$A$ gaseous mixture has $2$ moles of oxygen and $4$ moles of Argon at a temperature $T$. Neglecting all vibrational modes of the molecules,the total internal energy of the system is ($R$ = Universal gas constant). (in $RT$)

The capacity of a vessel is $3 \, L$. It contains a mixture of $6 \, g$ oxygen,$8 \, g$ nitrogen,and $5 \, g$ $CO_2$ at $27^{\circ}C$. If $R = 8.31 \, J/(mol \cdot K)$,then the pressure in the vessel in $N/m^2$ will be (approx.)

If $4$ moles of an ideal monoatomic gas at temperature $400 \,K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 \,K$, the temperature of the mixture is:

$A$ gas mixture contains $n_1$ moles of a monoatomic gas and $n_2$ moles of a gas of rigid diatomic molecules. Each molecule in the monoatomic and diatomic gas has $3$ and $5$ degrees of freedom respectively. If the adiabatic exponent $\left(\frac{C_p}{C_V}\right)$ for this gas mixture is $1.5$, then the ratio $\frac{n_1}{n_2}$ will be

$A$ gaseous mixture contains $7 \ g$ of nitrogen and $20 \ g$ of argon. Assuming the gases are ideal,what are the specific heats $C_P$ and $C_V$ (in $J/g \ K$) for the mixture?

If two moles of diatomic gas and one mole of monoatomic gas are mixed,then the ratio of specific heats $\gamma$ for the mixture is: