$A$ gaseous mixture consists of $2$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$. Neglecting all vibrational modes,the total internal energy of the mixture of the gases is (in $RT$)

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2: 3$. The ratio of their partial pressures,when enclosed in a vessel kept at a constant temperature,is $4: 3$. The ratio of their densities is:

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 $T_0$.

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 .....

$A$ mixture of $7 \, g$ of nitrogen and $11 \, g$ of carbon dioxide is kept in a container at a temperature of $T = 290 \, K$. If the pressure of the mixture is $1 \, atm$ $(1.01 \times 10^5 \, N/m^2)$,then the density of the mixture is approximately . . . . . . $kg/m^3$.

$A$ mixture of $4$ moles of hydrogen,$1$ mole of helium,and $1$ mole of water vapor is treated as an ideal gas mixture. What is the molar specific heat of the mixture at constant pressure?