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 s

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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)

TestHub · Accepted Answer

The average time taken by a moving particle between successive collisions or impacts is referred to as the mean free time $(τ)$ .

The average distance a moving particle travels between successive collisions or impacts is referred to as the mean free path $(λ)$ .

$λ = \frac{k T}{\sqrt{2} π d^{2} P}$

and $v_{rms} = \sqrt{\frac{3 R T}{M}}$

So, the mean free time $τ = \frac{λ}{v_{rms}}$

Therefore, $τ \propto \frac{1}{\sqrt{T}}$

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