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 $R=8 \, J K^{-1} mol^{-1}$).

The specific heat of the mixture of two gases at constant volume is $\frac{13}{6} R$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be:

$A$ gaseous mixture has $2$ moles of oxygen and $4$ moles of Argon at a temperature $T$. Neglecting all vibrational modes of the molecules,the total internal energy of the system is ($R$ = Universal gas constant). (in $RT$)

$A$ mixture of carbon dioxide and oxygen has volume $8310 \text{ cm}^3$,temperature $300 \text{ K}$,pressure $100 \text{ kPa}$ and mass $13.2 \text{ g}$. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . . . . . . . (Assume both carbon dioxide and oxygen gases behave like ideal gases) $[R = 8.31 \text{ J/mol.K}]$

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

$A$ closed container of volume $0.02 \ m^3$ contains a mixture of neon and argon gases at a temperature of $27^{\circ}C$ and a pressure of $1 \times 10^5 \ N/m^2$. The total mass of the mixture is $28 \ g$. If the atomic weights of neon and argon are $20$ and $40$ respectively,find the mass of each gas in the container in $g$,assuming they behave as ideal gases. $(R = 8.314 \ J/mol \cdot K)$