How Do You Find Entropy for a Material Given Specific Equations?

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SUMMARY

The discussion focuses on calculating the entropy of a material defined by the equations U=C1PV2 and PV2=C2T. The key equations involved are dS/dU = 1/T and dU/dV = -P. A participant suggests using the Helmholtz free energy equation F = U - TS to derive entropy but realizes that the second condition is not utilized. The correct approach involves using the equation dU = TdS - PdV for reversible processes, allowing for the isolation of dS and subsequent integration with the provided formulas.

PREREQUISITES
  • Understanding of thermodynamic equations, specifically dU = TdS - PdV
  • Familiarity with Helmholtz free energy and its application
  • Knowledge of integrating thermodynamic relationships
  • Concept of reversible processes in thermodynamics
NEXT STEPS
  • Study the derivation and application of the Helmholtz free energy equation
  • Learn about integrating thermodynamic equations for entropy calculation
  • Explore the implications of reversible processes in thermodynamics
  • Investigate the relationship between internal energy and entropy in thermodynamic systems
USEFUL FOR

Students and professionals in thermodynamics, particularly those involved in material science and energy systems, will benefit from this discussion.

lifeonfire
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Homework Statement



For a material given by U=C1PV2 and PV2=C2T
Find the entropy

Homework Equations



dS/dU = 1/T; dU/dV = -P

I don't know if I require anything else

The Attempt at a Solution



So from 2 equations I got U = C1
C2T

But dU/dT is not equal to S. Which equation do I use to get the entropy? I was thinking of using F = U-TS. Which will give F = C1PV2 - TS And then doing dF/dT but then I didn't use the 2nd condition at all.

What am I missing?
 
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Hi lifeonfire! :smile:

Your relevant equations are not always true, the first requires V to remains constant, while the second requires S to remain constant.

For reversible processes, the equation dU=TdS-PdV is true without conditions on state variables.
From this you can isolate dS, apply the formulas given for your material, and integrate.
 

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