Episode 12 - Heat, temperature and the engine

Tomlin Hawthorne

Go to your kitchen drawer, in your mind. In it there's a metal spoon and a wooden spoon. They've been lying side by side all night, in the same drawer, in the same room.

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Pick them both up. Which one is colder?

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The metal one. Obviously. You can feel it.

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Except it isn't. They're exactly the same temperature. They have to be: they've been sitting together for twelve hours. Put a thermometer on each and it'll give you the same number.

Tomlin Hawthorne

So your hand, which you've trusted all your life as a thermometer, is not measuring temperature at all. It's measuring something else. Today we find out what. And then we follow a young Frenchman as he discovers that there's a limit, set by nature and not by engineering, on how much use you can ever get out of heat.

Tomlin Hawthorne

Last time, two glasses of water and a drop of ink in each. If you did it, you saw the ink in the hot glass spread out in a minute or two, and the ink in the cold one hang about in lazy threads for much longer. Nobody stirred. The water molecules did it. In the hot glass they're moving faster, so they knock the ink about faster. You were watching the jiggle of atoms with a kettle and a bottle of food colouring.

Tomlin Hawthorne

So today's question follows straight on. What is heat? And why can no engine be perfectly efficient?

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I want to start with a painting. Turner's Rain, Steam and Speed, in the National Gallery in London. 1844. A black locomotive comes straight at you across a bridge through a storm of gold and grey, its firebox glowing, and everything around it is dissolving. If you look hard, there's a hare running ahead of it on the track.

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It's a painting about a new kind of power. And here's the thing I find remarkable. By 1844, the steam engine had been remaking the world for seventy years. It had pumped the mines, driven the mills, built the railways, and moved half the population of England into cities. And nobody understood it. Nobody could have told you what heat was, or how good an engine could possibly be. The Industrial Revolution was carried out by brilliant mechanics working by rule of thumb.

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The man who changed that was called Sadi Carnot. He was French, and the name mattered. His father, Lazare Carnot, was one of the leaders of the Revolution, the man who organised its armies. They called him the Organiser of Victory. He named his son after a Persian poet.

Tomlin Hawthorne

Sadi grew up in the shadow of France's defeat. And like a lot of young French engineers after Waterloo, he had a theory about why they'd lost. It wasn't generals. It was coal and steam. Take away England's steam engines, he wrote, and you take away her coal and iron, her navy, her wealth. You'd ruin her.

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So in 1824, at twenty-eight, he published a short book. Its title translates as Reflections on the Motive Power of Fire. In it he asked a question no one had put clearly. Never mind this engine or that engine. What's the best that any engine could ever do? Is there a limit?

Tomlin Hawthorne

The book sold almost nothing. Eight years later Carnot caught cholera in a Paris epidemic and died at thirty-six. Because of the disease, most of his belongings were burned, including nearly all his papers. One slim book and a few notes survived. It turned out to be enough to found a science.

Tomlin Hawthorne

But to see what he found, we need to know what heat is. And for that we need the atoms.

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You'll remember Feynman's sentence. Everything is atoms, and they never stop moving.

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In a solid, they're held in place and they tremble. In a liquid they slide around each other. In a gas they fly about and bounce off the walls. And the faster they're moving, the hotter the thing is.

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That's it. That's what temperature is. It's a measure of how hard the atoms are jiggling, on average.

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When you put a thermometer in your mouth, the molecules of your tongue are knocking against the glass, and it's reporting how hard.

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And this gives us something rather wonderful straight away. If temperature is motion, then there has to be a lowest possible temperature. Because the atoms can slow down, and slow down further, but they can't do less than stop. There's a floor. It's at minus two hundred and seventy-three degrees Celsius, and it's called absolute zero. There's no ceiling. You can always jiggle harder. But there's a bottom to cold, and nothing in the universe can go below it. Deep space is about three degrees above.

Tomlin Hawthorne

Now, a distinction. Temperature and heat are not the same thing, and ordinary speech muddles them terribly.

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Temperature is how hard each atom is jiggling, on average. Heat is energy on the move from a hotter thing to a colder one.

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Here's the example. A sparkler, the kind children wave about on bonfire night. The sparks coming off it are at well over a thousand degrees. They land on your hand, and nothing happens. A bath is at forty degrees, and if you were lowered into one at sixty-five you'd be in hospital.

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The spark is hot, and it's a speck. Very hard jiggling, hardly any atoms. It has almost no energy to give you. The bath is mild, and enormous. Temperature is the intensity. The total is something else.

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And now the spoons. Why does the metal one feel colder?

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Both spoons are at room temperature, say twenty degrees. Your hand is at about thirty-three. So when you touch either one, energy flows from your hand into the spoon. That's heat. But metal passes that energy along quickly, away from your fingers and into the rest of the spoon, so more keeps flowing out of you. Wood passes it along slowly. The surface under your fingers warms up and the flow nearly stops.

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Your skin doesn't measure temperature. It measures how fast heat is leaving you. Which, if you think about it, is the thing an animal needs to know.

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Now. In Carnot's day none of this was understood. The reigning theory said heat was a substance. An invisible, weightless fluid called caloric, which soaked into things and made them hot, and flowed out again as they cooled. It had been named by the great French chemist Lavoisier, and it worked rather well. Heat does seem to flow. It does seem to be a quantity of something.

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The person who put the first hole in it is one of my favourite characters in science, and almost certainly not a nice man.

Tomlin Hawthorne

Benjamin Thompson was born in Massachusetts in 1753. When the American Revolution came, he backed the British, spied for them, and left in a hurry, abandoning a wife and child. In London he became a government official. Then he went to Bavaria, where he reorganised the army, invented a nourishing soup for the poor, laid out a great public park in Munich that's still there, and was made a count of the Holy Roman Empire. He chose the title Count Rumford.

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One of his jobs was supervising the boring of cannon. You take a solid brass casting and drill out the barrel, with a drill turned by horses. And Rumford noticed how hot the brass got. Hot enough to boil water.

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Now, according to the caloric theory, that's caloric being squeezed out of the metal by the drilling, like water out of a sponge. Fine. But Rumford thought: a sponge runs dry. So he used a deliberately blunt drill, one that cut hardly any metal at all, and kept the horses walking. The heat kept coming. He put the whole thing in a tank of water, and after two and a half hours the water boiled. Bystanders were astonished to see a great quantity of water boiled with no fire.

Tomlin Hawthorne

And he could have gone on boiling water for as long as the horses held out. The supply of heat was, he said, inexhaustible. And a material thing can't be inexhaustible. Whatever was coming out of that cannon, it wasn't a substance. The only thing being put in was motion. So heat must be a kind of motion.

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He published in 1798. And then, in a twist I couldn't make up, he moved to Paris and married Lavoisier's widow. The man who killed caloric married the widow of the man who'd invented it. It was a famously miserable marriage. She once poured boiling water on his roses.

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And here is one of the oddities of this story. Carnot, writing twenty-five years after Rumford, still believed in caloric. He built his entire argument on a theory that was false. And he got the right answer. Let's see how.

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He thought about a water wheel. A water wheel gets its power from water falling. What matters isn't how much water there is. A lake, sitting flat, turns nothing. What matters is that the water drops from a high place to a low one. The power comes from the fall.

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A steam engine, Carnot said, is the same. Heat falls. It goes in hot, at the boiler, and comes out cooler, at the exhaust. And it's the fall from hot to cold that does the work.

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Look what follows from that.

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First: you can't get work out of heat unless you have a difference in temperature. However much thermal energy you've got, if it's all at one temperature, it's a flat lake. The oceans contain a stupendous amount of heat energy. Enough to run civilisation for millennia. And a ship can't use a drop of it to turn its propeller, because the ship is the same temperature as the sea.

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Second: every engine has to throw some heat away. It has to have a cold end, somewhere for the heat to fall to. That waste heat isn't a flaw in the design. It's the outflow of the water wheel.

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Which is why every power station you've ever seen has cooling towers, those great concrete funnels with clouds coming off the top. That isn't smoke, by the way. It's steam, carrying away the heat that had to be dumped. A typical power station turns about a third of its fuel's energy into electricity and sends two-thirds into the sky. That's not incompetence. The engineers are quite close to what nature allows.

Tomlin Hawthorne

And third, the big one. Carnot showed that there's a ceiling on efficiency, and that it depends on only two things: the temperature at the hot end and the temperature at the cold end. Not on the fuel. Not on whether you use steam or air or anything else. Not on how clever you are. The bigger the fall, the better you can do. And you can never reach a hundred per cent, unless your cold end is at absolute zero, which it never is.

Tomlin Hawthorne

So here was something new in the world. A limit on technology that comes from physics. You can improve the bearings, polish the pistons, hire better engineers, and you'll creep up toward Carnot's ceiling. You will not get through it.

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A refrigerator, incidentally, is the same machine run backwards. An engine lets heat fall from hot to cold and takes out work. A fridge puts work in and uses it to push heat uphill, from the cold inside to the warm kitchen. Put your hand behind your fridge. That warmth is the heat that used to be in your milk.

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And that's why you can't cool the kitchen on a hot day by leaving the fridge door open. People try. All the heat it pumps out of the front comes out of the back, plus a bit extra from the motor. You'd be warming the room.

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Now, I said this law governs the fate of the universe, and I should justify that.

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Carnot's principle was reworked, after his death, by people who'd abandoned caloric. And what came out of it is a statement so simple it sounds like nothing. Heat, left to itself, flows from hot to cold. Never the other way.

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Your coffee cools to the temperature of the room. The room never makes it hotter. That's it. That's the Second Law of Thermodynamics, in its first form.

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But think it through. If heat only ever flows from hot to cold, then every difference in temperature, everywhere, is being evened out. Every fall is being used up. And it's the falls that make everything happen. An engine, a storm, a living cell: each runs on a difference. One day, a very long time from now, there'll be no differences left. Everything at one lukewarm temperature. A flat lake, from one end of the cosmos to the other, with nothing able to happen in it, for ever.

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The Victorians worked this out and called it the heat death of the universe. It appalled them. It's the last vision in H. G. Wells's The Time Machine, a dying red sun over a silent beach, and it haunts the end of the nineteenth century. And it's the subject of the next episode, where we find out why heat only flows one way. The answer is one of the most beautiful ideas I know, and it comes down to counting.

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The myth of the week is in your own vocabulary. We say: shut the door, you're letting the cold in.

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There's no such thing as cold. Not as a thing that moves. Cold is just less jiggling. What comes through the door is heat, going out. Nothing comes in. Your grandmother was right about the door and wrong about the physics.

Tomlin Hawthorne

And the question to take with you. It's about truth.

Tomlin Hawthorne

Carnot believed heat was a fluid. That's false. And from that false belief he derived, correctly, a law that has never been overturned and never will be. The water wheel was the wrong picture and it gave the right answer.

Tomlin Hawthorne

How can that be? What does it tell you about the relation between a theory being true and a theory being useful? Are there ideas in your own field that are, strictly, false, and that you wouldn't want to do without?

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Your challenge. Three small things to feel.

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One. The spoons. Go and actually do it. And then leave them both in the fridge for an hour and try again.

Tomlin Hawthorne

Two. If you have a bicycle pump, pump up a tyre hard and fast, and then touch the barrel of the pump near the bottom. It's hot. You've been squashing air, which means pushing its molecules, which means speeding them up.

Tomlin Hawthorne

Three. Find a wide rubber band. Hold it against your upper lip, which is very sensitive to temperature. Now stretch it quickly and touch it to your lip again. Then let it relax quickly and do the same. One of those is warm and one is cool. Work out which, and why it might be.

Tomlin Hawthorne

Next time. Episode thirteen. A British novelist once said that not knowing the Second Law of Thermodynamics is like never having read a work of Shakespeare. He meant it as a rebuke to people like you. By the end of the next episode, you'll be able to tell him what it says, and why. Bring a pack of cards.