Think of all of the developments throughout history that led to the conveniences you enjoy today.

If I had to pick the biggest game-changer in human technology, it would probably be the steam engine.

During the industrial revolution, the steam engine powered machines in farms and factories.

And, although it may not seem so, those advances eventually led to the technologies that you're using to watch me, right now.

So, the steam engine was a pretty big deal.

Developing a practical steam engine involved a lot of time and a lot smart people, and about a hundred years, and three main inventors.

And it took a solid understanding of thermodynamic processes - and heat engines - to make this world-changing technology, a reality.

[Theme Music] Heat engines, like steam engines, turn thermal energy into mechanical work, and they do it in a repeating cycle.

The process starts at a high operating temperature, which we label as T-_H, and ends up at a lower operating temperature, T-_L.

In the process, the engine takes the input heat that was used to raise the temperature, known as Q-_H, and turns some of it into work, while also releasing some heat - Q-_L - as exhaust.

Then the engine's temperature is raised once more, so it can start the cycle all over again.

OK, now think back to the first law of thermodynamics, which says that the change in the thermal energy of a system is equal to heat and work.

In the case of a heat engine, the change in thermal energy is zero, because it always returns to the temperature it started from.

So, the engine's input heat must be equal to the work it does, plus the heat it releases.

Now let's see how this plays out in a steam engine.

There are a few different types of steam engine, but we'll focus on the basic reciprocating type.

As long as you have something to "heat" the steam, like coal or oil, the engine keeps working.

That's the input heat.

The input heat is used to heat a volume of water, which turns to steam.

Then, an intake valve opens, allowing the steam into the engine.

The steam expands and moves a piston outward - that's the work done by the engine.

Then the intake valve closes, and an exhaust valve opens.

The exhaust valve leads to a condenser, which cools the steam back into water.

The lower temperature also lowers the pressure, creating a partial vacuum that makes the piston move back into its original position.

Then the water gets heated back into steam, and the cycle starts over.

As the engine runs, the motion of the piston can be translated into all kinds of different movement, which is how steam engines can do things like move trains and boats, and run factory lines.

But as the steam engine runs, it releases exhaust heat.

The more exhaust heat it produces, the less efficient the engine is, and the more energy you have to put in for the same amount of work.

Obviously, it's important for engines to be as efficient as possible to save energy.

And to design an efficient engine, engineers have to be able to calculate its efficiency.

Like we said earlier, an engine's input heat is equal to the work it does, plus its exhaust heat.

And the more work - and therefore, the less exhaust heat - you get out of the input heat, the more efficient your engine is.

So, efficiency is equal to the work done by an engine divided by its input heat.

We can also put this just in terms of input heat and exhaust heat - pretty easily, actually.

We know that work is equal to input heat minus exhaust heat.

So efficiency is equal to input heat minus exhaust heat, divided by the input heat.

Or, simplifying those terms: efficiency is equal to 1 - exhaust heat / input heat.

If your engine produced no exhaust heat at all?

We'd say that its efficiency was exactly 1.

It would be perfectly efficient.

But there's no such thing as an engine that produces no exhaust heat at all.

It wouldn't work, because the temperature needs to be lowered and then raised again for the engine to keep going.

But we can imagine an ideal engine, where none of the exhaust energy is waste heat - where there's no friction or anything like that.

An ideal engine would also be reversible - meaning, you could run it backward, putting in work to transfer heat from something with a lower temperature to something with a higher temperature.

This kind of hypothetical engine is called a Carnot engine, and we can use it to figure out the maximum possible efficiency of a real-life engine.

Last time, we talked about the four types of basic thermodynamic processes.

The Carnot engine combines two of those types into what's known as the Carnot cycle.

But in the Carnot cycle, those processes don't transfer heat between areas with different temperatures.

Because, if an engine involves heat transfer from an area with a higher temperature to an area with a lower temperature, then reversing the engine would involve transferring heat from lower to higher.

Which would violate the second law of thermodynamics!

So, in the Carnot cycle, heat won't flow between areas of different temperatures at all.

Instead, the cycle goes through two adiabatic processes, where heat is held constant, and two isothermal processes, where heat is transferred.

But the temperature is held constant, so the heat never flows between areas of different temperatures.

Now, you might be wondering how heat gets transferred, if there's no difference in temperature.

Well, remember how we described isothermal processes last time: In those cases, there are only very tiny differences in temperature, and they're immediately eliminated.

So, practically speaking, there is no transfer of heat between areas of different temperatures.

And this means, the process can still be reversed.

With all that in mind, here's how a Carnot engine works - at least in theory, because again: Carnot engines are totally hypothetical.

The first process in the cycle is isothermal.

The temperature is constant, but heat is slowly added.

That makes the gas's volume expand and its pressure decrease - path a-b on this diagram.

The second process is adiabatic.

The temperature drops while the heat stays constant, which also makes the volume expand and the pressure decrease.

That's path b-c on the diagram.

The third process is the opposite of the first one, and it's also isothermal.

The gas is compressed while the temperature is held constant, so it releases heat and its pressure increases while its volume decreases.

That's path c-d.

The last process is the opposite of the second: it's adiabatic, so the gas is compressed but its heat doesn't change.

That makes the gas's volume decrease and its pressure increase, like in path d-a.

Its temperature goes back up to the starting point.

The Carnot engine is the ideal engine, because it produces the most possible work from a given temperature difference.

And because a Carnot engine is as efficient as possible, the high and low temperatures are proportional to the input and exhaust heat.

Which is important, math-wise, because it means that in the equation for efficiency, you can replace Q-_H and Q-_L - the input and exhaust heat - with T-_H and T-_L - the higher and lower operating temperatures.

Which can help if you don't know an engine's input and exhaust heats, but you know its operating temperatures.

So!

The ideal efficiency for an engine is equal to: 1 - its low temperature / its high temperature.

The colder that lower operating temperature is, the more efficient the ideal version of the engine is.

So, say you need an engine to power a life-size Mario Kart that you're building for yourself.

You find an engine online, and you're thinking about buying it, but first you want to know how efficient it is.

The manufacturer's website says that for every second, the engine's input heat is 10 kilojoules at 500 Kelvin.

Its exhaust heat is 2 kilojoules at 300 Kelvin.

The efficiency equation says that the engine's efficiency is equal to: 1 - its exhaust heat / its input heat - in this case, 0.8.

That would be a very efficient engine, so you should be a little suspicious.

I mean, is that kind of efficiency even possible?

You can find out, by checking the ideal efficiency of the engine - the Carnot efficiency.

The ideal efficiency is equal to: 1 - its lower operating temperature / its higher operating temperature, which in this case is equal to 0.4.

It's impossible for this engine to have an efficiency higher than 0.4, so the manufacturer's website is...well, just lying.

So you probably shouldn't buy anything from them anyway.

And, actually, you probably wouldn't want an engine that was close to the efficiency of a Carnot engine, because Carnot engines are very slow.

During those isothermal processes, the temperature has to be kept constant while heat is transferred - which only works if the heat is transferred super slowly.

So the engine has to be really slow.

If you had a Carnot engine in your car, for example, it would take you a whole day to get out of your driveway.

Real-life heat engines are useful, because they use the flow of heat from something warmer to something cooler to produce work.

But what if you want heat to flow from something cooler to something warmer?

That's what things like air conditioners and refrigerators do, and they were originally developed using the principles scientists had learned from creating steam engines.

These cooling machines are a lot like the opposite of heat engines, in the sense that they use work to make heat flow in the opposite direction that it would normally go.

The refrigerator, for example, passes a cool liquid through the inside of the fridge.

The liquid absorbs heat - that's Q-_L - as it evaporates.

Then, the fridge uses a motor to do work on the now-warmer fluid, which has turned into a gas.

It's passed through coils on the outside of the refrigerator, where it releases the exhaust heat - Q-_H - and cools to become a liquid again.

Then the cycle starts over.

For heat engines, efficiency is measured by the work produced for a given amount of input heat.

And there's a similar concept for refrigerators: the coefficient of performance, or COP, which is equal to the amount of heat removed from the lower-temperature zone divided by work.

The more heat the fridge removes for a given amount of work, the higher the coefficient of performance.

Like we did with the efficiency equation, we can rewrite the COP equation just in terms of Q-_L and Q-_H.

The coefficient of performance is equal to Q-_L divided by Q-_H minus Q-_L.

To find the coefficient of performance for an ideal refrigerator, we do the same thing we did with the ideal Carnot engine: replace Q-_L with T-_L and Q-_H with T-_H.

So, for an ideal fridge, the coefficient of performance would be equal to: the lower operating temperature, divided by the higher operating temperature minus the lower operating temperature.

And of course, a real-life refrigerator can't have a higher coefficient of performance than an ideal refrigerator.

Now, it may not be surprising that steam engines and refrigerators are total opposites.

But!

Fridges and freezers and air conditioning are all game-changing inventions that were only made possible by our knowledge of steam engines.

Today, you learned about how engines turn thermal energy into work and how to calculate their efficiency.

We also described the Carnot engine.

And finally, we talked about cooling machines, like refrigerators.

Crash Course Physics is produced in association with PBS Digital Studios.

You can head over to their channel and check out a playlist of the latest episodes from shows like: PBS Space Time, Deep Look, and Blank on Blank.

This episode of Crash Course was filmed in the Doctor Cheryl C. Kinney Crash Course Studio with the help of these amazing people and our equally amazing graphics team, is Thought Cafe.