If the mean free path is doubled,the pressure | vedclass

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Question

(B) The formula for the mean free path $\lambda$ of gas molecules is given by $\lambda = \frac{1}{\sqrt{2}} \frac{kT}{\pi d^2 P}$.From this expression

Vedclass · Accepted Answer

$P/2$

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(B) The formula for the mean free path $\lambda$ of gas molecules is given by $\lambda = \frac{1}{\sqrt{2}} \frac{kT}{\pi d^2 P}$.From this expression,it is clear that the mean free path $\lambda$ is inversely proportional to the pressure $P$,i.e.,$\lambda \propto \frac{1}{P}$.If the mean free path is doubled $(\lambda' = 2\lambda)$,then the new pressure $P'$ must satisfy $\lambda' \propto \frac{1}{P'}$.Since $2\lambda \propto \frac{1}{P'}$,we have $P' = \frac{P}{2}$.Therefore,the pressure becomes $P/2$.

If the mean free path is doubled,the pressure becomes:

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