Question

at sea level, atmospheric pressure is 100kpa and the density of air is 1.3 kg/m3
assume the density of air decreases linearly with height above sea level.
what is the estimate of the total height of the atmosphere based on this information?
A. 7.8 km B.16 km C. 77 km D. 150 km
ANSWER IS b. But how?
2019 CIE AS & A level October November Physics Paper 12 Q. No. 10 (9702/12/O/N/19)

Answer 1

Explanation:

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Answer 2

Answer:

B

Explanation:

Let’s call altitude the variable a. At the top of the atmosphere a=X meters. At Earth sea level a=0. We want to know the value of X.

At a=X, density D=0 because there’s no air above.

At a=0, D=1.3 kg/m^3.

We are told that D increases linearly over the domain h from X to 0 — for whatever reason. Therefore the average density is 1.3/2 kg/m^3.

The mass of air per meter^2 is D*Δa where Δa is a uniform slice of altitude. Because average D =1.3/2, the average mass per slice =(1.3/2)Δa.

So the total air mass per meter^2 from a=X to 0

= (1.3/2)X kg/m^2

Its pressure = (1.3/2)Xg N/m^2 = 100000 Pa

[ by definition 1 Pa = 1 N/m^2 ]

So X = 100000/(1.3g/2) = 15687 m.