First slide

Mean free path

Question

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.

Moderate

A

(C) and (D)
B

(A) and (B)
C

(A) and (D)
D

(B) and (C)

Solution

Mean free path $λ = \frac{1}{\sqrt{2} π d^{2} (\frac{N}{V})}$
For closed container V = constant So $λ = constant$
Mean collision time $= \frac{λ}{V}$ as $V \propto \sqrt{T}$
So when $T i n c r e a s e s \Rightarrow V i n c r e a s e s \Rightarrow t i m e d e c r e a s e s$

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