Question:
In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as :
In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as :
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Mean time between collisions \(\tau=\lambda/v_{rms}\) with \(\lambda=\dfrac{kT}{\sqrt2\pi d^2P}\propto T/P\) and \(v_{rms}\propto\sqrt T\); the pressure \(P\) is held fixed.
Updated On: Nov 5, 2026
- \(\sqrt{T}\)
- \(T\)
- \(\dfrac{1}{T}\)
- \(\dfrac{1}{\sqrt{T}}\)
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The Correct Option is A
Solution and Explanation
Mean free path: \(\lambda=\dfrac{kT}{\sqrt2\,\pi d^2P}\), so at fixed \(P\), \(\lambda\propto T\).
Mean (rms) speed: \(v\propto\sqrt T\).
Mean time between collisions: \(\tau=\dfrac{\lambda}{v}\propto\dfrac{T}{\sqrt T}=\sqrt T\).
So \(\tau\) varies as \(\sqrt T\) (at constant \(P\), as stated in the question).
Answer: (1) \(\sqrt{T}\)
Mean (rms) speed: \(v\propto\sqrt T\).
Mean time between collisions: \(\tau=\dfrac{\lambda}{v}\propto\dfrac{T}{\sqrt T}=\sqrt T\).
So \(\tau\) varies as \(\sqrt T\) (at constant \(P\), as stated in the question).
Answer: (1) \(\sqrt{T}\)
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