Solved: "The Helmholtz free energy for a system of..."

Cesar Mcguire

Answered question

2022-05-09

The Helmholtz free energy for a system of N harmonic oscillators

cegielnikmzjkf

Beginner2022-05-10Added 14 answers

Given:
The total number of harmonic oscillator is N.
The partion function for a quantum harmonic oscillator is

(1 - e^{- β ϵ})^{- 1}

Calculation:
Substitute

(1 - e^{- β ϵ})^{- 1}

for Z in equation:

F = - N k T \ln ((1 - e^{- β ϵ})^{- 1}) F = N k T \ln (1 - e^{- β ϵ})

Thus the Helmholtz free energy is

N k T \ln (1 - e^{- β ϵ})

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