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

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 $4200000000000000000 \setminus {\text{m}}^{3}$, you can compute mass as $4.31 \times {10}^{21} \setminus \text{kg}$. Since the sphere has a volume of $V = \frac{4 \cdot \pi \cdot {r}^{3}}{3}$ (r stands for radius), you can compute the radius (and diameter of this sphere) now:

$4200000000000000000 \cdot 3 = 4 \cdot \pi \cdot {r}^{3}$ or
${r}^{3} = 1 x {10}^{18} \setminus \text{m}$ or ${r}^{3} = 1 \times {10}^{15} \setminus \text{km}$ or $r = 1000877 \setminus \text{m}$ or $r = 1000.88 \setminus \text{km}$

Diameter $D = 2001.75 \setminus \text{km}$

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