Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 14 - The Ideal Gas Law and Kinetic Theory - Problems - Page 384: 21

Answer

The atmosphere of Venus is 39 times thicker than that of Earth.

Work Step by Step

Here we use equation 14.2 $PV=NkT$ to find the desired ratio for the two planets. $PV=NkT$ The no. of gas molecules per unit = $\frac{N}{V}=\frac{P}{kT}$ We can write, $\frac{(\frac{N}{V})_{Venus}}{(\frac{N}{V})_{Earth}}=\frac{P_{Venus}/kT_{Venus}}{P_{Earth}/kT_{Earth}}=(\frac{P_{Venus}}{P_{Earth}})(\frac{T_{Earth}}{T_{Venus}})$ Let's plug known values into this equation. $\frac{(\frac{N}{V})_{Venus}}{(\frac{N}{V})_{Earth}}=(\frac{9\times10^{6}Pa}{1\times10^{5}Pa})(\frac{320\space K}{740\space K})\approx39$ So, we can conclude that the atmosphere of Venus is 39 times thicker than that of Earth.
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