Past exam of the chemistry A course of the University of Cambridge / 2023 / Paper 2 / A7 / c

The definition uses a fixed reference volume, so it is a reference-volume thermal expansion coefficient:Let $y=3e^{-\epsilon /(k_{B}T)}$. Sincewe obtainIt is positive and has units of inverse temperature. Equivalently, $\alpha =[\epsilon /(k_B{T}^2)]P_1(1-P_1)$: the response reflects changes in the thermally occupied excited population. The usual instantaneous fractional thermal expansion coefficient $V^{-1}dV/dT$ would instead equal $\alpha V_0/V$; substituting that different definition would change the answer.