One gram mole of an ideal gas $A$ with the ratio of constant pressure and constant volume specific heats $\gamma_{A} = 5/3$ is mixed with $n$ gram moles of another ideal gas $B$ with $\gamma_{B} = 7/5$. If the $\gamma$ for the mixture is $19/13$,then what will be the value of $n$?

Two identical containers contain the same gas at pressures $P_1$ and $P_2$ and temperatures $T_1$ and $T_2$,respectively. If the containers are connected,the common pressure is $P$ and the common temperature is $T$. What is the value of $P/T$?

Two moles of an ideal gas with $\frac{C_{P}}{C_{V}}=\frac{5}{3}$ are mixed with $3$ moles of another ideal gas with $\frac{C_{P}}{C_{V}}=\frac{4}{3}$. The value of $\frac{C_{P}}{C_{V}}$ for the mixture is

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be:

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:

Two rigid boxes placed on a table contain different ideal gases. Box $A$ contains $1 \text{ mole}$ of nitrogen at temperature $T_0$. Box $B$ contains $1 \text{ mole}$ of helium at temperature $(7/3) T_0$. Both boxes are brought into thermal contact,and heat flows until they reach a common final temperature $T_f$. (Neglect the heat capacity of the boxes). Express the final temperature $T_f$ in terms of $T_0$.