$A$ 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 $, RT$)

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of the mixture at constant volume is $\frac{\alpha^{2}}{4} R \ J/mol \ K$; then the value of $\alpha$ will be $.......$ (Assume that the given diatomic gas has no vibrational mode.)

$A$ mixture of ideal gases consists of $7 \, kg$ of nitrogen and $11 \, kg$ of $CO_2$. Then (Take $\gamma$ for nitrogen and $CO_2$ as $1.4$ and $1.3$ respectively):

Two different gases have pressure $P$ and temperature $T$. Their volume is $V$. If these two gases are mixed while keeping the volume and temperature the same,the pressure of the mixture will be...........

$A$ 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 $RT$)

Considering the gases to be ideal,the value of $\gamma = \frac{C_P}{C_V}$ for a gaseous mixture consisting of $3$ moles of carbon dioxide and $2$ moles of oxygen will be $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.