$\gamma = \frac{{{C_P}}}{{{C_V}}} = \frac{5}{3}$
we know $\Delta Q = n{C_P}\Delta T$ and $\Delta U = n{C_V}\Delta T$
==> $\frac{{\Delta U}}{{\Delta Q}} = \frac{{{C_V}}}{{{C_P}}} = \frac{3}{5}$
i.e. fraction of heat energy to increase the internal energy be $3/5.$
Considering only $P-V$ work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$
[Use the given data: Molar heat capacity of the gas for the given temperature range, $C _{ v , m }=12 J K ^{-1} mol ^{-1}$ and gas constant, $R =8.3 J K ^{-1} mol ^{-1}$ ]
(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 $1.6$
Choose the correct option out of the following for work done if processes $B C$ and $D A$ are adiabatic.

