What Does a Constant Number of Particles Mean for the Chemical Potential?

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SUMMARY

The discussion centers on the implications of a constant number of particles on the chemical potential (μ) and Helmholtz free energy (F) in thermodynamics. When F does not depend on the number of particles, it indicates that the chemical potential μ approaches zero. The correct definition of chemical potential is clarified as μ = F + PV, and the relationship between Helmholtz free energy and the number of particles is established through the equation dF = -SdT - PdV + μdN.

PREREQUISITES
  • Understanding of thermodynamic potentials, specifically Helmholtz free energy (F) and Gibbs free energy (G).
  • Familiarity with the concepts of chemical potential (μ) and its mathematical representation.
  • Knowledge of the first and second laws of thermodynamics.
  • Basic calculus for interpreting differential equations in thermodynamic contexts.
NEXT STEPS
  • Study the relationship between Helmholtz free energy and Gibbs free energy in detail.
  • Explore the implications of chemical potential in various thermodynamic systems.
  • Learn about the derivation and applications of the equation dF = -SdT - PdV + μdN.
  • Investigate the role of particle number in phase transitions and equilibrium states.
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying physical chemistry, chemical engineering, or related fields focused on energy systems and phase behavior.

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Homework Statement


What happens when the hemholtz free energy F of a system does not depend on the number of particles of the system?What does this mean for the chemical potential μ?

μ= U+PV -TS ,μ= F+PV


Homework Equations



F (OR A) F=U-TS

The Attempt at a Solution


I think the answer to this question requires deep understanding of the F
 
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Your definition of the chemical potential is a little off. It's G, the Gibbs free energy, that is equal to U+PV-TS. Once you correct the definition, you'll see what independence of N implies for μ.
 
change in Helmholtz free energy is given by :
dF = -SdT-PdV +μdN

μ is equal to zero

thanks
 

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