How Much Energy Would You Need To Replicate Elsa's Powers In Frozen?

Not all of us are fortunate enough to be born with magical powers, but science offers us the opportunity to create our own. A physics student with an apparent case of Elsa envy decided to investigate the matter by calculating the amount of energy that would be required to freeze Disney's Kingdom of Arendelle.

Writing in the Journal of Interdisciplinary Science Topics, Aaron Goldberg at McMaster University begins his quest by determining how much water was turned into ice when Elsa the Snow Queen had her "incident." Goldberg notes that Arendelle was inspired by Nærøyfjord in Norway. By plugging in data that included total surface area and estimates of ice density, he concluded that the total mass of ice that covered Arendelle was 99,043,217,000,000 grams.

Goldberg then suggests the theoretical means by which he would unleash his powers:

It is well known that the most efficient heat engine is a Carnot engine, which harnesses the temperature difference between two reservoirs to do work. This can be done in reverse, harnessing work to drive a temperature difference between two reservoirs, and is known as a Carnot refrigerator. In this case, the latter two reservoirs are the ice at -15 degrees Celsius , and the air at 20 degrees Celsius.

Goldberg reckons that the total mechanical work required by a Carnot refrigerator to power the transformation of the entire fjord from water to ice is 5,800,000,000,000,000 Joules.

He concludes:

This amount is equivalent to the energy released by the Hiroshima nuclear bomb 115 times over, or that released by 63 Nagasaki nuclear bombs. This immense number puts Elsa's power into perspective, implying either that the Snow Queen has enormous strength, or that Disney underestimated the ramifications of their animated fantasy.