Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 20 - The Micro/Macro Connection - Exercises and Problems - Page 567: 16

Answer

$2.5\times10^{-3}\,K$

Work Step by Step

Recall: Rms speed $v_{rms}=\sqrt {\frac{3k_{B}T}{m}}$ where $m$ is the mass of molecules, $T$ is the temperature and $k_{B}=1.38\times10^{-23}\,J/K$ is the Boltzmann's constant. For nitrogen molecule, $m=28\,u=28(1.66\times10^{-27}\,kg)=4.65\times10^{-26}\,kg$ Given that $v_{rms}=1.5\,m/s$. $\implies T=\frac{mv_{rms}^{2}}{3k_{B}}=\frac{(4.65\times10^{-26}\,kg)(1.5\,m/s)^{2}}{3(1.38\times10^{-23}\,J/K)}$ $=2.5\times10^{-3}\,K$
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