In a cubic container of inner side length $10 \ cm$, nitrogen gas at $100 \ kPa$ pressure is maintained at $300 \ K$. If the pressure inside the container is increased to $300 \ kPa$ by adding oxygen gas, the ratio of the number of $N_2$ molecules to $O_2$ molecules in the container is:

One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

When one mole of an ideal monatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5)$, what is the value of $\gamma$ for the mixture?

$A$ mixture of carbon dioxide and oxygen has volume $8310 \text{ cm}^3$, temperature $300 \text{ K}$, pressure $100 \text{ kPa}$ and mass $13.2 \text{ g}$. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . . . . . . . (Assume both carbon dioxide and oxygen gases behave like ideal gases) $[R = 8.31 \text{ J/mol.K}]$

$2 \text{ mole}$ of $N_2$ gas at $27 \, ^oC$ is mixed with $1 \text{ mole}$ of $He$ gas at $-73 \, ^oC$. Find the final temperature $T_{\text{mix}}$ of the mixture.

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 ...... $^\circ C$.