Partition functions
Statistical Thermodynamics (UG) · Chemistry
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Study notes
For a particle with two levels (0 and ε), write Z and find the average energy. Step 1: Z = e⁰ + e^(-ε/kT) = 1 + e^(-ε/kT). Step 2: P₀ = 1/Z, P₁ = e^(-ε/kT)/Z. Step 3: ⟨E⟩ = 0·P₀ + ε·P₁ = ε·e^(-ε/kT)/(1+e^(-ε/kT)). Step 4: At T→0: ⟨E⟩→0. At T→∞: ⟨E⟩→ε/2 — both levels equally filled!