Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 14 - Think and Solve: 44

Answer

We use an equation from page 246, because if air were incompressible and the density didn't vary with altitude, the situation would be like that of water. Find the depth at which the pressure equals $100,000 N/m^{2}$. $$P = (air \;mass \;density) \times g \times h$$ $$ h = \frac{ P}{(air\;mass\; density) \times g}$$ $$= \frac{100,000 N/m^{2}}{(1.2 kg/m^{3})(10 N/kg)} = 8300 m$$ As expected, if the density didn't get smaller with altitude, the atmosphere would not need to be as high to explain the observed pressure at the bottom.
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