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?

$1 \, \text{mole}$ of a gas having $\gamma = \frac{7}{5}$ is mixed with $1 \, \text{mole}$ of a gas having $\gamma = \frac{4}{3}$. What will be the $\gamma$ for the mixture?

If a gaseous mixture consists of $3$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$,then the total internal energy of the mixture is (neglect vibrational modes and $R$ - Universal gas constant). (in $RT$)

$A$ mixture of $28 \ g$ of nitrogen,$4 \ g$ of hydrogen,and $8 \ g$ of helium is kept in a vessel at a temperature of $400 \ K$ and a pressure of $8.3 \times 10^5 \ Pa$. What is the density of the mixture?

If two moles of diatomic gas and one mole of monoatomic gas are mixed,then the ratio of specific heats is:

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.