Question

a) Determine the variation of Earth's atmosphere in function of altitude (y), above the sea level, assuming a constant geavity (g) and that the density of the air is proportional to the pressure.

b) At what altitude the pressure of the air is the same as halve the pressure at sea level?

c) Graph pressure against altitude.

Answer 1

The pressure and density of air in the atmosphere varies exponentially with respect to the altitude.

Where, y is the altitude and H is the scale height. The scale height is the measure of length over which the pressure or density decreases to 1/e th of its original value.

Similarly density can also be written as

Here, are the density and pressure at the surface level.

Scale height is generally 10 km.

with that in mind,

exp(-y/10) = 1/2

y=10*0.693 = 6.9 km

so at 6.9 km, the pressure and density would be half the values at the ground.