Check out Aaron Goldberg, “Powering Disney’s Frozen with a Carnot Refrigerator,” Journal of Interdisciplinary Science Topics 3 (19 Feb 2014). Here’s the abstract:
Frozen is Disney’s latest film, in which the character Elsa unleashes winter on her entire kingdom. This paper quantifies the amount of water frozen and the amount of work required by a Carnot refrigerator to do so, arriving at values of 5.49772788 x 10^2 moles and 5.8 x 10^15 Joules, respectively.
You can read about how a Carnot refrigerator works here. Basically, it is possible to harness a temperature difference between two reservoirs to generate work (a Carnot engine). But you can turn the equation around and harness work to create this difference of temperature. This effect is called a Carnot refrigerator.
In layman’s terms this means
It has been shown that in Frozen, Elsa froze approximately 5.5 x 10^12 moles of water. To accomplish Elsa’s feat, a Carnot refrigerator would require 5.8 x 10^15 Joules of energy. 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.
I’m going with the second option on this one, but it would still be pretty cool if Elsa could generate enough energy to basically hold her own with the likes of Superman or the incredible Hulk. That’s a movie I’d go see.