Two gases $A$ and $B$ having the same pressure $P$, volume $V$, and absolute temperature $T$ are mixed. If the mixture has the volume $V$ and temperature $T$, then the pressure of the mixture is:

$A$ container holds $8 \, g$ of $O_2$ and $7 \, g$ of $N_2$ at a pressure of $10 \, atm$. If $O_2$ is removed,the pressure becomes ... $atm$.

Two vessels of equal volume contain the same gas. Their pressures and temperatures are $P_1, T_1$ and $P_2, T_2$ respectively. When they are connected,the common pressure and temperature are $P$ and $T$. Then $P/T$ is equal to:

One mole of a gas having $\gamma = \frac{7}{5}$ is mixed with one mole of a gas having $\gamma = \frac{4}{3}$. The value of $\gamma$ for the mixture is ($\gamma$ is the ratio of the specific heats of the gas).

If three moles of monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$,the value of adiabatic exponent $\gamma$ for the mixture is:

$A$ gaseous mixture consists of $2$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$. Neglecting all vibrational modes,the total internal energy of the mixture of the gases is (in $RT$)