Conservation of Energy

The law of conservation of energy is one of the most fundamental rules of physics: energy can never be created or destroyed; it can only be changed from one form to another. The total amount of energy in any isolated system stays exactly the same, no matter what happens inside. If energy seems to vanish, it has just turned into a form you cannot see (often heat). If energy seems to appear, it has come from another form. This single rule underlies everything in physics, chemistry, biology and engineering.

  • The ruleEnergy is not created or destroyedOnly changes form
  • Discovered1840sMayer, Joule, Helmholtz
  • Confirmed byEvery experiment everNo exceptions found
  • Common lossHeat (low-quality energy)Usually friction and air resistance
  • In Einsteins updateEnergy + mass conserved togetherE = mc^2
  • Perpetual motionImpossibleCannot get more energy than you put in

What conservation means

"Conservation" here means "stays the same". The law says: count up all the energy in a system before something happens, and count it up again afterwards. The total is exactly the same. Energy may have changed form (from kinetic to heat, or from chemical to electrical), but none has appeared or disappeared.

Examples:

  • A ball rolling down a ramp: gravitational potential energy at the top equals kinetic energy at the bottom (plus a little heat from friction). Total is constant.
  • Burning petrol in a car: chemical energy in the fuel converts to kinetic energy of the car, heat in the engine and exhaust, and sound waves. Add them all up and the total equals the original chemical energy.
  • A pendulum swinging: kinetic and potential keep swapping, but the total remains the same (until air friction gradually converts some to heat).
  • A solar panel powering an LED: light energy enters the panel, electrical energy flows to the LED, light energy comes out (plus some heat). Total energy conserved.

Why "isolated"?

The law strictly applies to "isolated systems": ones where no energy can enter or leave. In practice, very few real systems are truly isolated. Heat usually leaks in or out; light shines in; electromagnetic radiation passes through. As long as you account for all the energy crossing the boundary, conservation still holds.

The whole UNIVERSE is the ultimate isolated system. Total energy of the universe is constant (within our best understanding).

Fact The law of conservation of energy was first clearly stated by German physician Julius Robert Mayer in 1841, then independently by James Prescott Joule and Hermann von Helmholtz a few years later. Before that, scientists believed in "vital forces" in living things and "caloric fluid" for heat. Once the law was understood, it unified all of physics under a single elegant principle that has not been broken in nearly 200 years of careful experiments.

Where does "lost" energy go?

In everyday life, useful energy often seems to vanish. A car running out of fuel; a phone battery dying; an arrow slowing as it flies. Where did the energy go?

The answer is almost always heat. Friction, air resistance and other "losses" convert organised forms of energy (kinetic, electrical, chemical) into thermal energy: the random motion of particles. The total energy is still there, just spread out and useless.

  • Car brakes turn kinetic energy into heat in the brake pads.
  • A torch turns electrical energy into a little useful light, plus a LOT of heat.
  • A phone battery powers your screen, plus warming your hand through the back.
  • Friction between gears in any machine wastes some energy as heat.

Why heat is "low-quality" energy

Once energy has become heat spread evenly throughout a system, it becomes very hard to turn it back into useful forms. You cannot easily run a car off the warmth of your hand, even though there is plenty of thermal energy there.

This is the deep reason why perpetual motion machines are impossible. Every time energy changes form, some of it leaks away as heat. To keep a machine running forever, you would need to recapture and reuse 100 per cent of the heat, which the second law of thermodynamics forbids.

Did you know? The Patent Office in many countries flatly refuses to consider any patent application for a "perpetual motion machine" or "free energy device". Inventors regularly submit such proposals (usually based on misunderstandings or wishful thinking), but conservation of energy has held in every test for nearly 200 years. The US Patent Office has had a standing policy since the 1800s that perpetual motion claims are automatically rejected.

Einsteins extension: E = mc^2

In 1905, Albert Einsteins theory of special relativity showed that mass and energy are equivalent: they can be converted into each other according to the famous equation E = mc^2. This means the strict law of energy conservation is really a law of "mass-energy" conservation.

In ordinary chemistry, the mass change is so tiny that it cannot be measured: chemical conservation of mass and conservation of energy both hold separately to high accuracy. In nuclear reactions, however, the mass change is significant. A nuclear bomb converts a tiny fraction of uranium mass into a huge amount of energy. The Sun converts about 4 million tonnes of its mass into energy every second through fusion.

Energy efficiency

Because heat is so easy to lose and so hard to capture back, engineers spend a lot of effort improving energy efficiency: getting more useful work out of each unit of input energy.

  • LED bulbs convert 80-90 per cent of electrical energy into light (incandescent bulbs were just 5-10 per cent).
  • Modern petrol car engines: about 30-35 per cent of fuel energy goes to wheels; the rest is mostly heat in the exhaust.
  • Electric motors: typically 90-95 per cent efficient.
  • Combined-cycle gas power stations: around 60 per cent efficient.
  • Solar panels: typically 18-25 per cent of sunlight energy turned into electricity.
Try this Set up a small ball on a steep ramp. Roll it down and measure how far across the floor it travels. Now lift the ball to twice the height. The ball has twice the gravitational potential energy at the top, so 4 times the kinetic energy at the bottom (if no friction), meaning roughly 4 times the distance across the floor. But it never quite reaches the predicted distance because some energy was lost to friction. Conservation of energy holds, but you cannot see all the heat that was produced.
Deeper dive: why perpetual motion is impossible

For centuries, inventors have dreamed of building a perpetual motion machine: a device that, once started, would run forever without any input of energy. Some designs would also (the dream goes) provide free useful energy for other purposes. Despite hundreds of attempts and many ingenious designs, none has ever worked. The laws of thermodynamics tell us why.

The first law of thermodynamics is just the conservation of energy: you cannot create energy from nothing. Any machine that claims to produce more energy than it consumes is violating this law and will not work. (Designs of this sort are called "perpetual motion of the first kind".)

The second law of thermodynamics is more subtle. It says that in any energy conversion, some energy ALWAYS becomes lower-quality heat, spread out and unusable. Even a perfectly designed machine cannot capture all its own waste heat and turn it back into useful work. There is always some loss. This means no machine can run forever without an input of energy, even if it does not produce useful work. (Designs trying to do this are called "perpetual motion of the second kind".)

Plenty of clever ideas have been tried. Wheels with weights that swing out to be heavier on one side. Magnets that pull each other in a circle. Wheels with pipes of falling water. Devices using "free" energy from the zero-point vacuum. All of them eventually fail, usually because the inventor overlooked some source of friction or some hidden energy input.

The closest thing to perpetual motion is on the cosmic scale. The Earth has been orbiting the Sun for 4.5 billion years and the orbit is incredibly stable. But even this is not truly "perpetual": Earth slowly loses orbital energy through tidal interactions with the Moon, the orbits slightly distorted shape causes tiny ongoing changes, and the Sun itself will eventually run out of fuel in around 5 billion years. Everything ends, even orbits. Conservation of energy holds throughout.

For more, see what is energy and heat (thermal energy).