Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures, and number densities are the same. The molecular size of $A$ is half of that of $B$ and the mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} /s$, then the collision frequency in gas $A$ is . . . . . . $/s$.

$A$ thermally isolated cylindrical closed vessel of height $8 \ m$ is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass $8.3 \ kg$. Thus,the partition is held initially at a distance of $4 \ m$ from the top. Each of the two parts of the vessel contains $0.1 \ mol$ of an ideal gas at temperature $300 \ K$. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached,the distance of the partition from the top (in $m$) will be. . . . . . (take the acceleration due to gravity $g = 10 \ m/s^2$ and the universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$).

Two vessels of the same volume contain the same gas at the same temperature. If the pressure in the vessels is in the ratio of $1 : 2$,then

An ideal gas is expanding such that $PT^{3} = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

Select the correct statement.

If the pressure of $CO_2$ (real gas) in a container is given by $P = \frac{RT}{2V - b} - \frac{a}{4V^2}$,then the mass of the gas in the container is ...... $g$.