## Estimation and Unit Conversion

The atmosphere pushes down on the surface of the Earth with an average pressure of 14.7 pounds per square inch (psi). Estimate the total weight of the air in the atmosphere. The radius of the Earth is approximately 6000 km.14.7psi indicates that, above every square inch on the Earth’s surface there is enough air to weigh 14.7 pounds.

First we need to convert this to SI units:

14.7psi = 14.7 lb/in^{2} /(2.2 lb/kg * .025 m/in * .025m/in)*9.8N/kg

= 1.0x10^{5}N/m^{2} = 1.0 x 10^{5} Pascals

The total surface area of the Earth is: 4 * pi *(6x10^{6} m)^{2}.

Then the total weight of the air in the atmosphere is 6x10^{19}N.

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