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Q. 1.18

Expert-verifiedFound in: Page 13

Book edition
1st

Author(s)
Daniel V. Schroeder

Pages
356 pages

ISBN
9780201380279

Calculate the rms speed of a nitrogen molecule at room temperature.

Root mean square speed is 515.9m/s.

Gas is Nitrogen.

Temp = room temp = 25^{o}C= 298 K

The root mean square velocity is calculated as

$v=\sqrt{\frac{3kT}{m}}............................\left(1\right)$

where

T = temperature

k = Boltzmann constant

m = mass

Mass of Nitrogen is calculated as

$m=28\mathrm{u}\phantom{\rule{0ex}{0ex}}=28\times 1.6\times {10}^{-27}\mathrm{kg}\phantom{\rule{0ex}{0ex}}=4.65\times {10}^{-26}\mathrm{kg}$

Boltzmann constant is $=1.38\times {10}^{-23}{\mathrm{m}}^{2}{\mathrm{kgs}}^{-2}{\mathrm{K}}^{-1}$

Substitute the values in equation (1), we get

$v=\sqrt{\frac{3\times (1.38\times {10}^{-23}{m}^{2}kg{s}^{-2}{K}^{-1})\times (298K)}{4.65\times {10}^{-26}kg}}\phantom{\rule{0ex}{0ex}}v=515.9{\mathrm{ms}}^{-1}$

Root mean square speed is 515.9m/s.

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