What is conservation of energy?

Energy is the ability to make things happen: to move something, lift it, warm it or light it up. It comes in many forms, and it is measured in joules (J). Lifting an apple 1 metre takes about 1 joule.

The law of conservation of energy says energy is never made and never destroyed. It only changes from one form to another. Add up every form, and the total stays exactly the same.

Watch the skater. At the top of the ramp she has height energy (potential energy): PE = m × g × h, her mass times gravity (9.81) times height. As she drops, it turns into motion energy (kinetic energy): KE = ½ × m × v². At the bottom she is fastest; climbing the other side turns the motion back into height.

With no friction she rises to exactly the height she started from, for ever. With friction, a little motion becomes heat in the wheels, the bearings and the air every metre, so she comes up a bit short each time. The energy isn't lost: it has warmed things up. The top edge of the chart, the total, stays flat.

Notice something odd: the speed at the bottom, v = √(2gh), doesn't depend on mass. A heavy skater has more energy, but also more of herself to move.

A car's energy starts as chemical energy in petrol: about 32 million joules in every litre. The engine burns it, and most of it leaves as heat: out of the exhaust and through the radiator. Only about a fifth of the fuel's energy reaches the wheels. See CarClear.

At a steady speed, all the energy reaching the wheels goes into pushing air aside and flexing the tyres, and ends up as a little warmth in the air and the road. Speed up, and the car stores motion energy: ½ × m × v². At 60 km/h a 1,300 kg car carries about 180,000 J.

To stop, all of that must go somewhere. Ordinary brakes squeeze pads onto discs and turn it into heat: the discs can warm by tens of degrees in one stop. An electric car runs its motor backwards as a generator, turning much of that motion back into electricity in the battery. That's regenerative braking.

A bicycle runs on food. Your muscles turn about a fifth of the food energy into work at the pedals, and the rest into body heat, which is why you sweat. Climbing a hill stores that work as height energy. Rolling down, gravity hands it back as speed, but the air takes a growing share. See CycleClear.

To warm something up, you have to put energy in. For water the rule is simple: Q = m × c × ΔT. The heat needed is the mass, times the specific heat (4,186 joules to warm 1 kg by 1 °C), times the rise in temperature. Warming 15 litres by 40 °C takes about 2.5 million joules.

A geyser is almost perfect at turning electricity into heat: a 2,000 W element puts 2,000 joules into the water every second. Nothing is wasted at the element. But the tank then leaks heat to the bathroom all day through its foam, so a good tank is really a good flask. See WaterHeaterClear.

A microwave oven takes a longer road: electricity, then high voltage, then microwaves, then heat in the food. About two thirds of the power from the wall ends up in the food. The rest warms the magnetron and transformer, and the fan blows it out of the vents. See MicrowaveClear.

Once water reaches 100 °C, the extra energy stops raising its temperature. It goes into pulling molecules apart into steam instead: 2,257 joules for every gram that boils away. The energy is still all there, hiding in the steam.

A battery stores electrical energy as chemical energy: charging drives a reaction one way, and using it lets the reaction run back. A home inverter's 150 Ah battery holds about 1,800 watt-hours. See UPSClear.

No step is perfect. The charger warms up, the battery warms up and fizzes a little near full charge, and the inverter warms up turning 12 V back into 230 V. Put 100 units in from the wall, and only about 58 come back out to your fans. The other 42 are not destroyed: they have become heat, which is why an inverter needs air around it.

An air conditioner looks as if it breaks the rules. A 1.5-ton AC uses about 1.5 kW of electricity but takes about 5.3 kW of heat out of a room. It isn't making energy: it is moving heat that was already there, from the cool room to the hot street. The electricity pays for the pumping.

The books still balance. The outdoor unit blows out the room's heat plus the electricity: 5.3 + 1.5 = 6.8 kW of hot air. That ratio, heat moved ÷ electricity, is the COP. A fridge does the same inside your kitchen, which is why its sides feel warm. See ACClear and FridgeClear.

For centuries inventors tried to build a perpetual-motion machine: a wheel that turns for ever, or even does work, with nothing going in. The overbalanced wheel is the classic. The weights on one side swing far out, so surely that side is always heavier? But there are more weights tucked in on the other side, and as the wheel turns, gravity takes back every joule it gave. After each step of the pattern, the total height of the weights is exactly the same. Friction does the rest, and it stops.

The magnet ramp fails the same way. A magnet strong enough to pull the ball up the slope is strong enough to hold it when it tries to fall back through the hole. A pull that depends only on where the ball is gives back, on the way out, exactly what it gave on the way in. The Paris Academy of Sciences grew so tired of such machines that in 1775 it stopped examining them.

In 1905 Einstein found a surprise: mass is a form of energy, E = m c². Since c² is huge, a tiny mass holds an enormous amount of energy. In the Sun, four hydrogen atoms become one helium atom that is 0.7% lighter. The missing mass comes out as sunlight: over 4 million tonnes every second. Energy is still conserved, as long as you count mass too.

Why is energy conserved at all? In 1918 Emmy Noether proved a beautiful answer: because the laws of physics are the same today as they were yesterday. Any rule that doesn't change with time comes with a quantity that never changes, and that quantity is energy.

There is one famous twist. On the scale of the whole expanding universe, space itself is stretching, so the laws are not the same at every moment. Light from distant galaxies loses energy as it is stretched redder, and there is no simple total to keep. For anything smaller than the cosmos, the law holds perfectly.