What is energy? The idea that ties physics, chemistry and life

Energy is the capacity to do work, which in physics means pushing something over a distance, or to heat something up. It is measured in joules. Energy comes in many forms, from the motion of a car to the light from the Sun to the chemical bonds in food, and what makes it so useful is that it passes from one form to another without the total ever changing.

In short

• Energy is a number a system has, not a substance: it measures how much work or heating that system could do.
• It changes form constantly, but in any closed system the total stays the same. That is the law of conservation of energy.
• Power is how fast energy moves. A watt is one joule per second, and a kilowatt-hour is 3.6 million joules.

What does "the capacity to do work" mean?

Work, in physics, has a narrow meaning: a force acting on something while it moves. Lift a 1 kg bag of sugar 1 meter and you do about 9.8 joules of work against gravity, because the bag weighs 9.8 newtons and you moved it 1 meter. One joule is one newton of force applied over one meter, which in base units is a kilogram times a meter squared per second squared. Raising an apple of about 100 grams by 1 meter takes roughly 1 joule, which is a useful sense of how small the unit is.

Heating is the other way energy moves. Put a pan on a stove and the flame does no work on the pan in the physics sense, but energy still flows into it, and the pan's atoms jiggle faster. That jiggling is what temperature measures. Energy, then, is the shared currency behind both: anything that can push, lift, warm, light or move something has energy, and doing so spends some of it from one place and adds it somewhere else.

What forms does energy take?

Physicists sort energy into two families: energy of motion and energy of position or arrangement. The names multiply, but they are all the same quantity measured in the same joules.

• Kinetic energy is energy of motion, ½mv², where m is mass in kilograms and v is speed in meters per second. A 1,000 kg car at 20 m/s (72 km/h) carries ½ × 1,000 × 20² = 200,000 joules, which its brakes must turn into heat to stop it.
• Gravitational potential energy is energy of height, mgh, where g is about 9.8 m/s² on Earth and h is height in meters. Water held behind a dam has it, and a hydroelectric plant turns it into electricity.
• Thermal energy is the energy of atoms and molecules moving and jiggling at random, mostly kinetic energy on the scale of particles.
• Chemical energy is energy of how atoms are arranged in molecules. Burning fuel or digesting food rearranges them into lower-energy molecules, and the difference comes out as heat and work.
• Radiant energy is the energy carried by light and other electromagnetic waves, the form in which the Sun's energy reaches Earth and drives photosynthesis.
• Nuclear energy is energy of how protons and neutrons are arranged in a nucleus. Splitting uranium nuclei releases it in a reactor, as the nuclear power note explains.

Einstein's E = mc² adds one more entry: matter itself is a store of energy. A single gram of mass is equivalent to about 9 × 10¹³ joules, roughly what a 1-gigawatt power station generates in a full day. In nuclear reactions and in the Sun a small fraction of mass is converted, which is why they release so much; the theory of relativity is where that equation comes from.

Why can't energy be created or destroyed?

Energy can change form, but in a closed system the total never changes. This is the law of conservation of energy, and it is one of the best-tested ideas in science. It was pieced together in the 1840s. Julius Robert Mayer stated the equivalence of heat and work in 1842, James Prescott Joule measured it with a falling weight that turned a paddle in a tank of water and warmed it, and Hermann von Helmholtz set out the general principle in 1847.

In 1918 the mathematician Emmy Noether showed why it holds: if the laws of physics are the same today as tomorrow, a quantity must be conserved, and that quantity is energy. The law is a consequence of time itself having no special moment. It is also why every perpetual-motion machine fails. A machine that put out more energy than went in would be creating energy, and no measurement has ever found that happen.

The simple picture has an edge. On the scale of the whole expanding universe, light from distant galaxies loses energy as it stretches to longer wavelengths, and general relativity has no single agreed way to add up the total energy of the universe. For anything on Earth, in a lab or in a power plant, the law holds without exception.

A worked example: one breakfast, climbed up the stairs

Take a breakfast that provides 1,000 kilojoules, which a food label would list as about 240 kcal (1 kcal is 4.184 kJ). How high could a 70 kg person climb on it?

1. Lifting a body against gravity takes energy mgh. The person's weight is 70 kg × 9.8 m/s² = 686 newtons.
2. If every joule went into climbing, the height would be 1,000,000 J ÷ 686 N = about 1,460 meters, the height of a fair-sized mountain.
3. Muscles are not that efficient. They turn roughly 20 to 25 percent of food energy into mechanical work; the rest becomes heat, which is why climbing makes you warm. At 22 percent, the useful work is about 220,000 J.
4. 220,000 J ÷ 686 N is about 320 meters, close to the height of the Eiffel Tower, or about 100 floors of stairs.

None of the energy disappears. About a fifth ends up as gravitational potential energy in a body that is now higher up, and the rest warms the person and the air around them. In real life the climb would also have to share the breakfast with the body's own running costs: a person eating 2,000 kcal a day spends about 8.4 million joules, an average of nearly 100 watts, just staying alive. Inside cells, that food energy is passed along in a molecule called ATP.

How is energy measured?

The joule is the unit of energy in the International System of Units, but different fields kept their own units. They all convert exactly or nearly so:

Unit	In joules	Where you meet it
Joule (J)	1	Physics and engineering
Kilocalorie (kcal), the food "Calorie"	4,184	Food labels
British thermal unit (Btu)	about 1,055	Heating and air conditioning in the US
Kilowatt-hour (kWh)	3,600,000	Electricity bills
Electronvolt (eV)	1.602 × 10⁻¹⁹	Atoms, light and particle physics

Energy and power are easy to confuse. Power is the rate at which energy moves, measured in watts, and one watt is one joule per second. A 2,000-watt kettle delivers 2,000 joules each second. Heating 1 liter of water from 20 °C to 100 °C takes about 4,186 J per degree × 80 degrees = 335,000 J, so the kettle needs about 170 seconds, a little under 3 minutes. A kilowatt-hour is one kilowatt sustained for an hour: 1,000 × 3,600 = 3.6 million joules, which is the unit utilities bill in.

If energy is conserved, how can it be "used up"?

When people say a city uses energy, or that Bitcoin mining uses a great deal of it, the energy does not vanish. Electricity running a computer ends up as warm air. What gets used up is the energy's usefulness. Concentrated, orderly forms, like electricity or the chemical energy in fuel, spread out into low-grade heat that can do little further work. That one-way spreading is the subject of entropy and the second law of thermodynamics, and it is why the world needs a constant supply of fresh, concentrated energy, whether from fuel, the Sun or renewable sources.

The same bookkeeping runs through the rest of science. The greenhouse effect is a balance of the energy arriving from the Sun and the energy Earth sends back to space. A chemical reaction releases or absorbs heat depending on whether its products hold less or more energy than what went in. Life itself is a chain of energy conversions, from sunlight captured by plants to the food that powers a climb up the stairs.

Check yourself

• Without looking back, explain the difference between energy and power, using the kettle as the example.
• Why does a person climbing stairs on 1,000 kJ of food get only about a fifth of the way a perfect machine would?
• If energy is always conserved, what do people actually mean when they say energy has been used up?

Sources

• What is energy? — U.S. Energy Information Administration
• Forms of energy — U.S. Energy Information Administration
• International System of Units (SI): units — National Institute of Standards and Technology
• Electron volt-joule relationship — NIST, CODATA 2022
• Conservation of energy — OpenStax, College Physics 2e
• Conservation of energy — Wikipedia