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Chapter 5: Q. 102 (page 285)

Atmospheric Pressure The atmospheric pressure p on a balloon or plane decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the function
$p (h) = 760 e^{- 0.145 h}$
(a) Find the atmospheric pressure at a height of 2 kilometers (over a mile).
(b) What is it at a height of 10 kilometers (over 30,000 feet)?

Short Answer

Expert verified

(a) $568.68 m m$

(b) $178.27 m m$

Step by step solution

01

Step 1.Given inforamation

Let us consider the height above sea level beh.
And the atmospheric pressure above sea level as a function of height be $p (h) = 760 e^{- 0.145 h}$

02

Step 2.

Let us consider height be 2 kilometers
Therefore pressure will be

$p (2) = 760 e^{- 0.145 \times 2} = 760 (7482) = 568.68 m m$

03

Step 3.(b) What is it at a height of 10 kilometers (over 30,000 feet)?

Let us consider height be 10 kilometers
Therefore pressure will be

p (10) = 760 e^{0.145 \times 10} = 760 (0.2345) = 178.27 m m

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