Helmholtz free energy in the canonical ensemble

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SUMMARY

The Helmholtz free energy in the canonical ensemble is calculated using the formula A = -kT ln Z, where A represents the Helmholtz free energy, k is the Boltzmann constant, T is the temperature, and Z is the partition function. The discussion highlights the challenge of directly using A = U - TS due to the difficulty in expressing entropy S. Participants suggest consulting statistical physics textbooks or Wikipedia for the derivation of the formula.

PREREQUISITES
  • Understanding of canonical ensemble concepts
  • Familiarity with the partition function (Z)
  • Knowledge of thermodynamic potentials
  • Basic principles of statistical mechanics
NEXT STEPS
  • Study the derivation of the Helmholtz free energy formula from statistical physics textbooks
  • Explore the concept of the partition function in greater detail
  • Learn about the relationship between entropy and thermodynamic potentials
  • Investigate applications of Helmholtz free energy in physical systems
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Students and professionals in physics, particularly those studying statistical mechanics, thermodynamics, and anyone interested in the applications of the Helmholtz free energy in physical systems.

amedeo_fisi
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Hello everybody :D
My question is: given the distribution of the canonical ensemble, how do we get the helmoltz free energy?
I think we can't use A = U-TS because we don't know how to write S. So what's the solution? Thanks
 
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The simplest way is to use
$$
A = - k T \ln Z
$$
 
Thanks DrClaude, but I already know the result! How do you get that formula?
 
You should be able to find the derivation in any statistical physics textbook. You can also find a derivation on Wikipedia.
 

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