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(D) The mean free path $\lambda$ of molecules of an ideal gas is given by the formula:$\lambda = \frac{V}{\sqrt{2} \pi d^2 N}$where $V$ is the volume

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$(B)$ and $(C)$

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(D) The mean free path $\lambda$ of molecules of an ideal gas is given by the formula:$\lambda = \frac{V}{\sqrt{2} \pi d^2 N}$where $V$ is the volume of the container,$d$ is the molecular diameter,and $N$ is the number of molecules.Since the gas is in a closed container,the volume $V$ and the number of molecules $N$ remain constant as the temperature increases. Therefore,the mean free path $\lambda$ remains unchanged.The mean collision time $	au$ is defined as the ratio of the mean free path to the average speed of the molecules $(v_{av})$:$	au = \frac{\lambda}{v_{av}}$Since the average speed $v_{av}$ of gas molecules is proportional to $\sqrt{T}$,we have:$	au \propto \frac{1}{\sqrt{T}}$As the temperature $T$ increases,the average speed of the molecules increases,which causes the mean collision time $	au$ to decrease.Thus,statements $(B)$ and $(C)$ are correct.

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