Import Question JSON

$\text{Hint: } \lambda = \frac{V}{\sqrt{2} \pi d^2 N}$ $\text{Step: Analyse each option one by one.}$ $\text{The mean free path of molecules of an ideal gas is given by:}$ $\lambda = \frac{V}{\sqrt{2} \pi d^2 N} = \frac{k_B T}{\sqrt{2} \pi d^2 P} \left[PV = nk_B T\right]$ $\text{where, } V = \text{Volume of container, } N = \text{No of molecules}$ $\text{The mean collision time is given by:}$ $\tau = \frac{\lambda}{\text{average speed}}$ $\text{Since the gas is heated slowly in a closed container, the volume remains constant. So, the mean free path is unchanged. In other words, as temperature rises, the pressure inside the container will increase proportionally. From the mean free path formula, since both } T \text{ and } P \text{ increase proportionally, the mean free path remains unchanged.}$ $\text{The mean free path remains the same, but the average molecular speed increases with temperature. So, the mean collision time decreases.}$ $\text{Therefore, the correct statements are (B) and (C) only.}$ $\text{Hence, option (4) is the correct answer.}$