E=mc2
That's Einstein's famous formula for the amount of energy in matter. I call it the atomic energy formula. Most people look at the atomic energy formula, and say, "Wow, that must be a lot of energy!" But do they understand the formula? Do you? Do you know that "c" represents the speed of light? If you're like most people, you have never truly understood the meaning of this formula. You'll be happy to know the formula is easier to understand than you might have thought. In this page, I'll use the formula to compare the amount of atomic energy in a 1/16-inch diameter drop of water to the amount of chemical energy in a gallon of gasoline.
Follow along. It's easy. You'll see.
Did you know the kinetic energy formula looks very similar to the atomic energy
formula? Kinetic energy, the energy it takes to accelerate an object of a certain
mass to a certain velocity is given by the formula,
E=(1/2)mv2
Let's use the kinetic energy formula to see how much energy it takes to get a
1500-pound car moving at 60 mph.
1/2 * 1500 * 60 * 60 = 2,700,000.
So the kinetic energy of the car is about two and a half million. Two and a half
million what? Why, two and a half million square mile pounds-of-mass per hour per
hour. Don't worry about the units, just trust my high-school physics teacher, Mr.
Phillips, who kept hollering "UNITS! UNITS!" all year. And trust me--I
won't try to pull a fast one with the units. I'm telling you the truth when I say
energy can be measured in "square mile pounds-of-mass per hour per hour".
Sometimes it's easier to just accept some things. Trust me.
How much gasoline does it take to get a car up to 60 miles an hour? Well my car coasts about half a mile on a flat road once I've got it up to 60 mph. That means the kinetic energy in a car going 60 mph is the same as the energy needed to move the car half a mile on a flat road. To measure how much gas that takes, I could get it up to 60 mph, let it coast half a mile, and repeat the process -- a funny way to drive, don't you think? Well in point of fact that's just how I drive in Palmdale California, because the stop signs are a mile apart. I spend the first half-mile getting the car up to 60, and the next half-mile coasting to the next stop sign. I get somewhere between 10 and 20 miles to the gallon that way -- I'll just say 16. So each half-mile uses up 1/32 gallon, or 4 ounces, of gasoline. I've been told that a gasoline engine has an efficiency of about 25% -- that means it converts about a quarter of the chemical energy in gasoline to kinetic energy. So of the four ounces of gasoline, three are wasted. The remaining ounce of gasoline has an amount of chemical energy equivalent to the kinetic energy of a car going 60 mph, or two and a half million -- say it with me -- square mile pounds-of-mass per hour per hour. Very good.
A gallon of gasoline is 128 ounces so it has 128 times as much chemical energy as an ounce, or a total of 320 million square mile pounds-of-mass per hour per hour.
Now, how much atomic energy is there in a 1/16th-inch drop of water? The atomic energy formula, E=mc2, as I have already said, is very similar to the kinetic energy formula. To put it in perspective, the atomic energy in this drop of water is equal to twice the energy Isaac Newton would have used to accelerate the tiny drop of water to the speed of light, 186,000 miles per second. How much energy is that?
First, let's figure out how much the drop of water weighs. A pint of water weighs about a pound and measures 28.875 cubic inches. The drop of water occupies about 1/8000th of a cubic inch, which works out to about 1/225,000th of a pound. Now let's convert the speed of light to miles per hour: 670 million mph, then square it: 450 American quadrillion (1015) square miles per hour per hour (UNITS! UNITS!). Now multiply by the very tiny mass of the water drop, which results in "just" 2 American trillion (1012) -- all together now -- square mile pounds-of-mass per hour per hour. Great!
Now that we're done with both calculations, it's clear the atomic energy in a drop of water is much greater than the chemical energy in a gallon of gasoline. In fact, if you divide 2 trillion (atomic energy in a drop of water) by 320 million (chemical energy in a gallon of gasoline) you get 6000. (No, I didn't forget the units, Mr. Phillips. 6000 is dimensionless!)
In other words, the atomic energy in a drop of water is as much as the chemical energy in 6000 gallons of gasoline, enough for me to drive my car about 96,000 miles on the streets of Palmdale, California.
(Oh, by the way, all energy is atomic energy.)
(For a practical use of this formula, see the Fusion Catalyst.)