the pressure felt from the earth\'s atmosphere is due to the weight of a column

Question

the pressure felt from the earth's atmosphere is due to the weight of a column of air over an area. The weight of the atmosphere is approximately 15 pounds on each square inch of the earth's surface. the average density of the air at the earth surface is is about a1.275 kg/m(^3).(a) if the earth's atmosphere were a uniform density (it not!--the density decreases with increasing altitude), how thick would the atmosphere be? (b) what would be the total mass of the atmosphere? (btw the answers i am supposed to get are 8.29 km for thickness and 5.4x10^(18) kg for the total mass)

please explain the concepts that i must understand and be detailed please thank

Explanation / Answer

First convert 15psi to newtons per square meter (Pascals) ( 15 lb/in^2 ) ( 1/2.2 kg/lb ) ( 39.37 in/m )^2 ( 9.8 m/sec^2 ) = 103500 Pa The height h of the uniform density column would be: 103500 Pa = (1.275 kg/m^3) (9.8 m/sec^2) h so h = 8283 meters = 8.28 km Total mass, assuming radius of earth is 6378km: Vol = (4/3) Pi ((6378+8.28)^3 - 6378^3) = 4.24 10^9 km^3 Mass = (4.24 10^9 km^3) (1000 m/km)^3 (1.275 kg/m^3) = 5.4 10^18 kg

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