Question

Based on the Earth’s mean surface pressure, calculate the weight of the atmosphere in kg to 1 significant figure. Show your work.

Answer 1

Hey there!

Earth's mean surface pressure is estimated to be 14.7 lb / square inch.

Now our job is to calculate the earth's total surface area. So that the product of the surface area of the earth (in sq. inches) and the the mean surface pressure at one inch would give the total weight in lbs again.

Let's calculate the surface area of earth first. The surface area can be given as . Here the radius of the earth is about 4000 miles(approx.) .

Converting miles to inches ,

4000 miles x 5280 ft / mile x 12 inches / ft = 250 million inches.

Hence the radius if earth (R) in inches is 250 million inches.

Substituting in the surface area formula we get 4  x x (250 million inches)² = 8 x 10¹⁷ sq.inches

Hence by multiplying the total surface area with the average pressure 14.7 lb / sq. inch we get,

1.17 x 10¹⁹ pounds as the weight of the atmosphere.

Converting into kg (1 pound = 0.45 kg)

1.17 x 10¹⁹ x 0.45 = 5.3 x 10²⁰kg

I hope the explanation helps... Feel free to comment and discuss further... Cheers :)