If four identical samples of an ideal gas initially at same state () are allowed to expand to double — Thermodynamics and Thermochemistry Chemistry Question
Question
If four identical samples of an ideal gas initially at same state ($P_o, V_o, T_o$) are allowed to expand to double their volumes by the following processes: Process I: Isothermal reversible process, Process II: Reversible process $P^2V = \text{constant}$, Process III: Reversible adiabatic process, Process IV: Irreversible adiabatic expansion against constant external pressure. If the final states of gases are shown by different points in the graph represented, then match each point with the correct process:
💡 Solution & Explanation
Evaluating final pressures at $V=2V_0$: $P_{II} = P_0/\sqrt{2} \approx 0.7P_0$ (highest, pt 1). $P_I = 0.5P_0$ (pt 2). For adiabatic, $\Delta U_{irr} > \Delta U_{rev} \implies P_{IV} > P_{III}$ (pts 3, 4). Correct matches are I-2, II-1, III-4, IV-3.