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$(A)$ Process $I$ is an isochoric process $(B)$ In process $II$, gas absorbs heat
$(C)$ In process $IV$, gas releases heat $(D)$ Processes $I$ and $III$ are $not$ isobaric
(Give $2^{1.2}=2.3 ; 2^{3.2}=9.2 ; R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P _0$ and $10 P _0$
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT _0$ and $19 RT _0$
$(3)$ The work $| W |$ done during the process is $13 RT _0$
$(4)$ Adiabatic constant of the gas mixture is $1.6$


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

${P_A} = 3 \times {10^4}Pa,\;{P_B} = 8 \times {10^4}Pa$ and ${V_A} = 2 \times {10^{ - 3}}{m^3},\;{V_D} = 5 \times {10^{ - 3}}{m^3}$
In process $AB$, $600 J$ of heat is added to the system and in process $BC, 200 J $ of heat is added to the system. The change in internal energy of the system in process $ AC$ would be ...... $J$