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: 5

Answer

See the figure below.

Work Step by Step

The given figure shows that the pressure is constant while the volume is expanding, so it is an expansion-isobaric process. In this process, $$\dfrac{ \color{red}{\bf\not} P_1V_1}{T_1}=\dfrac{ \color{red}{\bf\not} P_2V_2}{T_2} $$ Thus, $$\dfrac{V_2}{V_1}=\dfrac{T_2}{T_1}$$ and since the $V_2\gt V_1$, so $$\dfrac{V_2}{V_1}=\dfrac{T_2}{T_1}\gt 0$$ Hence, $$ \dfrac{T_2}{T_1}\gt 0$$ $$\boxed{T_2\gt T_1}$$ This means that the system gains some energy from the surroundings since its final temperature is greater than the initial one. $$\boxed{Q\gt 0}$$ Also, $V_2\gt V_1$, so the work is negative. $$\boxed{W\lt 0}$$
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