Energy

Work and energy are measured in the same unit, the joule. Force is measured in newtons, and a newton is about the weight of a small apple. One joule is the work done when a force of one newton moves something one metre, so lifting that apple from the floor to a table one metre up takes roughly one joule. A bag weighing 5 newtons lifted through 2 metres takes 5 times 2, which is 10 joules.

The joule is a small unit, so everyday amounts come in thousands. A kilojoule is a thousand joules. Food labels still use an older unit, the Calorie, and one food Calorie is about 4 kilojoules. An adult who eats 2,000 Calories in a day takes in more than eight million joules, enough to lift a one-tonne car more than 800 metres.

Push a cart and it speeds up. The work you did has not vanished: the cart now carries it as kinetic energy, the energy a thing has because it is moving. It can hand that energy on by hitting something, which is how a hammer drives a nail.

Kinetic energy depends on two things. The first is mass: at the same speed a lorry carries more than a bicycle, in proportion to its mass. The second is speed, and here the rule is steeper. Kinetic energy grows with the square of the speed. Go twice as fast and you carry not twice the energy but four times as much. Three times the speed means nine times the energy. That is why a small rise in speed makes a crash so much worse.

A moving car cannot simply stop. Its kinetic energy has to go somewhere, and the job of the brakes is to take it. Brake pads squeeze against a spinning disc, and friction turns the car’s kinetic energy into heat in the brakes, which is why they can glow red after a long descent. The energy has not been destroyed. It has changed form, and it drifts away into the air.

The square rule decides how much road this takes. The distance a car covers after the brakes go on is its braking distance, and since the brakes remove roughly the same energy with every metre, four times the energy needs four times the road. On a dry road a car braking hard from 50 kilometres an hour stops in about 15 metres. From 100 it needs about 60.

Energy can also sit still. Lift a book onto a high shelf and the work you did is stored in its position, ready to come back as motion if the book falls. Stored energy of this kind is called potential energy, and the kind that comes from being lifted is gravitational potential energy. It equals the object’s weight multiplied by its height above where it started, so the same book on a shelf twice as high stores twice as much. A hydroelectric dam works on the same principle, holding a lake of water high above its turbines.

Stretching and bending store energy too. A drawn bow, a stretched rubber band and a wound clock spring hold elastic potential energy. Drawing the bow is work, and that work waits in the bent wood until the string is released and hands it to the arrow.

Watch a pendulum. At the top of its swing it hangs for an instant, high and motionless: all its energy is potential. As it falls it speeds up, and at the bottom it is at its lowest and fastest: the energy is now all kinetic. Then it climbs the other side, slowing as it rises, and the kinetic energy turns back into potential. The pendulum trades one form for the other, again and again, and the total stays the same.

A roller coaster makes the same trade on a bigger scale. A motor hauls the train up the first hill, and from then on it has no engine. Everything it does, it does on the energy banked on that climb. That is why no later hill can be higher than the first: to climb one, it would need extra energy, and there is nowhere for that to come from.

Kinetic and potential are only two of the forms energy takes. The energy stored in fuel, in food and in a battery is chemical energy. It is held in the bonds between atoms, and burning or digesting rearranges those bonds and lets it out. Light carries energy, and so does an electric current, and so does sound.

Then there is heat. A hot object looks still, but its atoms are not. They jiggle constantly, and the hotter the object, the harder they jiggle. The energy of all that random motion is called thermal energy. It is kinetic energy on a scale too small to see. This is the form that most other energy ends up in: rub your hands together and the work you do becomes thermal energy in your skin.

For a long time heat was thought to be a substance, an invisible fluid that flowed out of hot things. In 1798 Count Rumford, boring out cannon barrels in Munich, noticed that the drilling produced heat without limit, which no stored fluid could do. In the 1840s the English brewer’s son James Joule measured the link exactly. He let a falling weight turn a paddle wheel in a tank of water and found that the water’s temperature rose, always by the same amount for the same amount of work. Heat was energy.

With heat on the books, the accounts closed. In every process ever measured, the total energy afterwards equals the total before. No process creates energy and none destroys it. It only changes form or moves from place to place. This is the law of conservation of energy.

Run up a flight of stairs or walk up slowly: either way you lift the same weight through the same height, so you do the same work. What differs is how fast you do it. The rate of doing work, or of using energy, is called power.

Power is measured in watts. One watt is one joule every second. The unit is named after James Watt, the Scottish engineer whose improved steam engines of the 1770s made “how fast can it do work?” a commercial question. To sell his engines he compared them with the horses they replaced, and his horsepower is still in use: one is about 746 watts.

A person walking upstairs works at about 200 watts. A sprinter on the same stairs delivers the same number of joules in a third of the time, at three times the power.

A power rating tells you how greedy a device is. Your own body, sitting still, runs at about 100 watts, the same as an old-fashioned light bulb. A phone charger draws about 10. An electric kettle draws about 2,000, twenty times a resting person, because heating water takes a great deal of energy and a kettle is built to deliver it quickly.

Power alone does not decide the bill, though. What you pay for is energy, which is power multiplied by time. A kettle runs for three minutes; a fridge runs all day. So electricity is sold by the kilowatt-hour: the energy used by a 1,000-watt device running for one hour. That comes to 3.6 million joules, and a kettle gets through one in about half an hour of boiling.

No machine turns all the energy it is given into the thing you wanted. The share that does end up useful is the machine’s efficiency: useful energy out, divided by total energy in.

A petrol engine is a poor performer. Only about 30 per cent of the energy in its fuel moves the car. The other 70 per cent leaves as heat, through the exhaust and the radiator. An old filament light bulb was worse, turning about 5 per cent of its electricity into light. A good electric motor manages about 90 per cent.

In every case the lost share ends up as heat. That gives the electric heater a curious distinction. It is close to 100 per cent efficient, because in a heater the waste heat is the product: warmth is exactly what you wanted.

For centuries inventors have tried to build a machine that, once started, would run for ever and even do useful work, with no fuel at all. Wheels with sliding weights, self-filling water mills, magnets chasing magnets: every one has failed. Such a device is called a perpetual motion machine, and the conservation of energy explains the failures.

A machine cannot give out more energy than it takes in, so one that produces work from nothing is ruled out at once. Could a machine at least keep running on the energy it started with? Not for long. Wherever parts rub together or push through air, friction drains energy as heat, and that heat spreads into the surroundings and does not come back. The store only ever shrinks, and in the end the machine stops.

Follow almost any energy on Earth back to where it came from and you arrive at the same place. Food is chemical energy that plants built using sunlight. Petrol is the same kind of store, laid down by living things millions of years ago. Wind is air set moving because the Sun heats the ground unevenly, and the water behind a dam was lifted there as vapour by the Sun’s warmth.

So the chains you have followed in this reading share a first link. The sprinter on the stairs runs on food, and the food grew in sunlight. The kettle may be boiling on electricity from wind or from falling water. On Earth, nearly every joule arrived as sunshine before it was anything else.

Where does the Sun get its energy? In 1905 Albert Einstein showed that mass itself is a store of energy. His equation says that energy equals mass multiplied by the speed of light, squared. Light travels about 300,000 kilometres every second, and squaring so large a number makes a little mass worth a vast amount of energy. A single gram, fully converted, would yield about 90 trillion joules, enough to keep a 2,000-watt kettle boiling for more than a thousand years.

The Sun pays for its light this way. Every second, about four million tonnes of its mass disappear, turned into the energy that leaves it as sunshine. Even here the books balance: the mass that goes missing is exactly the energy that streams out.