Mass of Air above an area up to 470m

[Bob Ho]

Homework Statement

Determine the mass of air above a certain area on a typical winter day between ground level and 470m.

Homework Equations

The Attempt at a Solution

I found the total area which I need to find the mass of air for, which gave me 2.05x10^9m^2

I times that by the height of 470m, which gave me the volume, 9.66x10^11m^3

Now I think I need to find the density of air as a function of altitude, I am unsure on how to find the average density, do i need to find an equation and integrate? any help would be appreciated thanks.

 

[mgb_phys]

I would calculate the pressure at ground level, and the pressure at 470m and subtract them to get the pressure acting in the bottom 470m then multiply this by area.

You could assume that air pressure decreased exponentially with altitude (since there is less mass of air above) upto a value of (almost) zero pressure at some altitude at the top of the troposphere.

A good approximation for larger altitudes is: p = p_0 e - (h/h_0)
Where p_0 is pressure at 0 altitude
h is the altitude and h_0 is the scale height = the height at which the pressure has dropped to 1/e (approx 7km for earth)

Edit - for only 470m I would assume the density is the same and simply work out the mass of a column of air 470m high