Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $\frac{C_{P}}{C_{V}}$ value will be

$14 \, g$ 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).

One litre of oxygen at a pressure of $1 \,atm$ and two litres of nitrogen at a pressure of $0.5 \,atm$ are introduced into a vessel of volume $1 \,L$. If there is no change in temperature, the final pressure of the mixture of gas (in $atm$) is

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only $O_2$,$B$ only $N_2$ and $C$ a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of the $O_2$ molecules in vessel $A$ is $V_1$,and that of the $N_2$ molecules in vessel $B$ is $V_2$,what is the average speed of the $O_2$ molecules in vessel $C$?