The molar specific heat of a mixture at constant volume,if one mole of $He$ gas is mixed with three moles of $O_2$ gas,is: (in $R$)

One mole of a gas mixture is heated under constant pressure,and the heat supplied $Q$ is plotted against the temperature difference $\Delta T$ acquired. Find the approximate value of $\gamma$ for the mixture.

$A$ 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 $RT$)

Two ideal gases $A$ and $B$ having the same temperature $T$,same pressure $P$,and same volume $V$,are mixed together. If the temperature of the mixture is kept constant and the volume occupied by the mixture is reduced to $\frac{V}{2}$,then the pressure of the mixture will become:

$A$ container is divided into two chambers by a partition. The volume of the first chamber is $4.5 \, L$ and the second chamber is $5.5 \, L$. The first chamber contains $3.0 \, \text{moles}$ of gas at a pressure of $2.0 \, \text{atm}$, and the second chamber contains $4.0 \, \text{moles}$ of gas at a pressure of $3.0 \, \text{atm}$. After the partition is removed and the mixture attains equilibrium, the common equilibrium pressure existing in the mixture is $x \times 10^{-1} \, \text{atm}$. The value of $x$ is......... (in $.5$)

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.