- #1

blintaro

- 37

- 1

## Homework Statement

"It's possible to use the ideal gas law to show that the density of the Earth's atmosphere decreases exponentially with height, that is

ρ=ρ

_{0}exp(-z/z

_{0})

where z is the height above sea level, ρ

_{0}is the density at sea level and z

_{0}is called the "scale height" of the atmosphere.

a.) Determine value of z

_{0}:

b.) What is the density of the air in Denver, at an elevation 1600 m? What percent of sea-level density is this?

## Homework Equations

Ideal gas law: Pv=nRT

possibly P=P

_{0}+ ρgh ? Seems unlikely as ρ varies?

## The Attempt at a Solution

Not quite sure how to go about this one. Started with ideal gas law

Pv=nRT

assumed we'd be comparing two volumes of gas (at height z

_{0}and z) with equal number of molecules, at equal temperature, thus

P

_{1}v

_{1}=P

_{2}v

_{2}

Then substituted v=ρ(mass)

Again assuming equal mass would imply

P

_{1}ρ

_{1}=P

_{2}ρ

_{2}

Not really sure how to proceed to involve height instead of pressure or even if on right track... Somehow the latter seems more likely. Help would be appreciated!