The conservation of energy
by Chris Woodford. Last updated: March 21, 2021.
Gobble down five bananas and you'll have enough
energy to swim for about an
hour. 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 happens 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: 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.
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
Artwork: This house is an example of a closed system: the energy that's inside the red dotted line stays as it is or gets converted into other forms. We can't create any new energy inside the house out of nothing at all, and we can't make energy inside the house vanish without trace, though we can turn it into other forms. So what if one room of the house suddenly starts getting hotter? The heat energy making that happen must be coming from energy that's already inside the house in a different form (maybe it's wood in a fire that's being burned to release the chemical energy locked inside it). If that's not the case, we don't have a closed system: the "extra" heat must be coming into the house from outside (maybe strong sunlight streaming in through the window).
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.
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.
Artwork: Like everything else, cars must obey the law of conservation of energy. They convert the energy in fuel into mechanical energy that moves you down the road, but waste quite a lot of energy in the process. If you put 100 units of energy into a car (in the form of fuel), only 15 units or so move you down the road. The rest is wasted as heat losses in the engine (74 percent); parasitic losses (6%, making electricity, for example, to light the headlamps); and drivetrain losses (5%, sending power to the wheels). The 15 useful units of energy are used to overcome drag (air resistance), friction (in the brakes), and rolling resistance (in the tires). Every bit of energy we put into a car has to go somewhere, so the energy outputs (74% + 6% + 5% + 15%) must always exactly add up to the original energy input (100%). Figures for city driving from Where the energy goes, fueleconomy.gov.
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).
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.
“... the quantity of heat produced by the friction of bodies, whether solid or liquid,
is always proportional to the quantity of force expended.”
James Prescott Joule, The Mechanical Equivalent of Heat, 1845.
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.
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.