Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 49CP
Show that the variation of atmospheric pressure with altitude is given by P = P0e−αy where α = ρ0g/P0, P0 is atmospheric pressure at some reference level y = 0, and ρ0 is the atmospheric density at this level. Assume the decrease in atmospheric pressure over an infinitesimal change in altitude (so that the density is approximately uniform over the infinitesimal change) can be expressed from Equation 14.4 as dP = −pg dy. Also assume the density of air is proportional to the pressure, which, as we will see in Chapter 18, is equivalent to assuming the temperature of the air is the same at all altitudes.
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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?
The rate of change of atmospheric pressure P with respect to altitude h is
proportional to P, provided that temperature is constant. At 15°C the pressure is
101.3 kPa at sea level and 87.14 kPa at h = 1000 m. Answer the following
questions.
a) What is the atmospheric pressure at an altitude of 4000 m? Round to three decimal
places.
b) What is the atmospheric pressure at the top of Mount Greylock in Massachusetts, at
an altitude of 1063 m? Round to three decimal places.
CHECK ANSWER
kPa
NEXT
kPa
Atmospheric pressure follows the following differential equation:
dP/dh = −kP
Where k is a constant that depends on other physical constants such as temperature, the acceleration of gravity, the molecular weight of air, etc.
Suppose that the atmospheric pressure at sea level is 1013mb (millibars) and the atmospheric pressure in Mexico City, which is 2240m above sea level, is 764mb. Estimate the atmospheric pressure in the lagoons of Montebello, Chiapas, which are 1500m above sea level.
Note: Don't skip steps to get to the result
Chapter 14 Solutions
Physics for Scientists and Engineers
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