If a gaseous mixture consists of $3$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$,then the total internal energy of the mixture is (neglect vibrational modes and $R$ - Universal gas constant). (in $RT$)

The temperature of the mixture of one mole of helium and one mole of hydrogen is increased from $0^{\circ}C$ to $100^{\circ}C$ at constant pressure. The amount of heat delivered will be ...... $cal$.

$A$ mixture of $7 \, g$ of nitrogen and $11 \, g$ of carbon dioxide is kept in a container at a temperature of $T = 290 \, K$. If the pressure of the mixture is $1 \, atm$ $(1.01 \times 10^5 \, N/m^2)$,then the density of the mixture is approximately . . . . . . $kg/m^3$.

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only $O_2$,$B$ only $N_2$ and $C$ a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of the $O_2$ molecules in vessel $A$ is $V_1$,and that of the $N_2$ molecules in vessel $B$ is $V_2$,what is the average speed of the $O_2$ molecules in vessel $C$?

$A$ mixture of ideal gases has $2$ moles of $He$,$4$ moles of oxygen $(O_2)$,and $1$ mole of ozone $(O_3)$ at absolute temperature $T$. The internal energy of the mixture is ............. $RT$.

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: