The conservation of energy

by Chris Woodford. Last updated: November 28, 2022.

Gobble down five bananas and you'll have enough energy to swim for about an hour. [1] That's because your body is a complex machine capable of turning one kind of energy (food) into another kind (movement). Cars can pull off the same trick. Depending on which make and model you own, you probably know that it does so many kilometers or miles to the gallon; in other words, using a certain amount of energy-rich gasoline, it can transport you (and a moderate load) a certain distance down the road. What we have here are two examples of machines—the human body and the automobile—that obey one of the most important laws of physics: the conservation of energy. Written in its simplest form, it says that you can't create or destroy energy, but you can convert it from one form into another. Pretty much everything that has ever happened in the universe obeys this fundamental law. But why, and what use is it anyway? Let's take a closer look!

Photo: The conservation of energy: James Prescott Joule calculated that the water at the bottom of Niagara falls would be about a fifth of a degree warmer than the water at the top. Why? The water loses potential energy as it falls, which is converted into heat. [2] Photo courtesy of the Carol M. Highsmith Archive, Library of Congress, Prints and Photographs Division.

What is the conservation of energy?

The first thing we need to note is that the law of conservation of energy is completely different from energy conservation. Energy conservation means saving energy through such things as insulating your home or using public transportation; generally it saves you money and helps the planet. The conservation of energy has nothing to do with saving energy: it's all about where energy comes from and where it goes.

Write the law formally and it sounds like this:

In a closed system, the amount of energy is fixed. You can't create any more energy inside the system or destroy any of the energy that's already in there. But you can convert the energy you have from one form to another (and sometimes back again).

A "closed system" is a bit like a sealed box around whatever we're studying: no energy can leak into the box from the inside (or be introduced to the box from outside).

There are some even simpler, more familiar ways of stating the conservation of energy. "No pain, no gain" is a rough everyday equivalent: if you want something, you have to work for it. "There's no such thing as a free lunch" and "You don't get anything for free" are other examples.

Examples of the conservation of energy

The conservation of energy (and the idea of a "closed system") sounds a bit abstract, but it becomes an awful lot clearer when we consider some real-life examples.

Walking upstairs

Walk upstairs and you have more potential energy when you get to the top than you had at the bottom—but you haven't created energy out of thin air. The muscles in your body have to work against the force of gravity to move you upwards and your body loses energy (that it made from food) as it climbs. This is the energy that your body regains as potential energy.

Driving a car

Fill a car up with gasoline and you have a closed system. All the energy you have at your disposal is locked inside the gas in your tank in chemical form. When the gas flows into your engine, it burns with oxygen in the air. The chemical energy in the gas is converted first into heat energy: the burning fuel makes hot expanding gas, which pushes the pistons in the engine cylinders. In this way, the heat is converted into mechanical energy. The pistons turn the crankshaft, gears, and driveshaft and—eventually—the car's wheels. As the wheels turn, they speed the vehicle along the road, giving it kinetic energy (energy of movement).

If a car were 100 percent efficient, all the chemical energy originally locked inside the gasoline would be converted into kinetic energy. Unfortunately, energy is wasted at each stage of this process. Some is lost to friction when metal parts rub and wear against one another and heat up; some energy is lost as sound (cars can be quite noisy—and sound is energy that has to come from somewhere) Not all the energy the car produces moves you down the road: quite a lot has to push against the air (so it's lost to air resistance or drag), while some will be used to power things like the headlights, air conditioning, and so on. Nevertheless, if you measure the energy you start with (in the gasoline) and calculate how much energy you finish with and lose on the way (everything from useful kinetic energy and useless energy lost to friction, sound, air resistance, and so on), you'll find the energy account always balances: the energy you start with is the energy you finish with.

Now this only applies if your car is a "closed system." If you're driving along the straight and the road suddenly starts going downhill, you're going to be able to go much further than you'd be able to go otherwise. Does this violate the conservation of energy? No, because we're no longer dealing with a closed system. Your car is gaining kinetic energy from the gasoline in its tank, but it's also gaining kinetic energy because it's going downhill. This isn't a closed system so the conservation of energy doesn't apply anymore.

Boiling a kettle

Photo: An electric kettle like this converts electrical energy into heat energy. That's the reverse of the process that happens in the power plant that supplies your home, where electricity is produced using heat energy released by burning a fuel such as coal, oil, or gas.

Boil water with an electric kettle and you're seeing the conservation of energy at work again. Electrical energy drawn from the power outlet on your wall flows into the heating element in the base of your kettle. As the current flows through the element, the element rapidly heats up, so the electrical energy is converted into heat energy that gets passed to the cold water surrounding it. After a couple of minutes, the water boils and (if the power stays on) starts to turn to steam. How does the conservation of energy apply here? Most of the electrical energy that enters the kettle is converted into heat energy in the water, though some is used to provide latent heat of evaporation (the heat we need to give to liquids to turn them into gases such as steam). If you add up the total electrical energy "lost" by the electricity supply and the total energy gained by the water, you should find they're almost exactly the same. Why aren't they exactly equal? Simply because we don't have a closed system here. Some of the original energy is converted to sound and wasted (kettles can be quite noisy). Kettles also give off some heat to their surroundings—so that's also wasted energy.

Pushing a car uphill

In the everyday world, "work" is something you do to earn money; in physics, work has a different meaning. When you do a useful job with a force (a push or a pull), such as moving a car uphill, we say you're doing work, and that takes energy. If you push a car uphill, it has more potential energy at the top of the hill than it had at the bottom. Have you violated the conservation of energy by creating potential energy out of thin air?

No! To push the car, you have to do work against the force of gravity. Your body has to use energy to do work. Most of the energy your body uses is gained by the car as you push it uphill. The energy your body loses is pretty much equal to the work it does against gravity. And the energy the car gains is the same as the work done. So no energy is created or destroyed here: you're simply converting energy stored as fuel inside your body into potential energy stored by the car (because of its height).

Artwork: When you push a car uphill, the potential energy it gains comes from the energy your body loses in the process.

Who discovered the conservation of energy?

How do we know the conservation of energy is true? First, it sounds sensible. If you put a heavy log on a fire it might burn for an hour. If you put a second log, roughly the same size, on the fire, it's reasonable to suppose you'll get twice as much heat or the fire will burn twice as long. By the same token, if five bananas can supply your body with an hour's energy, ten bananas should keep you running for two hours—although you might not enjoy guzzling them all at once! In other words, the energy in (the logs you add to the fire or the bananas you eat) is equal to the energy out (the heat you get by burning logs or the energy you make by eating bananas).

Reasonable guesswork doesn't quite cut the mustard in science. Really, we need to be sure that the energy we start with in a closed system is the same as the energy we end up with. So how do we know this? One of the first people to confirm the law of conservation of energy experimentally was English physicist James Prescott Joule (1818–1889), who used an ingenious bit of apparatus to find what he called "the mechanical equivalent of heat." He used a falling weight to drive a large paddle wheel sealed inside a container of water. He calculated the potential energy of the weight (the energy it had because of its height above Earth) and reasoned that, as the weight fell, it transferred pretty much all its energy to kinetic energy in the paddle wheel. As the paddle wheel turned, it stirred the water in the container and warmed it up by a small but significant amount. Now we know how much energy it takes to warm a certain mass of water by a certain number of degrees, so Joule was able to figure out how much energy the water had gained. To his delight, he found out that this figure exactly matched the energy lost by the falling weight. Joule's brilliant work on energy was recognized when the international scientific unit of energy (the joule) was named for him.

Photo: The Mechanical Equivalent of Heat: In James Prescott Joule's famous experiment, a falling weight (1) pulls on a rope that passes over a pulley (2). The rope spins an axle (3) that turns a paddle inside a sealed container of water (4). As the paddle spins, the water heats up. Joule proved that the heat energy gained by the water was exactly the same as the potential energy lost by the weight.

Joule built on earlier work by Anglo-American physicist Benjamin Thompson (1753–1814), also known as Count Rumford. While working in a Germany artillery factory, Rumford noted that cannon barrels got hot when they were being drilled out. He swiftly realized that the heat was not a magic property of the metal (as many people supposed) but came from the mechanical, frictional process of drilling: the more you drilled, the hotter the metal got. Rumford's simple calculations produced results that, according to Joule, were "not very widely different from that which I have deduced from my own experiments." That was a sign both men were on the right track.

What about the conservation of mass?

Nuclear reactions seem to create energy out of nothing breaking up or joining together atoms. Do they violate the conservation of energy? No!

Albert Einstein's famous equation E=mc2 shows that energy and mass are different forms of the same thing. Loosely speaking, you can convert a small amount of mass into a large amount of energy (as in a nuclear power plant, where large atoms split apart and give off energy in the process). Einstein's equation shows us we sometimes need to factor mass into the conservation of energy. In a nuclear reaction, we start off with one set of atoms (a certain amount of energy in the form of mass) and end up with a different set of atoms (a different amount of energy locked in their mass) plus energy that's released as heat. If we factor in the mass of the atoms before and after the reaction, plus the energy released in the process, we find the conservation of energy is satisfied exactly. Since mass is a form of energy, it's clear that we can't destroy mass or create it out of nothing in the same way that we can't create or destroy energy. You'll sometimes see this referred to as the conservation of mass.

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Find out more

On this website

• Atomic energy
• Atoms
• Energy

On other websites

• The Mechanical Equivalent of Heat: A good Wikipedia article about James Prescott Joule's famous experiment.
• The Conservation of Energy: In this short video clip from his MIT lectures, Professor Walter Lewin demonstrates very impressively that you can't finish up with more energy than you started off with. Luckily for him, as it turns out!

Books

For younger readers

• Eyewitness Energy by Jack Challoner and Dan Green. Dorling Kindersley, 2016. A simple introduction to the science, technology, and history of energy. Ages 9–12.
• Energy by Chris Woodford. Dorling Kindersley, 2007. My own colorful introduction explains what energy is, where it comes from, and how we use it in our everyday lives. Ages 9–12.
• Power and Energy by Chris Woodford. Facts on File. This longer book of mine is a history of human efforts to harness energy, from ancient technologies like water power to the latest forms of renewable energy. Suitable for most readers from about ages 10 upward.

For older readers

• Great Experiments in Physics: Firsthand Accounts from Galileo to Einstein by Morris H. Shamos. Dover, 1959/1987. This utterly wonderful book (one of my favorite books ever!) contains reprints of papers reporting many of the greatest physics experiments of all time, including "Chapter 12. The Mechanical Equivalent of Heat" by James Prescott Joule. You may be able to read the whole paper via Google Books if you scroll through to page 166.
• Six Easy Pieces by Richard Feynman. Basic Books, 2011. Chapter 4 is a clear, simple, theoretical explanation of the conservation of energy.

Articles

Popular science

• How a missing penny explains the conservation of energy by Rhett Allain. Wired, May 2, 2017. There are no missing pennies: the energy books must always balance!
• Fact or Fiction?: Energy Can Neither Be Created Nor Destroyed by Clara Moskowitz. Scientific American, August 5, 2014. Can we find anything that violates the most fundamental energy law?

More scholarly

A few older articles from the archives explore the law in more depth:

• The Discovery of the Law of Conservation of Energy by G. Sarton et al, Isis, Vol. 13, No. 1 (Sep., 1929). This article traces the history of the conservation of energy back through Mayer, Joule, Carnot, and others.
• On the Principle of the Conservation of Energy by Ernst Mach, The Monist, Vol. 5, No. 1 (October, 1894), pp. 22–54 (33 pages). Mach discusses the broader signifance of the law and in terms of our concepts of energy.
• Conservation of energy in the human body, Scientific American, Vol. 81, No. 6, August 5, 1899.

1. ↑   Five medium ripe bananas contain about 500 calories according to the US Department of Agriculture database. How much energy you use during swimming varies according to stroke and vigor, and what your body's like, but 500 calories is a decent ballpark figure. Richard Muller explains the calculation more generally and notes that an hour's vigorous exercise of any kind burns off roughly 400 calories (I've rounded up) in Physics and Technology for Future Presidents (Princeton: Princeton University Press, 2008. p.26)
2. ↑   I cover this story in my book Atoms Under the Floorboards, p.38. It's covered at greater length in James Joule, Letter to the editors, Philosophical Magazine 27 (1845): 205, quoted in Shamos, M. H. (ed.) (1987), Great Experiments in Physics (Dover, New York), p. 169.