$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

If $1 \text{ mole}$ of a monoatomic gas $\left[ \gamma = \frac{5}{3} \right]$ is mixed with $1 \text{ mole}$ of a diatomic gas $\left[ \gamma = \frac{7}{5} \right]$,then the $\gamma$ of the 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 $^{\circ} C$)

$A$ mixture of $2$ moles of oxygen and $4$ moles of argon is kept at temperature $T$. Neglecting all internal vibrations,the total internal energy of the system is: (in $, RT$)

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 $MPa$)?

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be: