Mean Free Path — MCQ Practice

The mean free path of molecules of a gas at a pressure $P$ and temperature $T$ is $\lambda$. If the pressure is doubled to $2P$ and the temperature is halved to $T/2$, what will be the new mean free path?

If the molecular diameter of a gas is doubled, how does the mean free path change, assuming constant temperature and pressure?

Which of the following statements about the mean free path ($\lambda$) of a gas is INCORRECT?

A gas is contained in a rigid vessel. If its temperature is increased, what happens to the mean free path of the gas molecules?

Calculate the mean free path of nitrogen molecules at $27^\circ\text{C}$ and $1\,\text{atm}$ pressure. Assume the molecular diameter of nitrogen is $3.1 \times 10^{-10},\text{m}$. (Given: Boltzmann constant $k = 1.38 \times 10^{-23},\text{J/K}$, $1\,\text{atm} = 1.013 \times 10^5\,\text{Pa}$)

Two gases, A and B, have the same number density and molecular diameter. If the temperature of gas A is $T$ and its pressure is $P$, while the temperature of gas B is $2T$ and its pressure is $2P$, what is the ratio of their mean free paths ($\lambda_A / \lambda_B$)?