Energy is one of the most used words in physics and one of the hardest to pin down. In everyday speech it means pep, or the fuel in a tank. In physics, energy is the capacity to do work: to move something against a force or to change the state of matter. It comes in many forms: motion, height, heat, chemical bonds, electric currents, light and the nucleus of the atom. What makes energy so useful is not any one of those forms, but a rule that links them all.

Work and two basic kinds of energy

In physics, work is done when a force moves something through a distance. Holding a heavy suitcase still for an hour makes your arms ache, but in the physicist's sense you do no work on the suitcase, because it does not move. (Your muscles are busy inside, which is why you tire.) Lifting the suitcase onto a shelf does work on it.

Kinetic energy is the energy of motion. It grows with mass, and it grows much faster with speed: doubling an object's speed gives it four times the kinetic energy. That is why a crash at 100 kilometers per hour is far more destructive than one at 50, and why braking distances lengthen so quickly as speed rises. Potential energy is stored energy that depends on position or arrangement: a rock perched on a cliff, water held behind a dam, a stretched spring, or the chemical bonds in food and fuel. Potential energy is energy waiting to be released.

The great conservation law

In the 1840s several scientists, working separately, reached the same idea. The German doctor Julius Robert Mayer, the English brewer and physicist James Prescott Joule and the German physiologist Hermann von Helmholtz all argued that energy is never lost, only changed from one form to another. Mayer reached the idea partly by noticing, as a ship's doctor in the tropics, that sailors' blood looked redder there, and wondering what that said about the body's burning of food. His claim was largely ignored at first.

Joule's experiments were the most convincing. He let falling weights turn a paddle wheel inside an insulated tank of water. The churning water warmed very slightly, and he showed that a given amount of mechanical work always produced the same rise in the water's temperature. Heat, he concluded, is a form of energy, and work turns into it at a fixed rate. Helmholtz gave the idea its general form in 1847.

This is the law of conservation of energy: energy cannot be created or destroyed, only transformed from one form into another or moved from place to place. It is also called the first law of thermodynamics, and it is among the most thoroughly tested ideas in all of science. When the physicist Wolfgang Pauli noticed in 1930 that energy seemed to go missing in a kind of radioactive decay, he did not give up the law. To save conservation of energy, Pauli proposed an unseen particle that carried off the missing energy. That particle, the neutrino, was finally detected in 1956.

Perpetual motion and power

For centuries inventors designed wheels, magnets and pumps that would run forever and do useful work for free. All of them failed. A machine that produces energy from nothing is impossible, because it would violate the conservation of energy. As early as 1775 the French Academy of Sciences decided to stop examining proposals for perpetual motion, and patent offices today still treat them with deep suspicion. Claims of free energy devices still circulate online; the law tells you, before any test, that something in the story is missing.

A last useful idea is power. Power is the rate at which energy is transferred or used, measured in watts, after the Scottish engineer James Watt. A 10 watt bulb and a 100 watt heater may each run for an hour, but the heater uses ten times as much energy in that hour. Electricity bills charge for energy used, usually counted in kilowatt hours, rather than for power.

Worked example: the energy in a dam

Follow the energy through a hydroelectric plant. Sunlight warms the oceans and lifts water vapor into the sky. Rain falls on mountains, and a dam holds the water high above a valley, where it has gravitational potential energy. When the gates open, the water falls through large pipes and speeds up, turning potential energy into kinetic energy. The rushing water spins a turbine, and a generator turns the turbine's motion into electrical energy. That flows along wires to homes, where it becomes light, heat and motion again.

At no step is energy created. Some always escapes as heat in pipes, bearings and wires, so the electricity delivered is less than the potential energy the water started with. Large hydroelectric plants are among the most efficient power stations in use, converting roughly 90 percent of the water's energy into electricity. The same bookkeeping applies to a bicycle, a human body or a nation's whole power supply. Follow the energy step by step, and nothing ever appears from nowhere or vanishes without a trace. When a claim seems to break that rule, the safest bet is that someone has missed a step.