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## Introduction

In She-Ra and the Princesses of Power, before the events of the story, Princess Frosta created the Kingdom of Snows (most likely, as she is the ruler and held it together during the events of Princess Prom). The Kingdom of Snows has a very big castle, and that got me wondering how much energy was required in order to perform this feat.

## Calculations

### Finding the Size/Volume

Ice carpet thingy height = 108 px

Girl height = 32 px

Average adult woman height is 1.63 metres and since the thing is 3.375x the girl, it is 5.5 metres

Ice carpet thingy height = 10 px and is 5.5 m, which means there is one metre for every 0.55 pixels.

Castle height = 570 px = 313.5 m

Castle base = 482 px = 265.1 m; With a radius of 132.55 m

Volume of a cone gives us 5768004.99 m^3

### Finding Energy

Air is 80% nitrogen and 20% oxygen

Frozen nitrogen density is 1026.5 kg/m^3

Density of solid oxygen is 1426 kg/m^3

Nitrogen Mass = 5768004.99 x 1026.5 x 0.8 = 4.7366857e9 kg

Oxygen mass = 5768004.99 x 1426.5 x 0.2 = 1.64561182e9 kg

#### Nitrogen Freezing Energy

Nitrogen specific heat is 1040 j/kg, air temperature is 293 degrees kelvin, boiling point of nitrogen is 77,36 K, so: 4.7366857e9 x 1040 x (293-77.36) = 1.06227566e15 J

Nitrogen vaporization is 199000 j/kg, so: 4.7366857e9 x 199000 = 9.42600454e14 J

Melting temperature of nitrogen is 63,15 kelvins so: 4.7366857e9 x 1040 x (77.36-63.15) = 7.00006359e13 J

Fusion of nitrogen is 25800 j/kg so: 4.7366857e9 x 25800 = 1.22206491e14

And the total freezing energy is: 1.06227566e15 + 9.42600454e14 + 7.00006359e13 + 1.22206491e14 = 2.19708324e15 J; 520 Kilotons of TNT (Large Town level)

#### Oxygen Freezing Energy

Oxygen specific heat is 918 j/kg, air temperature is 293 degrees kelvin, boiling temperature of oxygen is 90.2 K so: 1.64561182e9 x 918 x (293-90.2) = 3.0636421e14 J

Heat of vaporization of oxygen is 214000 j/kg so: 1.64561182e9 x 214000 = 3.52160929e14 J

Melting temperature of oxygen is 54,75 kelvin so: 1.64561182e9 x 918 x (90.2-54.75) = '"5.355331e13 J

Fusion energy of oxygen is 13875 j/kg so: 1.64561182e9 x 13875 = 2.2832864e13 J

And the total freezing energy is: 3.0636421e14 + 3.52160929e14 + 5.355331e13 + 2.2832864e13 = 7.3491131e+14 J; 180 Kilotons (Large Town level)

## Final Tally

2.19708324e15 + 7.3491131e+14 = 2.9319946e+15 J; 700 Kilotons of TNT (Large Town level+)

This scales to the other Princesses as they have been depicted as comparable to each other in power with Frosta being the youngest of the Princesses (11 years old), as well as characters like the Sorcerers (which includes Micah and Shadow Weaver). Double Trouble may be able to mimic her power if they turned into her, but that isn’t shown or confirmed yet.

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