The mass of the atmosphere is 10^19 kg. assuming the density of the atmosphere is 1 kg/m^3, estimate the height of earth’s atmosphere. do you think your answer is an underestimate or an overestimate? explain why

To solve this problem we will use the concept given on the calculation of volume in a sphere (for which we will apply the approximation of the earth) as well as the relationship between density, mass and volume, like this:

Mass of atmosphere

Density of Atmosphere

Now the Volume would be,

The volume geometrically can be expressed as

Atmosphere is spread all over earth therefore the sphere surface area (of earth)

Diameter of the earth

Now calculating the height:

This value is estimated since the approximation of a sphere to the earth was made, and this, as we well know, does not comply with that approximation in detail.

We must add that the atmosphere decreases with the height so the value of 31 km is given for the first layer of the atmosphere.

the answer is to check all of them! they all apply well at least i think so!