Understanding Maxwell Relations to Deriving (∂U/∂P)V=-T(∂V/∂T)S

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SUMMARY

The discussion focuses on deriving the equation (∂U/∂P)V = -T(∂V/∂T)S using the thermodynamic identity dU = TdS - PdV. The user expresses difficulty with derivations, particularly in applying partial derivatives and Maxwell relations. They mention familiarity with the Thermodynamic Square and have successfully solved the problem, indicating a resolution to their initial query.

PREREQUISITES
  • Understanding of thermodynamic identities, specifically dU = TdS - PdV
  • Familiarity with Maxwell relations in thermodynamics
  • Knowledge of partial derivatives and their applications
  • Experience with the Thermodynamic Square concept
NEXT STEPS
  • Study the derivation of other Maxwell relations in thermodynamics
  • Learn advanced techniques for solving partial differential equations
  • Explore applications of the Thermodynamic Square in various thermodynamic problems
  • Review the implications of thermodynamic potentials on system behavior
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying physical chemistry or engineering, who seek to deepen their understanding of thermodynamic relations and derivations.

AAiden
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1. Derive (∂U/∂P)V=-T(∂V/∂T)S

2. I must use dU=TdS-PdV

3. Derivations are my weakest part of math. I checked many wikis about Total differentials, partial derivatives, Maxwell relations and derivations. I can use the Thermodynamic Square, I know how to find different Maxwell relations but I am running in circles trying to derive this equation. Thanks to anyone who can help me out!

(I am stale on my partial derivatives memory and I am failing to see how these potentials relate with these constants)
 
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Can you find a Maxwell relation for the right-hand side?
 
Yes, I already solved this problem, thanks.

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