One mole of an ideal monatomic gas (CV=3/2R, R=8.314 J mol^-1K^-1) at 300 K and 1 L is allowed to expand to 8 L by two different routes: (I) a…

(A) Reversible adiabatic: $TV^{\gamma-1}=$ constant with $\gamma=5/3$, so $T_2=300(1/8)^{2/3}=75$ K. True. (B) $|w|=C_V\Delta T=1.5\times8.314\times225=2.81$ kJ; the value $3.74$ kJ results from wrongly using $C_V\times300$. False. (C) A reversible adiabatic process has $\Delta S_{\text{sys}}=0$ and $\Delta S_{\text{surr}}=0$, so $\Delta S_{\text{universe}}=0$, not $17.3$. False. (D) In the free expansion into vacuum with insulation, $q=w=0$, $\Delta U=0$ and so $T$ is unchanged for an ideal gas; entropy is a state function, so $\Delta S_{\text{sys}}=R\ln(8)=17.29\ \mathrm{J\,K^{-1}}$ (computed numerically), while $\Delta S_{\text{surr}}=0$. Hence $\Delta S_{\text{universe}}=+17.3\ \mathrm{J\,K^{-1}}$. True. Correct: A and D.