$A$ 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 $...........\,RT$.

$2 \text{ mole}$ of $N_2$ gas at $27 \, ^oC$ is mixed with $1 \text{ mole}$ of $He$ gas at $-73 \, ^oC$. Find the final temperature $T_{\text{mix}}$ of the mixture.

Two gases occupy two containers $A$ and $B$. The gas in $A$,of volume $0.10 \, m^3$,exerts a pressure of $1.40 \, MPa$,and the gas in $B$,of volume $0.15 \, m^3$,exerts a pressure of $0.7 \, MPa$. The two containers are connected by a tube of negligible volume,and the gases are allowed to intermingle. If the temperature remains constant,what will be the final pressure in the containers (in $MPa$)?

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take the molar mass of helium $M_1 = 4 \ g/mol$ and that of hydrogen $M_2 = 2 \ g/mol$. The equivalent value of $\gamma$ for the mixture is:

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 $C$?

The container shown in the figure has two chambers,separated by a partition,with volumes $V_1 = 2.0 \, L$ and $V_2 = 3.0 \, L$. The chambers contain $\mu_1 = 4.0 \, mol$ and $\mu_2 = 5.0 \, mol$ of a gas at pressures $P_1 = 1.00 \, atm$ and $P_2 = 2.00 \, atm$. Calculate the pressure after the partition is removed and the mixture attains equilibrium.