Question

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

Answer 1

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