# The Science Behind Frozen: Queen Elsa is More Powerful Than an A-Bomb

How powerful would Queen Elsa have to be to freeze the kingdom of Arendelle? McMaster University student Aaron Goldberg asks this essential question in a recently published paper, in which he calculated exactly how much ice would be needed to cover the kingdom and, as a result, how much energy Elsa would have expended when she accidentally created a permanent winter.

In order to calculate the ice needed to cover Arendelle, Goldberg used the approximate area of Norwegian fjord called Nærøyfjord, which served as the inspiration for the fictional Arendelle. He determined by estimating the density of the ice that the total mass of the ice would have been 99,043,217,000,000 grams.

The frozen kingdom of Arendelle:

[Credit: Disney]

Then, in order to estimate the amount of energy Elsa's fit of cryokinesis would have expended, he equated her powers with a Carnot refrigerator, which is the most efficient type of heat engine. It functions by harnessing work to drive a temperature difference between two reservoirs, and the mechanical work needed to freeze Nærøyfjord would have come to 5,800,000,000,000,000 Joules of energy.

Goldberg concluded in his paper, "This amount is equivalent to the energy released by the Hiroshima nuclear bomb 115 times over, or that released by 63 Nagasaki nuclear bombs." That puts an extremely dark spin on an already frightening power, especially for a children's movie. (Although, to be fair, the movie is based on a Hans Christian Andersen fairy tale, which is hardly indicative of underlying optimism.)

He goes on to say, "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." We'll assume the former, since the whole point of magic is to make an anti-hero more powerful than a mere earthly weapon of mass destruction.