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

$1 \text{ mole}$ of a gas with $\gamma = 7/5$ is mixed with $1 \text{ mole}$ of a gas with $\gamma = 5/3$. The value of $\gamma$ for the resulting mixture is:

One mole of a gas with $\gamma = 7/5$ is mixed with one mole of a gas with $\gamma = 4/3$. What will be the $\gamma$ of the mixture?

Two ideal gases $A$ and $B$ having the same temperature $T$,same pressure $P$,and same volume $V$,are mixed together. If the temperature of the mixture is kept constant and the volume occupied by the mixture is reduced to $\frac{V}{2}$,then the pressure of the mixture will become:

$A$ gaseous mixture contains an equal number of hydrogen $(H_2)$ and nitrogen $(N_2)$ molecules. Specific heat measurements on this mixture at temperatures below $100\, K$ would indicate that the value of $\gamma$ (ratio of specific heats) for this mixture is

In a cubic container of inner side length $10 \ cm$, nitrogen gas at $100 \ kPa$ pressure is maintained at $300 \ K$. If the pressure inside the container is increased to $300 \ kPa$ by adding oxygen gas, the ratio of the number of $N_2$ molecules to $O_2$ molecules in the container is: