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How much energy does a 100kg human pack?

One of the things I absolutely love about dropping Panini off at JLS is to engage in some absolutely refreshing nerdy conversations. These are always interesting, often funny, and frequently educating to both of us.

Today, we talked about fusion and energy. It turns out he was just learning about the periodic table and the elements. He asked how a helium atom can be made from hydrogen atoms and enquired why the mass of the helium atom is less than the mass of the "ingredients" that went into it.

I, of course, took that opportunity to introduce fusion at a high level and said that some of the mass is turned into energy. He was amazed to learn, as we all are at first presentation, that mass is a compact form of energy. So he naturally asked "How much energy is there in a person if we turn them completely into energy?"

I said that's pretty easy to calculate. Let's make some simplifying assumptions. Take a person that weighs 100 Kilograms so we can work the numbers in our head while still paying attention to the road. Einstein's equation tells us that the mass of this person, if converted entirely into energy is given by E=mc2. If we assume c to be 300,000 kilometers per second, or 3x108 meters per second, then c2 is 9x1016. If we multiply this by the mass of the person, we get 9x1018 Joules.

Here is where the fun really starts. On face value, 9x1018 Joules is just a number, albeit a pretty large one in energy-speak. When you state a bland fact like "A 100 Kg person can be converted into 9x1018 Joules of energy if we completely annihiliate them, reactions will be very mixed, ranging from "Wow that's interesting" (meaning actually not) to "that's a huge amount of energy, isn't it?" (meaning, "I have no idea what that means").

To truly appreciate this fact, and "commune" with nature for a few seconds, we must translate that into something tangible. So we went down that path. Just how much energy is 9x1018 Joules? Winter is soon upon us, and the space heaters will be out. So we took a 1 kilowatt space heater as our reference point. The amount of energy a 1KW heater emits in one second is 1 kilojoule, or 1000 Joules. So if we took 9x1018 Joules of energy, which is the same as 9x1015 KJ, it would take the heater 9x1015 seconds to dissipate it. If we turn that into hours, we could say that much energy is equivalent to the energy from a 1KW heater over 9x1015/3600 = 2.5x1012 hours. Hmmm... Assume there's 25 hours in a day (as we often do :-) Then that's about 1012 days. Divide by 365 to get years and we have about 3x108 years or 300 million years.

So the amount of energy in a 100Kg person, which we could get if we totally annihilate them, can power a 1KW space heater for 300 million years. Say we switch the space heater to setting 2, which draws 2KW instead of 1KW. Then we'd still be able to power it for 150 million years.

Now each heater takes up about 1 square foot of space. Consider a side of a reasonably large building, not unlike the NASDAQ building in Manhattan with its Flat-panel lined external wall. If we took a building wall that is 100 feet wide and 30 feet tall (or vice versa), its area is 3000 square feet. If we stacked and lined up these heaters in a huge array to completely cover this side of the building, we can fit about 3000 space heaters neatly. If they were all running at 1KW, then this wall will radiate heat for 300x106/3000 = 100,000 years. At 2KW, this wall will still radiate heat continuously for 50,000 years.

The nice thing about translating facts into tangible things like this is that it lets us instantly visualize and appreciate these magnitudes in a way that isn't possible otherwise. Imagine how much different it is to say "A 100 Kg person, if totally annihilated, can power a 1KW space heater (which we can all feel the warmth of) for 300 million years" rather than "The mass in a 100 Kg person is equivalent to 9x1015 Kilo Joules of energy. Yuck! WTF is that?


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