Question 58 of 168

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 $\left(T\right),$ qualitatively, is: (Graphs are schematic and not drawn to scale)

ABCD

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Answer: (C)

The average time taken by a moving particle between successive collisions or impacts is referred to as the mean free time $\left(\tau \right)$.
The average distance a moving particle travels between successive collisions or impacts is referred to as the mean free path $\left(\lambda \right)$.
$\lambda =\dfrac{kT}{\sqrt{2}\pi {d}^{2}P}$
and ${v}_{rms}=\sqrt{\dfrac{3RT}{M}}$
So, the mean free time $\tau =\dfrac{\lambda }{{v}_{rms}}$
Therefore, $\tau \propto \dfrac{1}{\sqrt{T}}$