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  4. The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

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Q. The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

JEE MainJEE Main 2020Kinetic Theory

Solution:

$Mean\, free\, time = \frac{Mean\, free\, path}{Average\, speed}$
$=\frac{\frac{1}{\sqrt{2}\pi D^{2}n}}{\sqrt{\frac{8RT}{\pi M_{w}}}}$
$t\,\propto \frac{1}{\sqrt{T}}$