is a function that is in the conditions of Schwarz's theorem (which can be derived from stokes' theorem)
 

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