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 16 - A Macroscopic Description of Matter - Exercises and Problems - Page 464: 28

Answer

a) $\rm 98\;cm^3$ b) See the graph below.

Work Step by Step

a) Since the gas undergoes an isobaric process, its pressure remains constant. And we know, for an ideal gas, that $$\dfrac{ \color{red}{\bf\not} P_1V_1}{T_1}=\dfrac{ \color{red}{\bf\not} P_2V_2}{T_2}$$ in our case, the pressure is constant. $$\dfrac{ V_1}{T_1}=\dfrac{ V_2}{T_2}$$ We need to find the final volume of the gas, so we need to solve for $V_2$ $$V_2=\dfrac{ V_1T_2}{T_1}\tag 1$$ Plugging the known; $$V_2=\dfrac{ (50\times 10^{-6})(300+273)}{(20+273)} =97.78\times 10^{-6}\;\rm m^3$$ $$V_1\approx \color{red}{\bf 98}\;\rm cm^3$$ --- b) To draw a proper scale graph, we need to find the magnitude of the initial pressure (the constant pressure) which is given by $$P_1V_1=nRT_1$$ Hence, $$P_1=\dfrac{nRT_1}{V_1}$$ Plugging the known; $$P=\dfrac{(0.1)(8.31)(20+273)}{(50\times 10^{-6})}=\bf 4.87\times 10^6\;\rm Pa$$ See the figure below.
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