Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 17 - Work, Heat, and the First Law of Thermodynamics - Exercises and Problems - Page 498: 43

Answer

$653\;\rm J/kg\cdot K$

Work Step by Step

The oxygen’s specific heat at constant volume is $c_{\rm V}$ which is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius while keeping the volume constant. We know that oxygen’s specific heat at constant volume, from Table 17.4, is given by $$c_{\rm V}=20.9\;\rm J/mol \cdot K$$ and we need to find it in $\rm J/kg \cdot K$ where we know that the atomic mass of the oxygen atom is 16 g/mol, so the oxygen gas of two oxygen atoms is 32 g/mol which is 0.032 kg/mol. Multiplying the equation above by the reciprocal of 0.032 kg/mol. $$c_{\rm V}=\rm\dfrac{20.9\;\rm J}{1\;mol \cdot K}\left[\dfrac{1\;mol}{0.032\;kg}\right]$$ $$c_{\rm V}=\color{red}{\bf 653}\;\rm J/kg\cdot K$$
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