An ideal gas is enclosed in a cylinder at a pressure of $2 \, atm$ and a temperature of $300 \, K$. The mean time between two successive collisions is $6 \times 10^{-8} \, s$. If the pressure is doubled and the temperature is increased to $500 \, K$,the mean time between two successive collisions will be close to:

For a molecule of an ideal gas,the number density is $2 \sqrt{2} \times 10^8 \text{ cm}^{-3}$ and the mean free path is $\frac{10^{-2}}{\pi} \text{ cm}$. The diameter of the gas molecule is

$A$ container is divided into two equal parts $I$ and $II$ by a partition with a small hole of diameter $d$. The two parts are filled with the same ideal gas,but held at temperatures $T_{I} = 150 \, K$ and $T_{II} = 300 \, K$ by connecting them to heat reservoirs. Let $\lambda_{I}$ and $\lambda_{II}$ be the mean free paths of the gas particles in the two parts,such that $d \gg \lambda_{I}$ and $d \gg \lambda_{II}$. Then,the ratio $\lambda_{I} / \lambda_{II}$ is close to:

The value of critical temperature in terms of Vander Waals constants $a$ and $b$ is

The mean free path of molecules in an ideal gas $A$ is half that of another ideal gas $B$. The diameter of the spherical molecules of gas $A$ is twice the diameter of the molecules of gas $B$. If number densities of the gases $A$ and $B$ are $n_A$ and $n_B$, respectively, then the correct option is :

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