Confused by some aspects of thermodynamics

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SUMMARY

This discussion centers on the principles of thermodynamics, specifically the minimization of Helmholtz free energy (F) under fixed constraints of temperature, volume, and particle number. It clarifies that these constraints apply to the subsystem, excluding the reservoir. Additionally, it emphasizes the importance of the partition function (Z) in deriving the equation of state and calculating other thermodynamic properties such as pressure and entropy through established thermodynamic identities.

PREREQUISITES
  • Understanding of Helmholtz free energy (F) and its minimization principles
  • Familiarity with the partition function (Z) in statistical mechanics
  • Knowledge of thermodynamic identities and their applications
  • Basic concepts of equilibrium and non-equilibrium thermodynamics
NEXT STEPS
  • Study the derivation and applications of the Helmholtz free energy in thermodynamics
  • Learn how to calculate the equation of state from the partition function (Z)
  • Explore the relationship between thermodynamic potentials and their identities
  • Investigate the implications of equilibrium and non-equilibrium states in thermodynamic systems
USEFUL FOR

Students and professionals in physics, particularly those specializing in thermodynamics and statistical mechanics, as well as researchers seeking to deepen their understanding of thermodynamic properties and equations of state.

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I am quite confused by some aspects of thermodynamics. First of all, I just wonder, when the textbook says that "when the constraints are temperature, volume and particle number, minimise F for equilibrium" (and similar statements for G and H), does it mean that the temperature, volume and particle number of the sub-system (i.e. excluding the reservoir) is fixed?

And also, if Z, the partition function, is given, how should I proceed to find the equation of state?

Thank you. :-p
 
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Because
[tex]dF \leq -SdT -PdV + \mu dN[/tex]
then at fixed volume , temperature, and particle number, the free energy can only decrease, if we are at non-equilibrium. Thus temperature, volume, and particle number called "natural" arguments for the free energy.

If you know a partition function, you can calculate free energy. After that you can find pressure, enthropy, and thermodynamic potential using the thermodynamic identities
 

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