= Solution
At fixed positive <temperature>, $-R\ln(p/p_0)$ tends to \b[$+\infty$] as $p\to0^+$. This is a \b[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.
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