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

$N_1$ molecules of a gas at temperature $T_1$ are mixed with $N_2$ molecules at temperature $T_2$. The resulting temperature of the mixture gas is

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be:

$A$ 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) $[R = 8.31 \text{ J/mol.K}]$

$A$ vessel contains $3$ moles of $He$,$1$ mole of $Ar$,$5$ moles of $N_2$,and $3$ moles of $H_2$. If the vibrational modes are ignored,the total internal energy of the system of gases is (in $RT$)

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: