JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Heat & Thermodynamics

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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:

(A)T
(B) $\frac{1}{T}$ ✓ Correct
(C) $\frac{1}{T}$
(D) $T$

Answer: (B)

Solution

The mean time between collisions is

τ = \frac{λ}{v _{a v g}}

, where

λ

is the mean free path and

v_{a v g}

the average molecular speed. The mean free path is set by the size and number density of the molecules and carries no factor of

T

of its own here, while the average speed grows as

v_{a v g} = \frac{8 R T}{π m} \propto T

. Dividing a constant by something that rises as

T

leaves

τ \propto \frac{1}{T}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option

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