Physics · Statistical Mechanics
Consider a grand ensemble of a system of one-dimensional non-interacting classical harmonic oscillators (each of frequency ω). Which of the following relations is correct? Here, the angular brackets denote the ensemble average, N is the number of particles, E is the energy, T is the temperature, and kB is the Boltzmann constant.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1⟨E⟩ = ⟨N⟩kBT✓
- 2⟨E⟩ = NkBT
- 3⟨E⟩ = ⟨N⟩(kBT / 2)
- 4⟨E⟩ = N(kBT / 2)
Correct answer
⟨E⟩ = ⟨N⟩kBT
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