Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 13 - Temperature and Kinetic Theory - General Problems - Page 388: 83

Answer

2300 m.

Work Step by Step

The original length of the steel band is $L=2 \pi R_{earth}$. After the band is heated, the new length is $L+\Delta L=2 \pi R=2 \pi (R_{Earth}+\Delta R)$. The change in radius is the height of the heated band above the surface of the Earth. $$\Delta L=\alpha L\Delta T=2 \pi \Delta R$$ $$\Delta R = \frac{\alpha L\Delta T }{2 \pi }=\alpha R_{Earth}\Delta T$$ $$\Delta R =(12\times10^{-6}/C^{\circ}) (6.38\times10^6 m) (30C^{\circ})\approx 2300 m$$
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