How can wizards do such powerful things running on pure human metabolism? [duplicate]

Question

In fiction, we often see magic used for very flashy effects (like, say, fireballs). But human metabolic output doesn't seem powerful enough to account for things like this. Is it possible to build a magic system without an external source of energy?

Answer 1

According to how much can a magician lift?, we have about 400 W of power to play with (ignoring burst strength for the moment). That's a fair amount, but it's not exactly huge. For perspective, it would take our wizard longer than an hour to boil half a liter (500 g) of water starting at room temperature. Fireballs are way out of our league.

What if we use burst strength? From the same question, that tops out at around 1500 W, but wizards tend not to be world-class weight lifters. Still, they would probably be world-class spellcasters, so let's run the numbers anyway. We end up with around 20 minutes to boil the same half liter. You're not going to sustain burst strength for 20 minutes on end, and we don't want a fireball to take anything like that much preparation time anyway.

This is the point where I'd throw in equipment. When's the last time you saw a wizard practicing without his spell book, or his magic wand, or whatever it is he uses? We might suppose the equipment can store energy over a sustained period of time and then release it all at once. This can be done while the wizard is sleeping as well as during his waking hours, so we can get quite a lot of energy out of it. The bad news is that 400 W is optimistic in this case, unless our wizard eats an enormous amount of food every day and puts it all to magic (no regulating body temperature or other basic metabolic needs).

Let's assume we have 3000 food Calories to play with every day after deducting homeostasis etc. That's more than the "guideline" of 2000 you often see on Nutrition Facts in the US, but athletes often consume more than that anyway. This number may not be perfectly correct, but it should be within an order of magnitude of right. Those 3000 Calories translate to about 12.55 megajoules per day. That's quite a lot of energy. It's enough for our wizard to instantly (or at least rapidly) boil about 3.4 liters of water (almost a gallon) every day, and more if he's willing to go several days without casting spells.

If you look again at the 12.55 MJ figure in Wolfram|Alpha, you'll note that it is about a quarter of the energy released by burning a kilogram of gasoline. That means our wizard could, every day, create a fireball equivalent to the explosive output of about 360 mL of gas (about 1.5 cups), when properly misted and sparked. Again, if he needed a larger one (or multiple small ones), he could rest for several days beforehand.