$1 \text{ mole}$ of ideal monoatomic gas $(\gamma_1 = 5/3)$ is mixed with $1 \text{ mole}$ of diatomic gas $(\gamma_2 = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

$A$ 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 $= 28)$.

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5).$ What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas,the final equilibrium temperature of the gas in the container will be

Four moles of hydrogen,two moles of helium and one mole of water vapour form an ideal gas mixture. $[C_v$ for hydrogen $= \frac{5}{2} R, C_v$ for helium $= \frac{3}{2} R, C_v$ for water vapour $= 3 R]$. What is the molar specific heat at constant pressure of the mixture?

$A$ vessel has a capacity of $3 \ L$. If it contains a mixture of $6 \ g$ of $O_2$,$8 \ g$ of $N_2$,and $5 \ g$ of $CO_2$,what will be the pressure of the vessel at a temperature of $27^{\circ}C$? (Given $R = 8.31 \ J/mol \cdot K$)