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 499: 58

Answer

a) $-1013\;\rm J$ b) $1417 \;\rm J$

Work Step by Step

We can see that process A is an isochoric process. Thus, $$Q_A=nC_{\rm v}(T_f-T_i)\tag 1$$ So we need to find $T_i$ and $T_f$ of this process. We assume that nitrogen gas is an ideal gas, so $$P_iV_i=nRT_i$$ Hence, $$T_i=\dfrac{P_iV_i}{nR}$$ Plugging the known; (see the given graph) $$T_i=\dfrac{(3\times 1.013\times 10^5)(2000\times 10^{-6})}{(0.1)(8.31)}=\bf 731\;\rm K$$ By the same approach; $$T_f=\dfrac{P_fV_f}{nR}$$ Plugging the known; (see the given graph) $$T_f=\dfrac{(1\times 1.013\times 10^5)(2000\times 10^{-6})}{(0.1)(8.31)}=\bf 244\;\rm K$$ Plugging these two temperatures into (1); $$Q_A=(0.1)(20.8)(244-731) =\color{red}{\bf -1013}\;\rm J$$ --- We can see that process B is an isobaric process. Thus, $$Q_B=nC_{\rm p}(T_f-T_i)\tag 2$$ So we need to find $T_i$ and $T_f$ of this process. $$T_i=\dfrac{P_iV_i}{nR}$$ Plugging the known; (see the given graph) $$T_i=\dfrac{(2\times 1.013\times 10^5)(1000\times 10^{-6})}{(0.1)(8.31)}=\bf 244\;\rm K$$ By the same approach; $$T_f=\dfrac{P_fV_f}{nR}$$ Plugging the known; (see the given graph) $$T_f=\dfrac{(2\times 1.013\times 10^5)(3000\times 10^{-6})}{(0.1)(8.31)}=\bf 731\;\rm K$$ Plugging these two temperatures into (2); $$Q_B=(0.1)(29.1)(731-244) =\color{red}{\bf 1417}\;\rm J$$
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