$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture is

$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is (in $RT$)

For a mixture of non-reactive gases,derive the equation for total pressure.

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.)

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is . . . . . . .

$2$ moles of $O_2$ and $4$ moles of $Ar$ are filled in a container at temperature $T$. What is the total internal energy (in $, RT$)?