Past exam of the physics B course of the University of Cambridge / 2010 / Paper 1 / Section C / C10 / a

At fixed positive pressure, the extrapolated term $C_{mp}\ln (T/T_0)$ tends to $-\infty$ as $T\to 0^{+}$. That prediction is not physically realistic for an equilibrium sample. The classical ideal-gas description with constant heat capacity cannot extend unchanged to absolute zero. A real substance generally undergoes phase changes, and quantum statistics and thermal freeze-out change its heat capacity and entropy. For a nondegenerate equilibrium ground state, the third law gives entropy approaching zero; residual ground-state degeneracy can give a finite residual value rather than this negative divergence. This is a breakdown of the extrapolation, not a violation of the third law by a real gas.