$14 \, g$ of $CO$ at $27^{\circ} C$ is mixed with $16 \, g$ of $O_2$ at $47^{\circ} C$. The temperature of the mixture is .......... $^{\circ} C$ (vibration mode neglected).

$A$ 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:
(Given $2^{1.2}=2.3$; $2^{3.2}=9.2$; $R$ 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 $1.6$.

$A$ mixture of ideal gases has $2$ moles of $He$,$4$ moles of oxygen $(O_2)$,and $1$ mole of ozone $(O_3)$ at absolute temperature $T$. The internal energy of the mixture is ............. $RT$.

When $16 \, g$ of $O_2$ at $37^\circ C$ is added to $22 \, g$ of $CO_2$ at $27^\circ C$,what will be the final temperature in $^\circ C$?

In a thermally isolated system,two boxes filled with an ideal gas are connected by a valve. When the valve is in the closed position,the states of box $1$ and $2$ respectively are $(1 \, atm, V, T)$ and $(0.5 \, atm, 4V, T)$. When the valve is opened,the final pressure of the system is approximately ............... $atm$.

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5).$ What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.