Calc Adventure Time - The Ice Crown freezes the Earth

1:37
http://adventuretime.wikia.com/wiki/Finn_the_Human_(episode)/Transcript

Finn the Human said:

Farmworld Marceline: And the horrible crown, grieving its lost master, loosed a spasm of magic so wild and crazy the entire earth was buried in ice for four hundred boring years.

Click to expand...

The power of the ice crown freezes the Earth for 400 years in an alternate timeline. First off, let's freeze the oceans, which weigh 1,450,000,000,000,000,000 tons (1,450,000,000,000,000,000,000,000g). Specific heat of water is 4.186 joules/g. The average heat of the oceans is 17 C.

E = 1,450,000,000,000,000,000,000,000 X 4.186 X 17
= 1.031849e26 joules

Diameter of the Earth is 12756.2km.
375 pixels = 12756.2km
1 pixel = 12756.2km/375 = 34.0165333km
34.0165333km X 36 = 1224.5952km
1224.5952km + 6378.1km = 7602.6952km (7602695.2m)

Volume as a sphere (obviously).

V = 4/3πr^3
= 4/3 X π 7602695.2^3
= 1.84073533e21m^3

V = 4/3πr^3
= 4/3 X π X 6378100^3
= 1.08683241e21m^3

V = 1.84073533e21 - 1.08683241e21
= 7.5390292e20m^3

Weight of ice is 917kg per m^3.

M = 7.5390292e20 X 917
= 6.91328978e23kg

The temperature of the Earths atmosphere varies greatly, but on average it's 14 C. Specific heat of air is 1.005 kilojoules. Freezing temperature of air is -220 C.

E = 6.91328978e23 X 1.005 X 234
= 1.62579836e26 kilojoules
= 1.62579836e29 joules

Let's also add the heat fusion of air/oxygen (13800 joules/kg).

E = 7.56164629e20 X 13800
= 1.04350719e25 joules

Finally, to add all the values together.

E = 1.031849e26 + 1.62579836e29 + 1.04350719e25
= 1.62693456e29 joules
= 38.884669216061183761 exatons

Final Results
Ice crown freezes the Earth = 38.885 exatons