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

1. √T
2. 1/T
3. 1/√T
4. T

Correct answer: √T

Solution

At constant pressure, number density n = P/(kT) ~ 1/T, so the mean free path lambda ~ 1/n ~ T. Mean speed ~ sqrt(T), hence mean time between collisions tau = lambda/v ~ T/sqrt(T) = sqrt(T).

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