Please Pass the Science
by dr. scott berk
Simplistic, misleading, and somewhat condescending. . . but never boring!
I have a question for Doctor Berk.
If I were to be converted into energy, how much would I be worth? That is to say, if a 100 kg human were to be converted into pure energy by some miraculous process, and the energy could be stored and released at any old rate, how much electricity would be generated? I have the feeling that were I made into pure energy, I could power the whole earth for generations? Why not?
Why not, indeed! Ron, this is the kind of question I wish I was asked more often. A meaty, original question! A question that makes you ponder the very make-up of the universe! Most importantly, a question that is incredibly simple for someone like me to answer! For these reasons and more, I have decided to devote an entire column to the question of what I would somewhat whimsically call "Your Relative Worth." So, how much electricity is locked up inside your atoms, ready for harvesting to support perhaps billions of needy people? Of course, the only way to get at it would be to somehow convert all of your mass into energy with a huge efficiency. The best way to do this would be to meet your anti-matter twin (the anti-Ron, so to speak). As all Star Trek fans know, when matter and anti-matter combine, they completely annihilate themselves, transforming into gamma radiation with almost 100% efficiency. This reminds me of a lovely poem, written by Harold P. Furth and originally published in the New Yorker magazine. It is entitled "The Perils of Modern Living":
Well up above the tropostrataFor those of you who aren't "deep" enough to "appreciate" poetry, the above verse describes a meeting of Dr. Edward Teller, inventor and proponent of the hydrogen bomb, with an anti-matter version of himself on a far-off alien world. Of course, the meeting ends in tragedy and destruction, which is ironic because that's exactly what happened to the homeland of the Bikini Islanders who were displaced by Dr. Teller's thermonuclear tests. But I digress. . .
Virtually everybody has heard of Einstein's famous equation, E=mc2, which relates mass to energy by multiplying it by the speed of light squared. But what does this number mean? To answer your question, we can apply this formula, but we need to express the result in terms that we can all understand. One way to do this is to use a trick called dimensional analysis, which is a method of keeping track of all the units involved with a particular formula and juggling them around until they make sense. This technique got me through three college-level physics classes. The best thing is that you don't really have to understand why the formulae work, you just have to figure out what to do with the numbers. So, what kind of units are involved with this formula? Well, mass can be expressed in kilograms, as you note. The speed of light is a velocity. We'll express it in meters per second. By sticking with kilograms (kg) for mass, meters (m) for length, and seconds (s) for time, we've entered the realm of the so-called MKS system. It turns out that a huge number of useful units are defined starting with these simple measures. That's enough introduction! Let's dive in to the math:
Energy of Ron = Ron's mass (100 kg) x speed of light squared (3 x 108 m/s)2
Doing the multiplication and keeping track of the units, we get:
Energy of Ron = 9 x 1018 kg.m2/s2
Great. So what the hell is a kilogram meter squared per second squared, and how does that possibly relate to a unit of energy that we know of? Well, science fans, using the power of dimensional analysis, it's a snap! What is energy, anyway? It's work done, of course! Pushing a heavy object across the floor, for example, requires energy. You expend energy (work) by exerting a certain force for a certain distance. In the MKS system, the unit of force is known as a Newton (abbreviated N). It is the force required to accelerate a mass of one kilogram at a rate of one meter per second squared. So, let's take a look at those numbers again. Now, we can express our answer like this:
Energy of Ron = 9 x 1018 (kg.m/s2).(m) = 9 x 1018 N.m
The Newton-meter is a unit of energy! It's the work required to apply one Newton of force for one meter. Another name for a Newton-meter is a Joule. As long as your values are expressed using the MKS system, the number you get from Einstein's formula is, by definition, in Joules. In Ron's case, a whole lotta Joules, by the way. But what does that mean in the real world? You asked how much electricity could be generated upon your conversion to energy. On my electric bill, I am charged by the kilowatt-hour. This is also a unit of energy. To do the conversion from Joules to kilowatt-hours, we need one more definition, the watt. The watt is a unit of power and is defined as a unit of energy per second. Lucky for us, the watt is also defined based on the MKS system. It is equivalent to one Joule per second. A watt-second, therefore, is just another term for a Joule. The Joule is like a bridge between work done with matter (a Newton-meter) and work done with electricity (a watt-second). Energy is energy, whether you're lighting a light bulb or moving a piano! OK, so now we have:
Energy of Ron = 9 x 1018 Joule = 9 x 1018 watt-seconds
Since there are 3600 seconds in an hour, we just divide by 3600 to obtain:
Energy of Ron = 2.5 x 1015 watt-hours
A kilowatt hour is just 1000 watt hours, so, dividing by 1000, we get (drum roll, please!):
Energy of Ron = 2.5 x 1012 kilowatt-hours (kWH) of energy
Now, for the punch line. It takes about 350 kWH of electricity per month to power my little, old, three-bedroom colonial house, at a cost of about $45 or 12.8 cents per kWH. By this measure, you, Ron, would be worth about $320 billion in current, capable of powering 7.1 billion households like mine for a month. A month of free electricity for the whole world on Ron! Now that's what I call charity!
Of course, I wouldn't recommend this course of action, but hey, it's your mass. So the next time you're looking for a get-rich-quick scheme, consider converting yourself into pure energy. You wouldn't have a clue how to price yourself without Einstein's famous equation, dimensional analysis, and a healthy appetite for. . . SCIENCE!
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