Gibbs Free Energy and the Grand Potential

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SUMMARY

Gibbs Free Energy (G) is defined as G=E-TS+PV, applicable in scenarios involving heat exchange and mechanical work. The grand potential (g), expressed as g=E-TS-μN, is relevant for systems with heat exchange and chemical work. The discussion raises the question of whether a potential of the form (E-TS-μN+PV) can be conserved in a specific ensemble, noting that such a potential would vanish if it does not depend on at least one extensive variable, which is crucial for specifying the amount of substance involved.

PREREQUISITES
  • Understanding of thermodynamic potentials, specifically Gibbs Free Energy and grand potential.
  • Familiarity with the concepts of heat exchange, mechanical work, and chemical work.
  • Knowledge of extensive and intensive variables in thermodynamics.
  • Basic grasp of ensemble theory in statistical mechanics.
NEXT STEPS
  • Research the implications of extensive variables on thermodynamic potentials.
  • Study the relationship between Gibbs Free Energy and grand potential in different thermodynamic ensembles.
  • Explore advanced topics in statistical mechanics, focusing on ensemble theory.
  • Investigate potential applications of the grand potential in chemical systems.
USEFUL FOR

This discussion is beneficial for physicists, chemists, and students of thermodynamics who are exploring the intricacies of thermodynamic potentials and their applications in various physical systems.

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Gibbs Free Energy is the appropriate potential when there is both heat exchange and mechanical work (G=E-TS+PV). On the other hand the grand potential is appropriate when there is heat exchange and chemical work (g=E-TS-μN).
Is there any issue in defining a potential of the form (E-TS-μN+PV) such that it is conserved in some ensemble? If there is no problem, is there a consensus on a name for such potential and its corresponding ensemble?
 
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The problem is probably that the corresponding potential vanishes identically as G=mu N and g=-PV. You need the potential to depend on at least one extensive variable. If not, you can no longer specify the amount of substance you are talking about.
 

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