Question

If our atmosphere had a uniform density of 1.25 kg/m3 all the way up to a border with empty space above, that border would be Answer km above sea level. The pressure at sea level is 1 atm = 105 N/m2 and g = 10 m/s2. Enter your answer as an integer.

Answer 1

Answer:

The border is 8km above sea level.

Explanation:

We know that:

Density = 1.25 kg/m^3

Pressure = 10^5 N/m^2

g = 10m/s^2

Now, suppose that we have a virtual rectangle, such that its bases have an area of 1m^2 and the rectangle has a height equal to H.

This virtual figure has a volume V = 1m^2*H, and it is filled with air (which we know that has a density 1.25 kg/m^3)

Then the total mass inside that volume is:

M = (1.25 kg/m^3)*V = (1.25 kg/m^3)*(1m^2*H)

The weight of this mass is:

W = g*M = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)

And if we divide the weight in a given surface, let's say 1 m^2, we get the pressure per square meter, which we know is equal to  10^5 N/m^2

then:

P = 10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)

Whit this equation we can find the value of H.

10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)

10^5 N =  (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)

(10^5 N)/(10 m/s^2) = (1.25 kg/m^3)*(1m^2*H)

(10^4 kg) = (1.25 kg/m^3)*(1m^2*H)

(10^4 kg)/( 1.25 kg/m^3) = 1m^2*H

8,000 m^3 = 1m^2*H

(8,000 m^3)/(1m^2) =H

8,000 m = H

And we want this answer in km, knowing that 1,000m = 1km

8,000m = 8km = H

The border is 8km above sea level.