How Much Does Earth's Atmosphere Weigh?

[chem1guy]

Homework Statement

above each square ince of the Earth's surface is 14.7 pounds of air. the density of air at sea level is 1.27g/l. the Earth is 7930 miles in diameter and has a mass of 5.98x10^24kg.

use this data to determine the mass in kg of the Earth's atmosphere

determine the average density in g/mm

Homework Equations

4pieR2

The Attempt at a Solution

14.7 lb air/in2 x 1kg/2.205lb x (39.37in/1m)2=1.03x10'4/m2 air above surface
then
A=4pieR2=1.97x10'8mi2 x (1km/.6214)=5.11x10'14m2

then multiply the answers for 1.534x1017kg

is that close for the "a" part?

thanks

 

[D H]

is that close for the a part?

No.

Which are your symbols, and what is all this addition stuff?

Note: the "pounds" per square inch is a unit of force, not mass.

 

[chem1guy]

sorry typed it wrong. i reposted my work. i don't know where else to go

 

[D H]

I'll be a bit more explicit in where you went wrong.

The Attempt at a Solution

14.7 lb air/in2 x 1kg/2.205lb x (39.37in/1m)2=1.03x10'4/m2 air above surface

The "pounds" in "pounds per square inch" is a unit of force, not mass. Your mistake results from assuming it is a unit of mass.

 

[chem1guy]

ok thanks. i'll try to look up the difference b/c we have not covered this distinction in class

 

[chem1guy]

14.7psi x 702771g/m2 x 1kg/1000g= 10331kg/m2 of air above surface
A=4pieR2=1.97x10'8mi2 x (1km/.6214)=5.11x10'14m2 surface area

5.29x10'18 mass of atmosphere!?

 

[D H]

Looks good, but where did you come up with 702771g/m2?

 

[chem1guy]

I looked it up the conversion. I thought it might be in the problem but I can'tseem to find it working backwards

 

[chem1guy]

Volume of a sphere?? Does it have to do with density