In a dilute gas at pressure $P$ and temperature $T$, the mean time between successive collision of a

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In a dilute gas at pressure $P$ and temperature $T$, the mean time between successive collision of a molecule varies with $T$ as\

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(b) : For the gas, mean time between collisions, $	au=\frac{1}{n \pi d^{2}<U_{r}>}$\ where $\left\langle U_{r}ightangle$ is the average relative velocity between two particles and given by\ $\left\langle U_{r}ightangle=\frac{4}{\sqrt{\pi}} \sqrt{\frac{k T}{m}}$\ $	herefore \quad 	au \propto \frac{1}{\sqrt{T}}$\