One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of the mixture at constant volume is $\frac{\alpha^{2}}{4} R \ J/mol \ K$; then the value of $\alpha$ will be $.......$ (Assume that the given diatomic gas has no vibrational mode.)

Three ideal gases at absolute temperatures $T_1, T_2$,and $T_3$ are mixed. Their number of molecules are $n_1, n_2$,and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture will be .....

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.

Two gases occupy two containers $A$ and $B$. The gas in $A$,of volume $0.10 \, m^3$,exerts a pressure of $1.40 \, MPa$,and the gas in $B$,of volume $0.15 \, m^3$,exerts a pressure of $0.7 \, MPa$. The two containers are connected by a tube of negligible volume,and the gases are allowed to intermingle. If the temperature remains constant,what will be the final pressure in the containers (in $MPa$)?

$A$ cylinder consists of a gas mixture of helium and oxygen. If the mass of helium is $4 \,g$ and the mass of oxygen is $32 \,g$, then the ratio of specific heat of the mixture $\left(C_p / C_V\right)$ is: