$2\, moles$ of helium gas is mixed with $3\, moles$ of hydrogen molecules (taken to be rigid). What is the molar specific heat of the mixture at constant volume in $J/mol\, K$? $(R = 8.3\, J/mol\, K)$

$A$ 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 $RT$)

$A$ gas mixture consists of $3 \, moles$ of oxygen and $5 \, moles$ of argon at temperature $T$. Considering only translational and rotational modes,the total internal energy of the system is: (in $, RT$)

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?

$3$ 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

$A$ vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} C$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is $($Molecular mass of hydrogen gas $= 2$ and molecular mass of nitrogen gas $= 28)$.