Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 16.5-1

THE CANONICAL FORMALISM; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION

Physics — Statistical Mechanics · small-system-dispersion-probability

Problem

The energies of the orbital states of a given molecule are such that ε0=0\varepsilon_0 = 0, ε1/kB=200\varepsilon_1/k_B = 200 K, ε2/kB=300\varepsilon_2/k_B = 300 K, ε3/kB=400\varepsilon_3/k_B = 400 K and all other orbital states have very high energy. Calculate the dispersion σ≡⟨ε2⟩−⟨ε⟩2\sigma \equiv \sqrt{\langle\varepsilon^2\rangle - \langle\varepsilon\rangle^2} of the energy if the molecule is in equilibrium at T=300T = 300 K. What is the probability of occupation of each orbital state?

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