Question

Estimate the total mass of the Earth’s atmosphere. (The radius of the Earth is 6.37 3 106 m, and atmospheric pressure at the surface is 1.013 3 105 Pa.)

Answer 1

Answer:

m = 5.27e18 kg

Explanation:

The pressure of a fluid is the weigth of a column of that fluid over base of that column.

$P = \frac{weight}{base}$

The weight of the column is its mass multiplied by the acceleration of gravity. The acceleration of gravity varies with height, however the variation is small and can be ignored, consifering the acceleration of gravity constant.

$weight = m * g$

So:

$P = \frac{m * g}{base}$

If we consider the entirety of the atmosphere as a single column the base would be the surface of Earth. Approximating Earth as a sphere:

$S = 4 * \pi * r^2$

Now, we can obtain the mass of the atmosphere:

$m = \frac{4 * P * \pi * r^2}{g}$

$m = \frac{4 * 1 01325* \pi * 6373106^2}{9.81} = 5.27e18 kg$