$A$ gas mixture contains monoatomic and diatomic molecules of $2$ moles each. The mixture has a total internal energy of (symbols have usual meanings): (in $R T$)

One mole of monatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in $J K^{-1} mol^{-1}$) at constant volume is (Let $R=8 \, J K^{-1} mol^{-1}$).

Two rigid boxes placed on a table contain different ideal gases. Box $A$ contains $1 \text{ mole}$ of nitrogen at temperature $T_0$. Box $B$ contains $1 \text{ mole}$ of helium at temperature $(7/3) T_0$. Both boxes are brought into thermal contact,and heat flows until they reach a common final temperature $T_f$. (Neglect the heat capacity of the boxes). Express the final temperature $T_f$ in terms of $T_0$.

If two moles of diatomic gas and one mole of monoatomic gas are mixed,then the ratio of specific heats $\gamma$ for the mixture is:

$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture is

$A$ gas mixture consists of $3 \, moles$ of oxygen and $5 \, moles$ of argon at temperature $T$. Considering only translational and rotational modes,the total internal energy of the system is: (in $, RT$)