If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ} \mathrm{C}$ is Z , then the collision frequency of the same system at $127^{\circ} \mathrm{C}$ is :

(C) $\frac{2}{\sqrt{3}} \mathrm{Z}$

(A) $\frac{\sqrt{3}}{2} \mathrm{Z}$

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Heat & Thermodynamics

If the collision frequency of hydrogen molecules in a closed chamber at

2 7^{\circ} C

is Z , then the collision frequency of the same system at

12 7^{\circ} C

is :

(A) $\frac{3}{2} Z$
(B) $\frac{4}{3} Z$
(C) $\frac{2}{3} Z$ ✓ Correct
(D) $\frac{3}{4} Z$

Answer: (C)

Solution

Taking the mean free path fixed, the collision frequency is proportional to the mean speed, so

Z \propto v_{r m s} \propto T

(with

T

in kelvin).

\frac{Z _{2}}{Z _{1}} = \frac{T _{2}}{T _{1}} = \frac{400}{300} = \frac{4}{3} = \frac{2}{3} .

Hence

Z_{2} = \frac{2}{3} Z

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Single correct option

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