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JEE Main 2020 (2 Sep, Shift 2) · Mean Free Path & Real Gases

Mean Free Path & Real Gases question from JEE Main 2020 (2 Sep, Shift 2)

Q19JEE Main 2020 · 2 SEP · SHIFT 2Medium

Mean Free Path & Real Gases

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?

(A) the mean free path of the molecules decreases.

(B) the mean collision time between the molecules decreases.

(C) the mean free path remains unchanged.

(D) the mean collision time remains unchanged.

Show answer and solution

Answer: (c)

Closed container: number density $n$ is fixed, so $\lambda = \dfrac{1}{\sqrt{2}\,n\pi d^2}$ remains unchanged; (C) true, (A) false.
Mean collision time $\tau = \dfrac{\lambda}{\bar v}$ ; $\bar v$ increases with $T$ , so $\tau$ decreases; (B) true, (D) false.
So the answer is (c) (B) and (C).

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