Friday, September 16, 2016

Ask a Physicist: How Much Energy is in Me?

"Game Maker" wants to know:

I'm designing a fire-wielding superhero who uses his own body as fuel for his powers. How much heat energy would be created if a person were to burn off 50-100 lbs of fat in the span of 5 minutes? (Assuming he has the requisite "secondary superpowers" to avoid dying in the process).

Oh wow, great question—and one that we should be able to answer using almost nothing but math!

So first off, you'll want to keep in mind that a "food calorie"—or "Cal" spelled with a capital C—is actually a different unit from "physics calorie", which is spelled with a lower-case one. A "physics calorie" is defined as the amount of energy it takes to heat a milliliter of water by 1°C. A milliliter of water weighs exactly one gram, if that's helpful.

Now it's sort of silly to have two separate units with the same name, especially when one is a thousand times larger than the other, but that's the way it is—a "food calorie" is actually equal to 1,000 lower-case calories—it's the amount of energy it would take to heat up a full LITER of water by 1°C. So a single M&M, which contains three Calories, contains enough usable energy to heat a 2-liter of water by a little more than a degree C.

So. Numbers. The shortening on my shelf has 110 Calories in a 12 gram serving, giving us an energy density of about 9 Cal/g. There are about 450 grams in a pound, so 1 pound of fat could contain up to 4050 Calories.

So let's say your character is sitting in a six person jacuzzi, and wants to show off his powers. A six-person jacuzzi has a volume of about 300 gallons, or 1135 liters. And let's say the water is an ambient 70° F, or about 20°C. If he wants to heat that jacuzzi from 20°C to 40°C—the maximum recommended spa temperature—it'll take him about:

to do it. Dividing this by the 4050 Calories in a pound of fat, we find that our hero would slim down by:
in the process!

Maybe a different unit and a different analogy would help, because water is an incredible heat sink, which dampens the dramatic effect a bit. So let's work in joules, another unit of energy. An incandescent light bulb draws a power of about 60 watts, and a watt is one joule per second, so a light bulb uses 60 joules of energy per second. 4050 Calories, one pound of pure fat, contains about 17 million joules. Sixty pounds of fat gets you a billion joules.

So what does a Gigajoule of energy, released all at once, look like? According to the table on Wikipedia's "TNT Equivalent" page, that's the same amount of energy you'd find in a quarter-ton of TNT. For reference, the video embedded below is what a full ton of TNT looks like, so scale this down a bit and you'll have a good idea of your hero's full destructive capacity.

You specified "over five minutes", though, so we can divide that billion by the 300 seconds in 5 minutes to get an answer in watts—which is
roughly 3.3 Megawatts, equivalent to the power of ~55,000 incandescent light bulbs all running at once!

Whenever I do analysis like this, I always take a second to check Wolfram Alpha—they've got a "comparisons" section that's often useful for getting a sense of the numbers you're looking at, and this is no exception: If your hero is able to convert this energy to forms other than heat (e.g. strength), burning sixty pounds of fat would buy him the ability to exert 4,430 horsepower for five minutes, enough to leap to the top of tall buildings, or run at supersonic velocities.

He might need some goggles though, unless he's got invulnerability. Relativity of motion is kind of a pain when you're moving faster than the speed of sound—think "800 mph mosquito in your eye"!

Thanks for writing in!

Stephen Skolnick

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