$2$ moles of $O_2$ and $4$ moles of $Ar$ are filled in a container at temperature $T$. What is the total internal energy (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 $...........\,RT$.

If one mole of an ideal monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with one mole of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$,the value of $\gamma$ for the mixture is:

Two gases have the same pressure $P$,temperature $T$,and volume $V$. If they are mixed and the final volume and temperature remain $V$ and $T$ respectively,what will be the final pressure?

Three ideal gases at absolute temperatures $T_1, T_2$,and $T_3$ are mixed. Their number of molecules are $n_1, n_2$,and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture will be .....

$A$ closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5/3)$ and one mole of an ideal diatomic gas $(\gamma=7/5)$. Here,$\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66 \ J$ when heated at constant pressure. The change in its internal energy is . . . . . . $J$.