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 466: 47

Answer

$34.7\;\rm psi$

Work Step by Step

Let's assume that the volume of the tire is constant and that the gas inside it obeys the ideal gas law. Hence, $$\dfrac{P_1 \color{red}{\bf\not} V_1}{T_1}=\dfrac{P_2 \color{red}{\bf\not} V_2}{T_2}$$ Solving for $P_2$; $$P_2=\dfrac{P_1T_2}{T_1}\tag 1$$ Remember that we should use absolute pressure, not gauge pressure. So, the initial pressure is given by $$P_1=P_{\rm gauge}+P_A$$ Plugging the known; $$P_1=30+ 14.7=\bf 44.7\;\rm psi$$ Plugging into (1); $$P_2=\dfrac{(44.7)(45+273)}{(15+273)}=\bf 49.36\;\rm psi$$ Hence, your tires gauge pressure is given by $$P_f=49.36-P_a=49.36-14.7$$ $$P_{f,\rm gauge}=\color{red}{\bf 34.66}\;\rm psi$$
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