When physics and “superpowers” reconcile (or not), it’s all in great fun.
A show that I like for various reasons, but that has also shown a variety of great feats is “Avatar: The Last Airbender” and the subsequent “Avatar: The Legend of Korra.”
One of the most extreme examples of bending happens when Ghazan melts the Northern Air Temple Mountain:
Given: an approximate energy of 900kJ/kg to melt rock and an average density of 2.7g/cm^3 for rock .
 ( http://home.earthlink.net/~jimlux/lava.htm )
 ( http://en.m.wikipedia.org/wiki/Continental_crust )
Approximate: The temple has a footprint of about 500m x 500m = 250,000m^2. The mountain has rather sheer faces so let’s give it a cylindrical profile and say about 400m vertically is melted. That’s 100,000,000m^3 of rock.
Based on our givens, that is 270,000,000,000kg of rock or 243,000,000,000,000kJ of energy, 243 petaJoules.
Gazan outputs the energy equivalent of the Tsar Bomba, the largest nuclear device ever tested.
Or enough to power all the electricity in New York City for 6,136 days, i.e. 17 years.
If the energy all came from within him through conventional biology, he burned 5.8×10^13 kilocalories (or just capital “C” Calories – of which we are recommended to eat 2000 a day by food packaging), that’s 29,000,000,000 days or 79 million years of meals. If he was converting mass directly to energy, then via Einstein, he lost 2.7kg of pure mass (not bad!).
One could argue that characters are tapping into energy sources external to themselves when bending, nevertheless, it is interesting to know just how much of it they must be accessing.
See this Google Doc for further calculations with Zaheer, Avatar Kyoshi, etc.