Thermodynamic derivatives of the canonical partition function

Canonical differentiation gives

F = - β^{- 1} lo g Z, ⟨ E ⟩ = - \partial_{β} lo g Z, (Δ E)^{2} = \partial_{β}^{2} lo g Z .

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- Canonical energy fluctuation Thermodynamic derivatives of the canonical partition function

Canonical energy fluctuation

Canonical energy variance equals

\partial_{β}^{2} lo g Z = k_{B} T^{2} C_{V}

.

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 36A / b / ii / Solution

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