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 497: 6

Answer

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Work Step by Step

The given figure shows that the volume is constant while the pressure is decreasing, so it is an isochoric process. In this process, the work done is zero since the volume is constant. $$\boxed{W=0}$$ We know, for an ideal gas, that $$\dfrac{P_1 \color{red}{\bf\not} V_1}{T_1}=\dfrac{P_2 \color{red}{\bf\not} V_2}{T_2}$$ Hence, $$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}$$ and we can see, in the given graph, that $P_1\gt P_2$, so $$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}\gt 1$$ Hence, $$ T_1\gt T_2 $$ $$\boxed{\Delta T\lt 0}$$ This means that the temperature decreases during this process which means that the system loses some heat. Thus, $$\boxed{Q\lt 0}$$ See the bar-charts graph of this process below.
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