If one mole of an ideal monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with one mole of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$,the value of $\gamma$ for the mixture is:

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is . . . . . . .

The pressure and temperature of two different gases are $P$ and $T$,each having the same volume $V$. If they are mixed while keeping the volume and temperature constant,the pressure of the mixture will be:

If $7 \, g$ of $N_{2}$ is mixed with $20 \, g$ of $Ar$,the $C_{p} / C_{v}$ ratio of the mixture will be:

$A$ gaseous mixture has $2$ moles of oxygen and $4$ moles of Argon at a temperature $T$. Neglecting all vibrational modes of the molecules,the total internal energy of the system is ($R$ = Universal gas constant). (in $RT$)

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.