$A$ 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 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 $MPa$)?

The molar specific heat of a mixture at constant volume,if one mole of $He$ gas is mixed with three moles of $O_2$ gas,is: (in $R$)

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then:

$A$ 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 $RT$)

Two gases $A$ and $B$ having the same pressure $P$, volume $V$, and absolute temperature $T$ are mixed. If the mixture has the volume $V$ and temperature $T$, then the pressure of the mixture is: