Question

The density of air on the Earth decreases almost linearly with height from 1.22kgm–3 at sea level
to 0.74 kgm–3 at an altitude of 5000m.
Atmospheric pressure at the Earth’s surface on a particular day is 100000Pa. The value of g
between the Earth’s surface and an altitude of 5000 m can be considered to have a constant
value of 9.7ms–2.
What will be the atmospheric pressure at an altitude of 5000m?

Answer 1

The relationship between the density ρ and air pressure p is given as

ρ1ρ2=p1p2
where it is assumed that temperature does not alter with altitude.

∴ If ρs is density of air at sea level and ρ5000 the value of density at an altitude of 5000m, and similarly for air pressure, we have the equation
p5000=ps×ρ5000ρs
Inserting given values we obtain
p5000=105×0.741.22Pa

⇒p5000=60656Pa, rounded to units place.