In adiabatic expansion

Starting at temperature $300\; \mathrm{K},$ one mole of an ideal diatomic gas $(\gamma=1.4)$ is first compressed adiabatically from volume $\mathrm{V}_{1}$ to $\mathrm{V}_{2}=\frac{\mathrm{V}_{1}}{16} .$ It is then allowed to expand isobarically to volume $2 \mathrm{V}_{2} \cdot$ If all the processes are the quasi-static then the final temperature of the gas (in $\left. \mathrm{K}\right)$ is (to the nearest integer)

A mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure $P _0$, volume $V _0$ and temperature $T _0$. If the gas mixture is adiabatically compressed to a volume $V _0 / 4$, then the correct statement(s) is/are,

(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 $1.6$

The adiabatic elasticity of a diatomic gas at $NTP$ is ........ $N / m ^2$

The pressure and density of a diatomic gas $\gamma  = 7/5$ change adiabatically from $(P, d)$ to $(P', d').$ If $\frac{{d'}}{d} = 32,$ then $\frac{{P'}}{P}$should be

A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$