On increasing the number density of a gas in a vessel,the mean free path of the gas:

For the given concentration,if the ratio of the diameters of the molecules of two gases is $1: 2$,then the ratio of their mean free paths is

The internal energy of real gases is determined by which of the following?

Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} C$ and pressure $1.01 \times 10^{5} Pa$. Assume the molecular diameter $d = 0.3 nm$ and the gas is ideal. Given Boltzmann constant $k = 1.38 \times 10^{-23} J K^{-1}$. (Result in $nm$)

At a temperature of $314 \,K$ and a pressure of $100 \,kPa$, the speed of sound in a gas is $1380 \,ms^{-1}$. The radius of each gas molecule is $0.5 \,Å$. The frequency of sound at which the wavelength of the sound wave in the gas becomes equal to the mean free path of the gas molecules is (Boltzmann constant $k = 1.38 \times 10^{-23} \,JK^{-1}$):

In Van der Waals equation $\left( P + \frac{a}{V^2} \right)(V - b) = RT$,what do $a$ and $b$ represent?