   Chapter 9, Problem 2CQ

Chapter
Section
Textbook Problem

The 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.) (This question is courtesy or Edward F. Redish. For more questions of this type, see http://www.physics.umd.edu/perg/.)

To determine
The estimation of the height of the atmosphere.

Explanation

The pressure at any altitude in the atmosphere is calculated from given relation as P=P0+ρgh , where P0 is pressure at the sea level.

For our estimation of the atmospheric height, consider the pressure at sea level is P0=105Pa , and the pressure at extreme height is P=0Pa .

Formula for the height of the atmosphere is,

h=PP0ρg

• P0   is the pressure at the sea level
• P is pressure at any altitude
• h is the height of the atmosphere
• ρ is the acceleration due to gravity
• g is the acceleration due to gravity

Substitute 105Pa for P , 0Pa for P0 , 1

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