From the earliest steam machines to modern muscle cars, engines have long powered engineering.

I mean, the field is literally named after them. Engines provide us with energy we can use for all kinds of things, and how to optimize them is one of engineering’s central problems.

One of the keys to solving it is the concept of reversibility: the more reversible a system is, the less work it needs from its surroundings. In other words, a more reversible system needs less fuel to keep going. So if you’re trying to build the best engine you can, reversibility is a good place to start. [Theme Music] Engines drive our society and many of the machines we use every day.

And what’s inside many of our engines, are pistons. Pistons are disks or cylindrical parts that move back and forth in a cylinder against a liquid or a gas. In an internal combustion engine, like the one that’s under the hood of most cars, the pistons are pushed by the expanding gases in the cylinder, which turns a type of shaft or wheel.

This turns their repetitive, linear motion into a rotation that helps power the engine. When you’re dealing with a simple machine or mechanism, like a piston, there are two main types of energy you can put into or take out of the system: heat and work. You probably have a pretty good idea of what heat is.

Simply put, it’s thermal energy. It’s what you feel when you step out in the sun or stand by a warm fire. In engineering, we define heat with the letter Q.

Work, represented by the letter W, is a little more complex. It’s essentially any type of energy other than heat that crosses into a system. One way to measure it is by how much force is being applied over a distance.

There are a different types of work you’re likely to encounter as an engineer, but with all of them, the idea is that by putting work into a system, you can get some work out of it, usually in a more useful form. One type is pressure-volume work. This has to do with the expansion and compression of matter.

Squeezing a stress ball is a good example. Based on how much pressure you apply to the ball, the change in volume tells you how much work you were able to achieve. When the stress ball is expanded, we’d say the work is negative, because it’s being done by the ball.

When it’s compressed, the work is positive, because it’s being done on the ball. Pistons involve pressure-volume work, too. In a car, for example, the work done on the system comes from the fuel, which heats up gas in the cylinder when it’s ignited.

As the gas expands, it does work, with the increased pressure pushing the piston up. Then the gas cools again and the piston moves back down. This cycle produces work that turns the shaft or wheel.

Another type of work is shaft work, which is when a shaft or propeller rotates through a liquid or gas. There’s also electrical work, which is the work done on a charged particle by an electric field. You can think of it like the discharge from a battery.

As you’re watching this video, there's electrical work going on in your phone or computer. A lot of engineering is about optimizing your machines and processes to produce the most amount of work with as little input as possible. The more work a machine uses up, the more you need to get out of it, to have it be worth your while.

It’s like a job; the more time and effort you put in, the more you’ll want to get paid. That’s why work is well...work. With machines, optimizing work is all about reversibility.

You’ll never get more energy out of a system than what was put into it. That would violate conservation of energy. But if a process is reversible, that means it can go back to its initial state and start over with no additional work input.

In other words, when a process is reversible, you’re maximizing the amount of work you get for your input. But reversible processes are impossible in real life. They require slow, steady, incredibly small changes to make sure you don’t permanently change the system in a way that you can’t reverse without putting some additional work in.

Which...would require an infinite amount of time. So in the real world, all processes involving work are irreversible. They can be reset, to some extent, but you need to put in a bit of elbow grease to get them there.

A reversible process is more like the best-case scenario – one you can get close to, but never actually reach. In engineering, it’s not so much about whether a process is reversible, but how reversible it is. The closer you can get to reversibility, the more efficient and optimal the process will be.

To see what I mean, let’s go back to that piston. You want the piston to move up and down in the cylinder, to turn a crank, and generate power. There’s also gas in the cylinder.

Bringing the piston up expands the gas and pushing it down compresses the gas. When the gas is under compression, it will expand on its own. But it won’t compress again unless a force is applied to it.

It’s like the stress ball – after you squeeze it, it will expand back to its original size. But the ball won’t randomly crumble back in on itself without an outside force. Say this piston is designed so the force compressing the piston comes from a brick.

When you remove the brick, the gas below the piston will expand will expand freely, and the piston will rise. But to get the gas to compress again and the piston to go back down, you need to lift the brick to put it back on top of the piston. Since the system needs outside work to get it back to where it was, with the gas compressed, this process is irreversible.

Next, let’s say you trying to break the brick in two. The system starts out like before, with the gas compressed by the weight of a full brick. Then you remove one half-brick, leaving it right where the piston was, near the bottom of the cylinder.

The gas still expands, but it doesn’t push the piston as far, since there’s still half a brick’s worth of weight holding it down. Then you remove the other half-brick, and like the first one, you leave it at the same height, let’s say on a shelf right next to the piston or something. This allows the gas to expand as much as it did when you were using one brick, pushing the piston all the way up.

But, think about the amount of work it will take to reverse this process and get the piston to go back down. Before, you had to lift the entire brick all the way from where the piston started to where it stopped when the gas was done expanding. But this time, half the brick is already part of the way up the cylinder, because that’s where you removed it.

So you start by lifting that half-brick up to the top, which compresses the gas and pushes the piston part of the way down. Then, you lift the other half-brick to where the piston is now, pushing the piston down all the way back to where it started. So, instead of having to lift the whole brick all the way up the piston, now you effectively only have to lift half a brick all the way up the piston; it just took two steps instead of one.

That’s a lot less work, which means the process is that much less irreversible than it was with one brick. And now you can start problem-solving as an engineer. If breaking the brick in two makes the process more reversible, how can you make it even better?

A simple answer is to keep breaking the brick into smaller and smaller pieces. Eventually, you’d turn it into infinitely tiny grains of sand. This time, you start with a pile of sand with the same weight as the full brick, pushing the piston down.

Then you remove one grain of sand at a time, leaving each grain at the same height that the piston was when you removed it. Gradually, the piston rises, producing work. But each movement is so small that to reverse the process and move the piston down, all you really have to do is shift each grain of sand sideways.

Remember, we’re talking about increments that are infinitely small, so you effectively aren’t lifting anything. You can keep the shifting grains of sand sideways, and slowly, the weight on the piston will increase, compressing the gas and bringing you right back to where you started. Which is definitely less work than lifting a whole brick, or even a half brick.

In fact, apart from that one grain you’ve lifted from the bottom to the top, the amount of work required to put each grain of sand back on the piston is exactly the same as the work ‘produced’ when you take it off. Everything is happening so slowly and gradually that you aren’t losing energy as heat, which means you don’t need to ‘add’ work to replace that lost energy. So you don’t need to put in any external work to push the piston back down, and you can use the same amount of work produced by the system to get it right back to where it started.

And there you have it: a reversible process. Again, this would be pretty much impossible to accomplish in real life. For one thing, you can’t actually have infinitely tiny grains of sand.

Even a single molecule isn’t infinitely tiny. Plus, you’d need an infinite amount of time to get through all these infinitely small steps. But as you break the brick into smaller pieces, you can get closer and closer.

It’s also worth noting that the closer you get to the reversible version of this process, the longer it will take, which would not be useful for most applications. If this type of piston was in the engine of your car, you’d be better off walking. So reversibility sounds good, but you need to work with irreversible systems if you really want to achieve something.

As an engineer, the goal is to figure out how close you can get a system to being reversible, while still keeping it time, effort, and cost effective. Which brings us to efficiency. In general, the efficiency of any system is the ratio of what you get out of it, compared to what you have to put into it.

It’ll have a value ranging from 0% to 100%, with 100% being maximum efficiency. In this case, efficiency helps quantify how close a system is to perfectly reversible. It’s the amount of work produced by the system you’re looking at, as a percentage of the amount of work that would be produced by the ideal — but impossible — reversible system.

The result is η, the efficiency. If something is 100% efficient, that means it’s a completely reversible system. If it has 0 efficiency, it’s totally irreversible.

You can see how important efficiency is by going back to cars and engines. The more efficient your vehicle is, the more energy you can get out of your fuel, and the farther you can go on a tank of gas. That’s why you’ll want to keep efficiency relatively high in most engineering systems.

It’s especially important whenever you want to sustain a process for a long time, like a cross-country road trip. But sometimes you’ll need to sacrifice efficiency to accomplish your goals. You might need to put a lot of work into a system to do something quickly or get a big output.

Think of a drag race. Converting between types of energy might also be more important than getting a big output for your input, like turning a hand crank to get a small amount of electricity when the power is out. In these situations, converting energy might be worth the low efficiency.

Engineering is all about trade-offs. It’s awesome when you can have great marks all around, but that’s probably not going to happen very often. In today’s lesson, we learned all about how to design the most efficient machines and processes.

We began by going over heat and work: the two main types of energy. We then moved on to reversibility and irreversibility and found that most processes are somewhat irreversible in nature. Putting all of this together, we worked through a problem with a piston and learned how to use efficiency to measure a system.

I’ll see you next time, when we’ll learn about the first law of thermodynamics and the conversation will really heat up. Crash Course Engineering is produced in association with PBS Digital Studios. You can head over to their channel to check out a playlist of their amazing shows, like PBS Space Time, Above the Noise, and Physics Girl.

Crash Course is a Complexly production. And this episode was filmed in the Dr. Cheryl C. Kinney Studio with the help of these wonderful people. And our amazing graphics team is Thought Cafe.