Explanation Given information: The atmosphere pressure is P 0 and atmospheric density is ρ 0 at some reference level y = 0 . Atmospheric pressure is a pressure exerted by the weight of the atmosphere. It is also called as a barometric pressure. Consider an infinitesimal thickness of air, d y at distance y from the surface of the Earth. The infinitesimal changes in the pressure d P is, d P = − ρ g d y (I) ρ is the density of the air. g is the accele4ration due to gravity. Negative sign shows the pressure decreases with altitude. Formula to calculate the pressure at any point is, P = ρ g h h is the altitude. g is the acceleration due to gravity. To rearrange the above expression is, ρ g h = P ρ = P g h Let 1 g h = k , where k is a constant. ρ = k P (II) Substitute k P for ρ in equation (I). d P = − k P g d y d P P = − k g d y Apply integration in the above equation

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 15, Problem 66P

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Chapter 15, Problem 65P

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The pressure on Earth's atmosphere as a function of height y above sea level can be determined by assuming g to be constant and that the density of air is proportional to the pressure, i.e., px P. Note that this assumption is not very accurate since temperature and other weather effects can influence pressure. [Hint: Po = 1.013 × 105 N/m², po = 1.29 kg x m-³] (1) Start by finding a relation between the pressure Po and the density of air po at 0° at sea level (y=0) and the pressure P and density p at height y. Using this relation find an expression for p as a function of P, i.e., p = p(P). (2) Find the pressure as a function y. (3) At what altitude above sea level is the atmospheric pressure equal to half the pressure at sea level?

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Principles of Physics: A Calculus-Based Text

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The variation of atmospheric pressure with altitude is P = P 0 e − a y .

Solution Summary: The author explains that atmospheric pressure is exerted by the weight of the atmosphere and is also called as a barometric pressure.

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Chapter 15 Solutions