 Solution

At fixed positive temperature, $-R\ln (p/p_0)$ tends to $+\infty$ as $p\to 0^{+}$. This is a physically meaningful unbounded-volume limit for a fixed mole number: $V_m=RT/p\to \infty$, so the number of accessible translational configurations grows without bound. For an ideal gas the entropy difference is $R\ln (V_{m,2}/V_{m,1})$ at fixed temperature. No finite vessel reaches an infinite entropy, and $p=0$ at finite temperature is not a finite-volume one-mole state. The divergence is approached by dilution; it does not conflict with the third law, which concerns a different temperature limit.