Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 14, Problem 87CP
To determine
To show: The variation of atmospheric pressure with altitude is
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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
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kPa
The density of air is 1.3 kg/m at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of
uniform density up to some height, after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.) t
O 1 km
O 10 km
O 100 km
O 1000 km
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Chapter 14 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 14.1 - Suppose you are standing directly behind someone...Ch. 14.2 - The pressure at the bottom of a filled glass of...Ch. 14.3 - Several common barometers are built, with a...Ch. 14.4 - You are shipwrecked and floating in the middle of...Ch. 14.6 - You observe two helium balloons floating next to...Ch. 14 - Prob. 1OQCh. 14 - Prob. 2OQCh. 14 - Prob. 3OQCh. 14 - Prob. 4OQCh. 14 - Prob. 5OQ
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- How many cubic meters of helium are required to lift a light balloon with a 400-kg payload to a height of 8 000 m? Take Hc = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression pair = 0e-z/8 000, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forwardA horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipes?arrow_forwardA manometer containing water with one end connected to a container of gas has a column height difference of 0.60 m (Fig. P15.72). If the atmospheric pressure on the right column is 1.01 105 Pa, find the absolute pressure of the gas in the container. The density of water is 1.0 103 kg/m3. FIGURE P15.72arrow_forward
- Why is the Earths atmosphere denser near sea level than it is at a high altitude? Be sure to explain why the atmospheres density is not uniform and why the air isnt all in contact with the Earths surface.arrow_forward(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?arrow_forwardThe weight of Earths atmosphere exerts an average pressure of 1.01 105 Pa on the ground at sea level. Use the definition of pressure to estimate the Height of Earths atmosphere by approximating Earth as a sphere of radius RE = 6.38 106 m and surface area A = 4RE2.arrow_forward
- A hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?arrow_forwardThe temperature of the atmosphere is not always constant and can increase or decrease with height. In a neutral atmosphere, where there is not a significant amount of vertical mixing, the temperature decreases at a rate of approximately 6.5 K per km. The magnitude of the decrease in temperature as height increases is known as the lapse rate (Γ). (The symbol is the upper case Greek letter gamma.) Assume that the surface pressure is p0 = 1.013 × 105 Pa where T = 293 K and the lapse rate is (−Γ = 6.5 K/km). Estimate the pressure 3.0 km above the surface of Earth.arrow_forwardVariation of Pressure in the atmosphere. The pressure of the atmosphere decreases as we move higher in the atmosphere. The decrease in pressure is proportional to the decrease in density of air. р = 2|2° P P Where P = pressure at any point in the atmosphere, and p = density of air at any point in the atmosphere Po pressure at sea level = 1.013 x 105 Pa, and Po air density at sea level = 1.3 kg/m³. a) What is the density p in terms of po, P, and Po? b) Start from the formula dP = - p g dy to determine the pressure at any height y. Note: P is variable c) What is the pressure if the height is 5.0 km above sea level? d) At what height above sea level is the pressure equal to ½ Po ?arrow_forward
- The volume of an air bubble increases by a factor of 3.19 times as it rises from the bottom of a lake (density = 1000 kg/m 3). This is due to the drop of the absolute pressure by a factor of 1/3.19. Ignoring any temperature changes, What is the depth of the lake? Take g = 9.8 m/s2. One atmospheric pressure = 1.013 x 105 N/m2. Please round your answer to one decimal place. Equation: ??ℎ+??=ρgh+Pa= 3.19 ??arrow_forwardWhat would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.00 atm and the air density is 1.28 kg/m^3.arrow_forwardThe density of air is 1.3 kg/m3 at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height, after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.)arrow_forward
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