JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Heat & Thermodynamics

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)

(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)
✓ Correct

Answer: (D)

Solution

The mean free time between collisions varies inversely with the average molecular speed, and that speed grows as

T

. Hence

τ \propto \frac{1}{v _{a v g}} \propto \frac{1}{T}

, a

T^{- 1/2}

dependence in which

τ

is large at low temperature and falls off along a decaying curve as the temperature rises.

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option

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