Equal masses of $N_2$ and $O_2$ gases are filled in containers $A$ and $B$ respectively. The volume of container $B$ is twice the volume of container $A$. What is the ratio of the pressure in container $A$ to that in container $B$?

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

If the density of the Sun is $1.4 \, g \, cm^{-3}$, the pressure is $1.4 \times 10^9 \, \text{atm}$, and the molar mass of the gas in the Sun is $2 \, g \, mol^{-1}$, then the temperature of the Sun will be: [Take $R = 8.4 \, J \, mol^{-1} \, K^{-1}$]

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

The number of air molecules in a $(5 \,m \times 5 \,m \times 4 \,m)$ room at standard temperature and pressure is of the order of

When $2 \, g$ of a gas are introduced into an evacuated flask kept at $25 \, ^\circ C$,the pressure is found to be $1 \, atm$. If $3 \, g$ of another gas is added to the same flask,the pressure becomes $1.5 \, atm$. The ratio of the molecular weights of these gases will be: