## 5.7 Entropy, Part 2: Efficiency

Critical Questions:

• Why can’t we build a machine with 100% efficiency?

After a shamefully long delay, let’s take a look at the consequences of entropy. In the previous section, I described entropy as a measure of the statistical probability of a state.

One of the most significant results of this kind of thinking is that, because high-entropy states are more likely than low-entropy ones, the total entropy of the universe will always tend to increase over time. We have to say “tend to” here because things like all of the air particles in a room jumping to one side can, technically, happen. But if every process obeys this statistical reasoning, then instances of spontaneous entropy decrease are so unlikely that they are essentially impossible, so the total entropy of everything will always be naturally increasing.

Here’s where we can connect things back to energy. First of all, if you want to reduce the amount of entropy in a certain area – like arranging the bricks into a wall – you have to expend some energy.

## 5.6 Entropy, Part 1: What Is It?

Critical Questions:

• What is entropy?

In order to gain a full appreciation for energy, the last idea you’ll need to understand is something called entropy. It’s kind of a tough one, but I guarantee it’ll be worth it if you persevere to the end of this chapter!

The reason I’ve saved it for last is that many people find entropy quite difficult to understand. There are two reasons for this: one is that it’s another purely abstract concept; the other is that there are about twenty different ways to define entropy, and they all seem very different from each other.

Luckily for us, however, there is one easy way to understand entropy that we can explain with a simple example.

Take a large cardboard box, a can of red paint, and a can of blue paint.1 We’re going to paint the inside of the box in these two colours: red for the left-hand side, and blue for the right.

Once the paint has dried, grab 8 ping pong balls again2 and put them into the box.

1. Note: the actual colours are not important. Let your aesthetic sense be your guide.
2. This is no coincidence. I will not hide the fact that I like ping pong balls.

## 5.5 Heat and Temperature

Critical Questions:

• What is the difference between heat and temperature?
• What happens when water freezes or boils?

It may seem out of place to start talking about heat and temperature in the middle of a chapter about energy, but in fact, there are many connections between these ideas. And in order to understand the ways in which we can and can’t use energy, we have to know something about heat.

The first thing science teachers do when teaching this topic to young people is try desperately to communicate the idea that heat and temperature are, in fact, two very different things. I never really understood why this seemed so important to them, but nevertheless, they’re right.

Heat, in physics, is a quantity of energy that is transferred from one object to another. When you hold your hand over a fire and your hands get hotter, heat has been transferred from the air into your skin.

Temperature, on the other hand, is a measurable property of any object. Specifically, it is a measure of how quickly the particles in that object are vibrating.

You see, it’s fine to picture solid matter as being made up of all of these atoms and molecules and whatnot, but these particles do not sit around waiting for stuff to happen. Even in a seemingly still, solid object, the particles that make up matter are constantly vibrating and bumping into each other.1 And when heat is transferred into an object, its particles vibrate more than before.

1. This is called Brownian motion, named after the Scottish botanist Robert Brown, who noticed this behaviour when looking through a microscope at grains of pollen.

## 5.4 Perpetual Motion Machines

Critical Question:

• What are perpetual motion machines, and why are they impossible?

There was an episode of The Simpsons in which Lisa made a perpetual motion machine, which angered Homer because “it just keeps going faster and faster.” Later, he called her into the room and yelled, “In this house, we obey the laws of thermodynamics!”

He had every right to be angry, but Lisa is not alone in her fascination with the idea of a machine that never stops. As we’ve already seen, motion requires energy, and energy isn’t always easy to come by. But if we had a machine that could keep moving forever without assistance, the possibilities would be endless.

Alas, this is one of those cases that really is too good to be true.

## 5.3 Conservation of Energy

Critical Questions:

• What is energy?
• What do all of the different types of energy have in common?
• How do we use food to move ourselves around?

Now that we’ve described a bunch of different types of energy (in the previous post), we can talk about how they behave. Following on Mr. Feynman’s comments, each of these types of energy has a very specific mathematical formula, so we can calculate exactly how much of each type of energy we have in a given situation.

The most interesting thing about energy is this: it cannot be created or destroyed; it can only change forms.

I’ve already hinted at this idea when talking about the examples from the previous post. Any kind of potential energy can turn into kinetic energy when the object in question is free to move. The simplest example involves one of those wind-up toys you probably had as a kid, or at least you probably saw them in old cartoons.

To make these toys work, you turn a little crank; this tightens a spring inside the toy, which means that you have increased the toy’s elastic potential energy. When you let go of the crank, the spring turns some gears, which cause the toy to spin, or walk, or drive away. Whatever it does, it’ll probably move somehow – in other words, it’s gained kinetic energy. But meanwhile, the spring is no longer wound up, so it’s lost all its potential energy.

## 5.2 What is Energy?

Critical Questions:

• What is energy?
• What do all of the different types of energy have in common?

Despite its abstract and purely mathematical nature (as discussed in the previous section), we’re still going to have to come up with a good definition of energy for the purposes of this site.

The term ‘energy’ in physics means something very similar to what it means in everyday English. If you’re lying in bed and you don’t have the energy to get up, you may actually be lacking in something that could be equated with the scientific idea of energy. (Or you could just be a slothful person.) We would also say that it takes energy to light up our homes and to drive our cars, and this usage fits with the physics one as well.

Already we can see that energy has a lot of different forms – your ability to get out of bed is quite different from a car’s ability to drive down the road, for example. And yet they all have some shared quality in order for us to be able to use the same word to describe them. We do have some excellent mathematics to help us define that similarity, but for now I’d like to propose a loose definition – one which is simplified almost to the point of inaccuracy, but which will nevertheless allow us to come to a better understanding of the topic.

## 5.1 Introduction to Energy and Heat

In my experience, the subject of energy tends to be badly taught in lower-level physics classes. I’ve met a lot of students who, when asked what energy is, can promptly recite the following answer: “Energy is the ability of a system to do work.” Continuing with this website’s theme of trying it yourself, I recommend that you take a field trip to the nearest university campus or high school science class and perform this very experiment, and watch the pride in the students’ eyes as they prove their intelligence to you.

But if you want to throw a bit of a wrench into things, try following up your first question with another: what is work? Many students will frown slightly. Some will say that it is a force exerted over a distance. Others will simply shrug and point at the formula. In other words, most physics students don’t really understand what energy is.