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Q.

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.

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a

(A) and (B)

b

(C) and (D)

c

(B) and (C)

d

(A) and (D)

answer is D.

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Detailed 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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