- #1

Any Help

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## Homework Statement

:[/B]

The density of the Earth's atmosphere varies with altitude, and can be approximated by an exponential: ρ(h)=ρ0e^(-h/h0) where ρ0 = 1.3 kg/m3 (the approximate density at sea level) and

*h*0 = 8.2 km (this is determined empirically). Calculate the mass of 15 km of the atmosphere above a 1m2 area at sea level.

## Homework Equations

Mass= density. volume volume= area . hight

## The Attempt at a Solution

I tried to solve it in two different ways but both gives me incorrect answer

**, The correct answer is 8900kg**

My First attempt: I substitute the height in the equation then i got p(h)=1.3xe^(-15/8.2) p(h)=0.19936 kg/m^3

My First attempt

Mass= p(h) x volume =0.19936x area x height = 0.19936x1x15x10^3=

**2990.4kg**but the answer is not correct?!

**My second attempt:**I expand the equation to get mass=V.p(h)=h.A.p0.e^(-h/h0) then integrate it to get mass= [h^2/2 . A.p0.e^(-h/h0)+ h.p0/h0 .e^(-h/h0)] from h=0 to h=15000

mass=

**23478038kg**also not correct!