One mole of a gas with $\gamma = 7/5$ is mixed with one mole of a gas with $\gamma = 4/3$. What will be the $\gamma$ of the mixture?

In a container of volume $16.62 \ m^3$ at $0 \ ^{\circ}C$ temperature,$2 \ moles$ of oxygen,$5 \ moles$ of nitrogen,and $3 \ moles$ of hydrogen are present. Then,the pressure in the container is (Universal gas constant $R = 8.31 \ J \ mol^{-1} \ K^{-1}$) (in $Pa$)

$A$ closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5/3)$ and one mole of an ideal diatomic gas $(\gamma=7/5)$. Here,$\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66 \ J$ when heated at constant pressure. The change in its internal energy is . . . . . . $J$.

Two monoatomic ideal gases at temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and the number of their molecules are $n_1$ and $n_2$ respectively,the temperature of the 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?

Sound travels in a mixture of $2$ moles of helium and $n$ moles of hydrogen. If the root-mean-square (rms) speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound,then the value of $n$ will be: