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

If $22 \, g$ of $CO_2$ gas at $27 \, ^\circ C$ and $16 \, g$ of $O_2$ gas at $37 \, ^\circ C$ are mixed,the final temperature of the mixture will be ...... $^\circ C$.

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1=4\ g$ and that of hydrogen $M_2=2\ g$. If the internal energy of the $He$ sample is $100\ J$ and that of the hydrogen sample is $200\ J$,then the internal energy of the mixture is ..... $J$.

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

The pressure of a mixture of $64 \ g$ of oxygen, $28 \ g$ of nitrogen, and $132 \ g$ of carbon dioxide gases in a closed vessel is $P$. Under isothermal conditions, if the entire oxygen is removed from the vessel, the pressure of the mixture of the remaining two gases is:

In a container of volume $16.62 \ m^3$ at $0 \ ^{\circ}C$ temperature,$2 \ moles$ of oxygen,$5 \ moles$ of nitrogen,and $3 \ moles$ of hydrogen are present. Then,the pressure in the container is (Universal gas constant $R = 8.31 \ J \ mol^{-1} \ K^{-1}$) (in $Pa$)