What if a machine could run forever?

Spin a toy top and it wobbles, slows and falls over.

What if a machine could keep going forever? It would never need batteries or fuel!

Spin a top, push a swing or pedal a bike and then stop: sooner or later everything slows down. Engines need fuel, and electric motors need electricity.

So here is a thought experiment that inventors have chased for centuries: what if you could build a machine that, once started, kept running forever and even did useful work, all without any fuel? In this lab you can look at their clever designs, then follow the energy to find out why none of them can work.

A perpetual motion machine is a device that would keep operating, and keep delivering useful work, with no external energy supply. Many designs over the centuries relied on weights, magnets, water or pumps arranged so that some part always seemed to be pushing the machine onward.

This lab asks whether such a machine could exist. The answer comes from two of the most thoroughly tested laws in physics: the conservation of energy and the second law of thermodynamics. Both are statements about where energy comes from and where it goes, so the lab follows the energy step by step.

Every real machine needs something to keep it going.

A car needs fuel. A fan needs electricity. Even you need food!

Every real machine takes in energy and changes it into other forms. A car engine burns fuel, a fan turns electricity into moving air, and your body turns food into movement and warmth.

No machine turns all its energy into the job we want. The OpenStax physics textbook lists a gasoline engine as about 30 percent efficient, which means most of the fuel's energy ends up as heat. Even a good electric motor, at about 98 percent, warms up a little as it runs.

OpenStax College Physics defines efficiency as useful work or energy out divided by total energy in. Its table of representative values gives about 17 percent for a steam engine, 30 percent for a gasoline engine, 35 percent for a diesel engine, 42 percent for a coal power plant and 98 percent for an electric motor.

In a coal-fired plant, for example, about 40 percent of the coal's chemical energy becomes electrical energy and the other 60 percent becomes mostly thermal energy, released through exhaust gases and cooling towers. The energy is not destroyed, but it is no longer doing the job we wanted.

Let's pretend we build a wheel that turns all by itself.

It never needs a push. Could it really happen? Let's follow the energy.

Imagine a wheel with heavy weights around its rim that seem to pull one side down forever, or a pump that lifts water to turn a waterwheel that runs the same pump. Inventors have drawn ideas like these for centuries.

In every design, the machine would have to give out energy, as motion, light or electricity, while taking none in. And it would have to do this even though rubbing parts and moving air steal some of its energy every second. In this thought experiment we test that idea against what physics says about energy.

Two separate claims hide inside a perpetual motion design. A machine of the first kind would put out more energy than it takes in, creating energy from nothing. A machine of the second kind would take heat from its surroundings and turn all of it back into work, endlessly recycling the energy it loses to friction.

The first violates the conservation of energy. The second runs into the second law of thermodynamics: OpenStax notes that friction can turn kinetic energy completely into thermal energy, but the reverse never happens on its own. Any proposed machine can be checked by adding up where its energy comes from and where it goes.

Energy can change from one kind to another. But it never appears from nothing.

And every moving machine loses a little energy as warmth. So it always slows down.

The law of conservation of energy says the total amount of energy never changes. It can move from place to place or change form, from motion to heat, for example, but it is never created out of nothing. So a machine cannot give out more energy than it was given.

And every real machine loses some energy as heat. Rubbing parts get warm, and moving air carries energy away. That heat spreads out and never turns back into motion by itself. With nothing new coming in, the machine gradually runs down.

Conservation of energy: in any process the total energy is constant; it may change form or move between systems, but it is not created or destroyed (OpenStax §7.6). A machine that outputs net work over a full cycle, with no input, would need energy from nowhere.

The second law: heat flows spontaneously only from hot to cold, and no cyclical process can convert heat from a reservoir completely into work (OpenStax §15.3). Efficiency could reach 100 percent only if no heat at all were transferred to the environment, which no real machine achieves. So even a machine fed nothing but its own losses must wind down.

Long ago, people drew wheels they hoped would spin forever.

They never worked. Today, inventors must show their machine really works.

The Museo Galileo in Florence, Italy, traces the oldest known description of a perpetual motion machine to 7th-century India: a wheel meant to turn forever as liquid mercury flowed inside its hollow spokes. Later designs appeared in an architect's notebook in France around 1230. In the 1490s, Leonardo da Vinci studied one of these wheels in detail and showed why it could not work.

Today the U.S. Patent and Trademark Office does not usually ask inventors for a working model, except for cases involving perpetual motion.

The Museo Galileo dates the oldest description to 7th-century India, where the mathematician Brahmagupta designed an overbalanced wheel driven by mercury in hollow spokes; in the 12th century Bhāskara curved the spokes. In Europe the earliest reference is a drawing in the notebook of the architect Villard de Honnecourt (1225 to 1235). In the mid-1490s Leonardo da Vinci analyzed a wheel with hinged arms and concluded it could not work.

The U.S. Patent and Trademark Office's examining manual says a working model is not ordinarily required to show a device operates, with the exception of cases involving perpetual motion, and lists a perpetual motion machine among inventions rejected as inoperative.