Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [ $R$ is the gas constant]
| $List-I$ | $List-II$ |
| ($P$) Work done in the complete cyclic process | ($1$) $R T_0-4 \ R T_0 \ln 2$ |
| ($Q$) Change in the internal energy of the gas in the process $JK$ | ($2$) $0$ |
| ($R$) Heat given to the gas in the process $KL$ | ($3$) $3 \ R T_0$ |
| ($S$) Change in the internal energy of the gas in the process $MJ$ | ($4$) $-2 \ R T_0 \ln 2$ |
| ($5$) $-3 \ R T_0 \ln 2$ |

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($1$) Which of the following options is the only correct representation of a process in which $\Delta U=\Delta Q-P \Delta V$ ?
$[A] (II) (iv) (R)$ $[B] (II) (iii) (P)$ $[C] (II) (iii) (S)$ $[D] (III) (iii) (P)$
($2$) Which one of the following options is the correct combination?
$[A] (III) (ii) (S)$ $[B] (II) (iv) (R)$ $[C] (II) (iv) (P)$ $[D] (IV) (ii) (S)$
($3$) Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?
$[A] (III) (iv) (R)$ $[B] (I) (ii)$ $(\mathrm{Q})$ $[C] (IV) (ii) (R)$ $[D] (I) (iv) (Q)$
