Finding Entropy with three natural variables

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SUMMARY

The discussion focuses on deriving the entropy function S(T, Ba, P) from the Gibbs free energy equation G = U - TS + PV - BaM. The key conclusion is that the relationship S(T, Ba, P) = -(dG/dT)Ba,P can be established by manipulating the differential form of G. The participants emphasize the necessity of incorporating the magnetic energy term B\,dM into the internal energy equation dU to accurately account for the effects of magnetic fields on the system.

PREREQUISITES
  • Understanding of thermodynamic potentials, specifically Gibbs free energy.
  • Familiarity with differential calculus in thermodynamics.
  • Knowledge of magnetic thermodynamics and the role of magnetic fields in energy equations.
  • Proficiency in manipulating partial derivatives in multivariable functions.
NEXT STEPS
  • Study the derivation of thermodynamic potentials, focusing on Gibbs free energy.
  • Learn about the implications of magnetic fields in thermodynamic systems.
  • Explore the application of partial derivatives in thermodynamic equations.
  • Investigate the relationship between entropy and other thermodynamic variables.
USEFUL FOR

Students and professionals in physics and engineering, particularly those specializing in thermodynamics and magnetic systems, will benefit from this discussion.

Katie1990
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Homework Statement



Given

G =U −TS+PV −BaM

show that

S(T,Ba,P) = -(dG/dT)Ba,P


Homework Equations





The Attempt at a Solution



I know how to proceed if there are two variables and attemped to use this giving

dG = dU - TdS - SdT +PdV +VdP - BadM -MdBa

Using central equation

dG = = SdT +VdP -BadM - MdBa

I am unable to proceed from here
 
Physics news on Phys.org
If you are going to include magnetic energy in the problem, your [itex]dU[/itex] equation will need to include a [itex]B\,dM[/itex] term. Does this help you finish?
 

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