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

$A$ box contains a mixture of ${H_2}$ and $He$ gases. Which of the following statements are correct?

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be:

When one mole of an ideal monatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5)$, what is the value of $\gamma$ for the mixture?

Two identical containers contain the same gas at pressures $P_1$ and $P_2$ and temperatures $T_1$ and $T_2$,respectively. If the containers are connected,the common pressure is $P$ and the common temperature is $T$. What is the value of $P/T$?

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)