Episode 06 - Energy: the great bookkeeping

Tomlin Hawthorne

On the table in front of you are two things. A chocolate-chip cookie, and a lump of TNT of exactly the same weight. Which one contains more energy?

Tomlin Hawthorne

It's the cookie. And it isn't close. Gram for gram, the cookie holds about five times as much energy as the high explosive. If that sounds absurd, you have the wrong idea of what energy is, and so did I, and so did everyone until about 1850. Today we fix it. And we'll find out why you can eat one of those and not the other, though I'd advise against testing it in either direction.

Tomlin Hawthorne

Welcome to Part Two. In Part One we collected some tools: models, scales, estimates, and the two great opening moves by Galileo and Newton. For the next five episodes we're going to look at the world those two built, the clockwork universe, at the height of its confidence. And then we'll watch it crack. Last time I gave you a sentence to read: Newton's law of gravity. Double one of the masses and the force doubles. Double the distance and it drops to a quarter. And yes, two specks of dust a billion miles apart attract each other. The law has no small print. It says every and it means it. Today's question: what is energy, and why can it never be created or destroyed?

Tomlin Hawthorne

I want to start in Venice in 1494, with a Franciscan friar named Luca Pacioli. He was a mathematician, a friend of Leonardo da Vinci, who illustrated one of his books, and he has a strong claim to being the most influential writer you've never read. Because in 1494 he published the first printed description of double-entry bookkeeping. You know the principle even if you've never kept accounts. Every transaction is written down twice. Money that leaves one column arrives in another. If I pay you ten ducats, my cash goes down ten and your cash goes up ten. And so at any moment, however complicated the business, the two sides must balance. If they don't, there's no mystery about it. Somebody has made a mistake, or somebody is stealing. Goethe called it one of the finest inventions of the human mind. I don't think he was being ironic. Hold that picture. A ledger that always balances, where an imbalance means you've missed something. Now here's Richard Feynman, in his first-year lectures at Caltech in the early sixties, explaining energy to eighteen-year-olds. He does it with a story about a child and some toy blocks. A mother gives her son twenty-eight blocks. They're indestructible, can't be split, can't be broken. Every evening she counts them. Twenty-eight. Twenty-eight. Twenty-eight. One evening there are twenty-seven. She looks about and finds one under the rug. Fine. Another evening, twenty-six. She's baffled, until she notices the window is open, and looks out, and there are two on the lawn. Another evening there are thirty. Which is alarming. It turns out a friend came round with his own blocks and left a couple. She sends them home and shuts the window. Then one day she counts twenty-five. And there's a toy box in the room, and the boy won't let her open it. So she gets clever. She knows a block weighs three ounces, and she knows the empty box weighs sixteen. So she weighs the box, subtracts sixteen, divides by three, and that tells her how many blocks are inside without looking. Another day the bathwater's dirty and she can't see the bottom. But she knows each block raises the water level by a quarter of an inch. So she measures the water. As time goes on, her formula gets longer. Blocks she can see, plus a term for the weight of the box, plus a term for the height of the bathwater, and so on. And the total always comes to twenty-eight. Now here's the turn, and it's why this is a great piece of teaching. Feynman says: take away the first term. Imagine there are no blocks to see at all. All you have is a formula, a list of things to measure and add up, and the answer never changes. That's energy.

Tomlin Hawthorne

There are no blocks. Nobody has ever seen a lump of energy. It's not a substance, not a fluid, not a glow. It's a number you can calculate, in a growing list of different ways, and when you add up all the ways, the total stays the same. Always. In every process anyone has ever examined. It's nature's ledger. And like Pacioli's, when it doesn't balance, it means there's an account you haven't found yet. So let's look at the accounts. I'll follow a bit of energy through an ordinary day. It starts in the Sun, and arrives as sunlight. Call that the first account: light. A wheat plant catches it and uses it to build sugar and starch out of air and water. The energy is now stored in the arrangement of atoms. Second account: chemical. The wheat becomes your toast. You eat it. Your body takes the molecules apart and the energy is released, and some of it goes into your legs as you cycle to work. Third account: motion. You cycle up a hill. At the top you're moving slowly, but you're high up, and you could get all that motion back by rolling down. The energy hasn't gone. It's stored in your position. Fourth account: height. Physicists call it potential energy, energy you're owed. You roll down, fast, and at the bottom you brake. The bike stops. So where's the energy now? Touch the brake pads. They're hot. Fifth account: heat.

Tomlin Hawthorne

It took a long time to see this, because the accounts look so different from one another. Let me tell you about two of the people who did the auditing. The first you met last week. Émilie du Châtelet, who translated Newton into French. In the 1730s there was a fierce argument about how to measure the oomph of a moving object. Newton's followers said it's the mass times the speed. Double the speed, double the oomph. Leibniz, Newton's great rival, said no, it's the mass times the speed squared. Double the speed, four times the oomph. Du Châtelet settled it by pointing to an experiment by a Dutchman with the splendid name of 's Gravesande. He dropped brass balls into soft clay from different heights and measured the dents. A ball going twice as fast doesn't sink twice as deep. It sinks four times as deep. Three times as fast, nine times as deep. So the energy of motion goes with the square of the speed. And this matters to you every time you drive. At sixty miles an hour you aren't carrying twice the energy you have at thirty. You're carrying four times. That's four times the stopping distance and four times the damage. It is the least intuitive and most important fact on the road. The second auditor is James Joule, the son of a brewer in Manchester. He was rich, shy, self-taught, and obsessed with measuring temperature very, very precisely, which is the kind of hobby you can have if your family owns a brewery. In the 1840s the general view was that heat was a substance. An invisible fluid that flowed from hot things to cold. Joule didn't believe it. He thought heat was a form of motion, and that you could turn one into the other at a fixed rate of exchange. So he built a machine. A weight on a string, which, as it fell, turned a paddle wheel inside a sealed barrel of water. The weight falls, the paddles churn, the water gets very slightly warmer. And he measured how much. A given amount of falling always produced the same amount of warming. Every time. Height had a fixed price in heat. There's a story about his honeymoon that I can't resist. In 1847 the physicist William Thomson, later Lord Kelvin, was walking in the Alps near Chamonix, and who should he meet coming up the road but Joule, with his new bride, and a very long thermometer. He wanted to measure the temperature of the water at the top and the bottom of a waterfall, because if he was right, the water at the bottom ought to be a fraction of a degree warmer, from the fall. History doesn't record what Mrs Joule made of this. The unit of energy is named after him. A joule is about the energy it takes to lift an apple one metre, which Newton would have enjoyed.

Tomlin Hawthorne

Right. The cookie. We need one more distinction, and it clears up a great deal of confusion in ordinary life. Energy and power. Energy is an amount. Power is how fast you're spending it. Energy is the money in the account. Power is your rate of spending. Power is measured in watts. And here's a number worth carrying around: a human being at rest runs on about a hundred watts. You, sitting there listening, are giving off heat at about the rate of an old-fashioned light bulb. A room with thirty people in it has a three-kilowatt heater running, which is why parties get warm. And what you buy from the electricity company, the kilowatt-hour, is an amount of energy: a thousand watts for an hour. Ten people's body heat for an hour. It costs a good deal less than a cup of coffee. So. A chocolate-chip cookie contains about five times the chemical energy of the same weight of TNT. That's simply measured. You burn each one and see how much heat comes out. Why doesn't the cookie explode? Because the difference between food and a bomb isn't energy. It's power. The cookie releases its energy over hours, as you digest it, and it needs oxygen from the air to do it. The TNT carries everything it needs inside its own molecules and releases the lot in about a millionth of a second. A small amount of energy, delivered almost instantly, is an enormous power. That's all an explosion is. It's the same reason a slap hurts and a slow push doesn't. And it's why petrol, which holds even more energy than the cookie, sits calmly in your tank. I find it a useful thought. The most energetic things in your house are the butter and the cooking oil.

Tomlin Hawthorne

Now, the myth of the week. And this one is in every newspaper. We say we're using up energy. That the world is running out of energy. That we need to save it. But I've just told you energy can't be destroyed. The total never changes. So what on earth are we worried about? Both things are true, and here's how. Follow the bicycle to the end. The energy went from sunlight, to sugar, to motion, to hot brake pads. And then? The pads cool. The heat spreads into the air. It's all still there, every bit of it. The air around your bike is a few millionths of a degree warmer. And it's now completely useless. You can't gather that warmth back up and cycle home on it. So energy isn't used up. It's degraded. It goes from concentrated, useful forms, like fuel and sunlight, to spread-out, lukewarm, useless ones. The quantity is conserved. The quality runs downhill. What we call an energy crisis is really a quality crisis. And the law that governs the quality, why it only ever runs one way, is the Second Law of Thermodynamics. It gets all of episode thirteen, and it is, I think, the most profound idea in this series. I'm telling you now so you'll know it when it arrives.

Tomlin Hawthorne

The question to take away comes from Feynman himself. Right after the story of the blocks, he says something I find astonishing in a first-year lecture. He says it's important to realise that in physics today, we have no knowledge of what energy is. We know how to calculate it. We know it never changes. We can't say what it's a quantity of. Now you, I suspect, have met this before. In economics there's a thing called value. Everyone uses the word, it can be measured in a common unit, it passes from hand to hand and takes many forms, and if you ask an economist what it actually is, you get either a shrug or a four-hundred-page book. In political theory there's power, which has the same slippery quality. So is energy like that? An abstraction we've invented because it makes the books balance? Or is it a real thing in the world that we just can't see directly? And how would you tell the difference? Your challenge this week has two parts. One. Drop a rubber ball on a hard floor and watch. Each bounce is lower than the last. The energy of the ball is going down. Where is it going? You're not allowed to say "it's lost." Listen as well as look, and afterwards, if you've got a very good thermometer and a brewery, measure the floor. Two. Find your electricity bill and look up how many kilowatt-hours you used last month. One kilowatt-hour is about a dozen cookies' worth of energy. Work out your household's monthly consumption in cookies. I think you'll find it's a number in the thousands, and that it changes how you feel about both electricity and cookies. Next time. We've said energy is conserved, and I've told you that's a fact. But why should it be? Is it just how things are? It turns out there's a reason, a beautiful one. It was found in 1918 by a woman who wasn't allowed to be paid for lecturing, and whom Einstein called a genius in the pages of the New York Times.