Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S16 / 1 / c / Solution

At fixed volume, logarithmic differentiation of the Saha ionization equation givesDifferentiation the internal energy then yieldsAt low temperature $\zeta \to 0$ and $C_V\to 3R/2$. At high nonrelativistic temperature the gas is fully ionized, $\zeta \to 1$, and $C_V\to 3R$. The large intermediate excess reflects energy spent increasing ionization, as well as heating and creating additional translational particles. “Very high” here remains below regimes where relativistic, radiative or pair-creation contributions invalidate the model.