- #1
anomalocaris
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Homework Statement
The atmospheric pressure deceases exponentially with height. At 5.5 km, the pressure is half that at sea level. At what height is the pressure one eighth that of sea level?
Homework Equations
All I can think of is Pat=ρgh
I know 1 atm=101325 Pa=101.325 kPa and that this is the atmospheric pressure at sea level.
The Attempt at a Solution
[itex]\frac{101325 Pa}{2}[/itex]=ρ(9.8 m/s2)(5.5 km)
50662.5 Pa=ρ(9.8 m/s2)(5500 m)
50662.5 Pa=ρ(53900 m2s-1)
ρ=0.93993 kg/m3
I thought that in solving for density, I could change the equation to make
[itex]\frac{101325 Pa}{8}[/itex]=(0.93993 kg/m3)(9.8 m/s2)h
and then solve for h.
h=(12665.625 Pa)/((0.93993 kg/m3)(9.8 m/s2))
h=1380 m=1.38 km
This was my homework and for the life of me I do not know how I got this right, because the answer I found above is "incorrect." The correct answer should be 16.5 km. Does anyone have any ideas as to where I am going wrong? I'm wondering if I used the wrong formula? I do not think I understand the concept so well.
Thank you!