$3$ moles of mono-atomic gas $(\gamma = 5/3)$ is mixed with $1$ mole of a diatomic gas $(\gamma = 7/5)$. The value of $\gamma$ for the mixture will be

$A$ jar has a mixture of hydrogen and oxygen gas in the ratio of $1 : 5$. The ratio of mean kinetic energies of hydrogen and oxygen molecules is

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:

Three moles of oxygen are mixed with $2 \, moles$ of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture?

$A$ mixture of $2$ moles of oxygen and $4$ moles of argon is kept at temperature $T$. Neglecting all internal vibrations,the total internal energy of the system is: (in $, RT$)

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