
$I.$ Area $ABCD =$ Work done on the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in cycle $= 0$
Which of these are correct
| Column $I$ | Column $II$ |
| $(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and the Chamber $II$ has vacuum. The valve is opened. | $(p)$ The temperature of the gas decreases |
| $(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $\mathrm{P} \propto \frac{1}{\mathrm{~V}^2}$, where $\mathrm{V}$ is the volume of the gas | $(q)$ The temperature of the gas increases or remains constant |
| $(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $\mathrm{P} \propto \frac{1}{\mathrm{~V}^{4 / 3}}$, where $\mathrm{V}$ is its volume | $(r)$ The gas loses heat |
| $(D)$ An ideal monoatomic gas expands such that its pressure $\mathrm{P}$ and volume $\mathrm{V}$ follows the behaviour shown in the graph $Image$ | $(s)$ The gas gains heat |

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 $MJ$ | ($4$) $-2 \ R T_0 \ln 2$ |
| ($5$) $-3 \ R T_0 \ln 2$ |


$(i)$ What is $W$ along path $ibf$ ?
$(ii)$ If $W = 13$ cal for path $fi$, what is $Q$ for the path $fi$ ?
$(iii)$ Take $E_{int,i} = 10\,\, cal$ then what is $E_{int,f}$ ?