If Earth's atmosphere were frozen into a solid sphere, what would be its diameter?

1 Answer
G_Ozdilek · NickTheTurtle
Apr 10, 2017

If you assume atmosphere is consisted on only nitrogen (solid), the radius of the sphere would be 49.3 km.

Explanation:

Solid nitrogen (at minus 210 degrees Celcius, you can reach) has a density of #10265 ("kg")/"m"^3#. Since the total volume of the atmosphere is #4200000000000000000\ "m"^3#, you can compute mass as #4.31xx10^21\ "kg"#. Since the sphere has a volume of #V=(4*pi*r^3)/3# (r stands for radius), you can compute the radius (and diameter of this sphere) now:

#4200000000000000000*3=4*pi*r^3# or
#r^3=1x10^18\ "m"# or #r^3=1xx10^15\ "km"# or #r=1000877\ "m"# or #r=1000.88\ "km"#

Diameter #D=2001.75\ "km"#

The following internet site might be helpful to visualize:

www.quora.com/What-is-the-volume-of-air-in-Earth%E2%80%99s-atmosphere-and-volume-of-water-on-Earth

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