Question

Estimate the total mass of the Earth’s atmosphere, using the known value of atmospheric pressure at sea level.

Short answer

The total mass of the Earth’s atmosphere is \(5.28 \times {10^{18}}\;{\rm{kg}}\).

Step-by-step solution

Understanding the air pressure

The weight of the atmosphere produces air pressure with an area equivalent to the surface area of the Earth. Use the pressure force relation to find the total mass.

Calculating the total mass

The relation of air pressure is given by,

\(\begin{array}{c}P = \frac{F}{A}\\P = \frac{{mg}}{A}\\m = \left( {\frac{{P \times A}}{g}} \right)\\m = \left( {\frac{{P \times 4\pi {r^{^2}}}}{g}} \right)\end{array}\)

Here, \(A\) is the area, \(F\) is the weight of the atmosphere, \(P\) is the atmospheric pressure, \(m\) is the total mass, \(r\) is the radius of the Earth and \(g\) is the gravitational acceleration.

On plugging the values in the above relation,

Thus, the total mass of the Earth’s atmosphere is \(5.28 \times {10^{18}}\;{\rm{kg}}\).