# Finding the mass of the earth's atmosphere

1. Feb 22, 2004

### deltabourne

A barometer having a cross-sectional area of 1.00 cm^2 at sea level measures a pressure of 76.0 cm of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on 1 cm^2 of Earth's surface. Given that the density of mercury is 13.6 g/mL and the average radius of Earth is 6371 km, calculate the total mass of Earth's atmosphere in kilograms (Hint: The surface area of a sphere is 4pir^2)

I have no idea where to start on this one, and how to relate the mercury to find the mass of the atmosphere.. can anyone point me in the right direction?

2. Feb 23, 2004

### Tom Mattson

Staff Emeritus
I don't think you even need the density of mercury. You know the pressure and the area over which the pressure acts. Since P=F/A, you can determine the force that exerts the pressure (which is the weight of the air above the barometer). That gives you the mass of a column of air with a cross section of 1cm2. To get the mass of the entire atmosphere, you need to use the formula for the area of a sphere that was given.