Approximating Earth's atmosphere as a layer of gas 6.8 km thick, with uniform density 1.3 kg/m3 , calculate the total mass of the atmosphere.

The total mass of the atmosphere is  4.508 x 10⁹ kg

Explanation:

Given;

thickness of gas layer, h = 6.8 km

density of Earth's atmosphere, ρ = 1.3 kg/m³

the surface area of Earth is given as 5.10 x 10⁸ km²

Volume of the atmosphere is calculated as;

V = Ah

where;

A is the surface area of Earth

h is the thickness of gas layer

V = (5.10 x 10⁸ km²)(6.8 km)

V = 3.468 x 10⁹ km³

The total mass of the atmosphere is calculated as;

mass = density x volume

m = ρV

m = (1.3 kg/m³)(3.468 x 10⁹ km³)

m = 4.508 x 10⁹ kg

Therefore, the total mass of the atmosphere is 4.508 x 10⁹ kg.