The air density at the top of Mount Everest ( hErerest = 8850 m ) is 35.00 % of the air density

Name: Problem 35, Chapter 13: University Physics with Modern Physics
Uploaded: 2021-06-27T20:36:46-08:00
Duration: 3 min 32 s
Channel: Averell Hause
Description: The air density at the top of Mount Everest ( hErerest = 8850 m ) is 35.00 % of the air density at sea level. If the air pressure at the top of Mount McKinley in Alaska is 47.74 % of the air pressure at sea level, calculate the height of Mount McKinley, using only the information given here.

step 1 So here we can say that the density of air at the top of Everest would be equaling to 35 % or 0

Question

The air density at the top of Mount Everest ( $h_{\text {Ererest }}=$ $8850 \mathrm{~m}$ ) is $35.00 \%$ of the air density at sea level. If the air pressure at the top of Mount McKinley in Alaska is $47.74 \%$ of the air pressure at sea level, calculate the height of Mount McKinley, using only the information given here.

   The air density at the top of Mount Everest ( $h_{\text {Ererest }}=$ $8850 \mathrm{~m}$ ) is $35.00 \%$ of the air density at sea level. If the air pressure at the top of Mount McKinley in Alaska is $47.74 \%$ of the air pressure at sea level, calculate the height of Mount McKinley, using only the information given here.

University Physics with Modern Physics

Wolfgang Bauer, Gary… 1st Edition

Chapter 13, Problem 35

Instant Answer

Solved by Expert Averell Hause

06/27/2021

Step 1

00 \%$ of the air density at sea level. We can express this as: \[ \rho_{\text{Everest}} = 0.35 \cdot \rho_{\text{sea level}} \] where $\rho_{\text{Everest}}$ is the air density at the top of Mount Everest and $\rho_{\text{sea level}}$ is the air density at sea Show more…

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The air density at the top of Mount Everest ( $h_{\text {Ererest }}=$ $8850 \mathrm{~m}$ ) is $35.00 \%$ of the air density at sea level. If the air pressure at the top of Mount McKinley in Alaska is $47.74 \%$ of the air pressure at sea level, calculate the height of Mount McKinley, using only the information given here.

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Key Concepts

Hydrostatic Equilibrium

Hydrostatic equilibrium refers to the balance between the gravitational force pulling air molecules downward and the pressure gradient force pushing them upward. This principle underlies the derivation of the barometric formula and explains the continuous decrease in pressure and density with increasing altitude.

Barometric Formula

The barometric formula describes how atmospheric pressure (and, under isothermal conditions, density) decreases exponentially with altitude. It is derived from the condition of hydrostatic equilibrium and is fundamental for calculating variations in atmospheric parameters with height.

Scale Height

Scale height is a key parameter in the exponential decay model of the atmosphere. It represents the altitude interval over which the atmospheric pressure or density decreases by a factor of e (approximately 2.718). It is essential for relating relative changes in pressure or density to differences in altitude.

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