Answered: The spread of pollutants through the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The spread of pollutants through the atmosphere is governed partly by the effects of winds but also by the natural tendency of molecules to diffuse. The latter depends on how far a molecule can travel before collid ing with another molecule. Calculate the mean free path of diatomic molecules
in air using σ = 0.43 nm² at 25 °c and (a) 10 bar. (b) 103 kPa. (c) 1.0 Pa.

Expert Solution

Step 1

Given Data

Temperature is : $T = 25 ° C = 298 K$
$σ = 0.43 {nm}^{2}$

(a)

Here

$P = 10 bar = 10 \times 10^{5} Pa$

Now the mean free path can be calculated as

$\begin{array}{rcl} λ & = & \frac{R T}{\sqrt{2} N_{A} σ P} \\ = & \frac{8.314 \times 298}{\sqrt{2} \times 6.022 \times 10^{23} \times 0.43 \times 10 \times 10^{5}} \\ = & 67 nm \end{array}$

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