One mole of a monatomic ideal gas (with CV,m=3/2R and R=8.314 J K^-1 mol^-1) undergoes the changes listed in List-I. Match each with the entropy…

P: at constant volume $\Delta S=C_V\ln(T_2/T_1)=\tfrac32(8.314)\ln2=+8.64\ \mathrm{J\,K^{-1}}$, so P→5. Q: entropy is a state function, so for the gas $\Delta S=R\ln(V_2/V_1)=R\ln4=+11.53$; the insulated container exchanges no heat, so the surroundings change by zero and $\Delta S_{universe}=+11.53$: Q→4. R: in a reversible isothermal expansion the gas absorbs $q_{rev}=RT\ln2$ from the surroundings, so $\Delta S_{surr}=-R\ln2=-5.76$: R→3 (the system gains +5.76 and the universe total is 0). S: a reversible adiabatic process has $q_{rev}=0$, so $\Delta S_{gas}=0$: S→1. Item 2 (+5.76) is the entropy gain of the gas in R, not a listed answer. The correct code is P→5, Q→4, R→3, S→1.