InterviewSolution
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InterviewSolution
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By now much will the mean free path of a gas molecule in a vessel at constant `T` change if the pressure is reduced by `10%`?A. `10%` increaseB. `10%` decreaseC. `11.1%` increaseD. `11.1%` decrease |
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Answer» `lambda prop (T)/(P)` `lambda(mean free path)=(overline (c ))/(sqrt(2)pi sigma^(2)overline(c )N)=(1)/(sqrt(2) pi sigma^(2)N^(*))` ` :. Lambda prop (1)/(sigma^(2))` (`sigma=` molecular diameter, `overline(c )=` average velocity) `lambda=(KT)/(sqrt(2)pi sigma^(2)P)(K= Boltzmann constant =(R)/(N)=1.38xx10^(-23)JK^(-1)mol^(-1))` `lambda prop (1)/(P)` (at constant `T`) `lambda prop T` (at constant `P`) `lambda_(1)P_(1)=lambda_(2)P_(2), (lambda_(1))/(T_(1))=(lambda_(2))/(T_(2))` `:. lambda_(1)P_(1)=lambda_(2)xx0.9 P_(1)` ` implies lambda_(1)=0.9lambda_(2) implies lambda_(2)=1.11 lambda_(1)` `:. lambda_(2)=111.1 %` Increases in `lambda_(2)=111.1-100=11.1%` This shows `lambda` will increase by `1//9`, if `P` is reduced by `10%`. |
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