Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V} = \frac{3}{2}$ for the mixture,then the value of $n$ is:

$A$ closed container of volume $0.02 \ m^3$ contains a mixture of neon and argon gases at a temperature of $27^{\circ}C$ and a pressure of $1 \times 10^5 \ N/m^2$. The total mass of the mixture is $28 \ g$. If the atomic weights of neon and argon are $20$ and $40$ respectively,find the mass of each gas in the container in $g$,assuming they behave as ideal gases. $(R = 8.314 \ J/mol \cdot K)$

$A$ gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $\frac{C_P}{C_V}$ of the mixture is

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $T_1, T_2$,pressures $P_1, P_2$,and volumes $V_1, V_2$ respectively. If the valve connecting them is opened,what is the temperature of the equilibrium mixture?

$2$ moles of $O_2$ and $4$ moles of $Ar$ are filled in a container at temperature $T$. What is the total internal energy (in $, RT$)?

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1=4\ g$ and that of hydrogen $M_2=2\ g$. If the internal energy of the $He$ sample is $100\ J$ and that of the hydrogen sample is $200\ J$,then the internal energy of the mixture is ..... $J$.