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 $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed such that there is no loss of energy. If $F_{1}$ and $F_{2}$,$m_{1}$ and $m_{2}$,$n_{1}$ and $n_{2}$ are the degrees of freedom,masses,and number of molecules of the first and second gas respectively,then the temperature of the mixture of these two gases is:

The molar heat capacity of a mixture of two gases at constant volume is $13R/6$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be:

$A$ 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 non-reactive monoatomic ideal gases have their atomic masses in the ratio $2: 3$. The ratio of their partial pressures,when enclosed in a vessel kept at a constant temperature,is $4: 3$. The ratio of their densities is:

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.)