$A$ gaseous mixture contains an equal number of hydrogen $(H_2)$ and nitrogen $(N_2)$ molecules. Specific heat measurements on this mixture at temperatures below $100\, K$ would indicate that the value of $\gamma$ (ratio of specific heats) for this mixture is

If $2 \text{ moles}$ of an ideal monoatomic gas at a temperature of $27^{\circ} C$ is mixed with $4 \text{ moles}$ of another ideal monoatomic gas at a temperature of $327^{\circ} C$,then the temperature of the mixture of the two gases is: (in $^{\circ} C$)

$A$ closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it,the final equilibrium temperature (in $K$) of the gas in the vessel will be closest to:

The ratio $C_P / C_V$ for a gas mixture consisting of $8 \ g$ of helium and $16 \ g$ of oxygen is

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 $n$?

$A$ mixture of two moles of hydrogen and one mole of argon gas is taken in a closed container at room temperature. Consider the following two statements:
$(i)$ The average kinetic energy of each molecule of $H_2$ and $Ar$ are the same.
$(ii)$ The partial pressure due to argon gas is more than that due to hydrogen gas.