Previous: Playing with Power: P-Values Pt 3: Crash Course Statistics #23
Next: Pre-Columbian Theater, Spanish Empire, and Sor Juana: Crash Course Theater #22



View count:287,796
Last sync:2022-12-29 20:30
We’ve introduced the 0th and 1st laws of thermodynamics, so now it’s time to move on to the second law and how we came to understand it. We’ll explain the differences between the first and second law, and we’ll talk about the Carnot cycle and why we can never design a perfectly efficient engine.

This episode is sponsored by CuriosityStream:

Crash Course Engineering is produced in association with PBS Digital Studios:


Çengel, Yunus A., and Michael A. Boles. Thermodynamics: An Engineering Approach. 8th ed., McGraw-Hill Education.


Crash Course is on Patreon! You can support us directly by signing up at

Thanks to the following Patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:

Mark Brouwer, Erika & Alexa Saur Glenn Elliott, Justin Zingsheim, Jessica Wode, Eric Prestemon, Kathrin Benoit, Tom Trval, Nathan Taylor, Divonne Holmes à Court, Brian Thomas Gossett, Khaled El Shalakany, Indika Siriwardena, SR Foxley, Sam Ferguson, Yasenia Cruz, Eric Koslow, Caleb Weeks, Tim Curwick, D.A. Noe, Shawn Arnold, Ruth Perez, Malcolm Callis, Ken Penttinen, Advait Shinde, William McGraw, Andrei Krishkevich, Rachel Bright, Mayumi Maeda, Kathy & Tim Philip, Jirat, Eric Kitchen, Ian Dundore, Chris Peters

Want to find Crash Course elsewhere on the internet?
Facebook -
Twitter -
Tumblr -
Support Crash Course on Patreon:

CC Kids:
Thanks to CuriosityStream for supporting PBS Digital Studios.

We’ve made some improvements in recent decades when it comes to how we power our society. But by and large, our world still runs on fossil fuels and nonrenewable energy.

And as long as we’re dependent on these limited resources, we’ll need to design the most efficient ways to harvest their energy. But, that’s difficult, because the laws of physics are not in our favor. The fact is, you can’t make a super-efficient system without any waste.

No matter how good of an engineer you are, you can’t invent a perfect engine. Why? It’s because of an energy crisis that pervades our universe.

And it’s caused by entropy and the second law of thermodynamics. [Theme Music] Since we’ve started designing engines, we’ve constantly tried to improve them. Our first engines weren't that efficient, but we’ve come a long way since. Take, for example, a heat engine.

Simply put, a heat engine is a machine or system that converts heat into other forms of energy. And we can see how efficient they are, by looking at their thermal efficiency. The thermal efficiency of a heat engine is the amount of useful work it can produce based on the amount of heat that we give it.

So the more work we get out, the more efficiently we use our fuel, and the less of it we need. That’s why engineers are constantly trying to make engines that are as thermally efficient as possible. Many of the internal combustion engines that you find on the road are around 20% thermally efficient, meaning that 20% of the heat that’s applied n the engine actually does work.

There are some prototypes of automotive engines that are 40% efficient. And there’s even an air-cooled gas turbine that delivers an over 61% combined cycle efficiency. That’s impressive, but still it’s not even close to 100%.

This seems to be our limit for how efficient our engines can be – at least for now. So what gives? Why aren’t they any better?

Well, we’re restricted by thermodynamics. You see, the first law makes it all seem pretty simple. If we can’t create or destroy energy, then any change in energy that we have, must have an equal and opposite change in energy somewhere else.

But in reality, it’s a bit more complicated than that. Based on the first law alone, you might think that you could simply recycle energy over and over again. But while energy can’t be created or destroyed, it can change into less useful or even unusable forms.

In fact, every real-world energy conversion has some amount of energy that changes into a form that’s unavailable to do work. And this less-usable energy that’s lost is usually heat. But can’t we just convert that heat back to work?

Well yes, but not entirely. Heat can never be turned into another, work-performing type of energy with 100% efficiency. So every time you have a transfer of energy, you’ll end up with some more “useless” energy.

For example, let’s say you have a hot bowl of soup in a cold room. Over time, the soup will cool off, and whatever energy it loses, its surroundings will gain. But you can’t take the energy from the cold room and use it to heat the soup back up, even though the exchange didn’t violate the first law.

Or think of it in terms of electricity running through a wire that goes to a radiator and generates heat. Electricity goes in, and heat comes out. But if you tried heating the wire, you wouldn’t get electricity back, even though, once again, the first law isn’t violated.

This is where the second law of thermodynamics comes in. While the first law is all about the total quantity of energy, the second law is all the quality of energy. The second law states that as energy is transferred or transformed, more and more of it, is wasted.

It basically restricts the inter-conversion between heat and work. 100% of the work that you put into a system can be converted into heat, but 100% of heat can’t be converted into work. So to understand what this really means, let’s look at a heat engine, an engine that converts heat into energy that does work. Say we put some heat energy into the engine.

The system will take the heat, go through a process, and give us energy in the form of work. But some of the heat will always be released at a cooler temperature as a secondary output. No heat engine could operate without doing this.

Basically, unless we’re only trying to get heat, we’re going to have some amount of inefficiency. So how did we find any of this out? Well, it all goes back to the work of two great minds.

The first of these minds belonged to Sadi Carnot, a French scientist who was probably more brilliant than we’ll ever know. Carnot came from a famous and influential family. His father was a mathematician and a military engineer whose name would eventually be emblazoned, along with those of other scientists, on the Eiffel Tower.

And Carnot followed in his father’s footsteps, joining the French army corps of engineers in 1814. But, then things got sticky. His father had become minister of the interior, under a fellow named Napoleon.

And after Napoleon met his literal Waterloo and the monarchy was restored, Carnot’s father was sent into exile. But Carnot was allowed to stay – languish is probably a better word. He spent years inspecting army facilities and writing reports that no one read.

Until, in 1819, he transferred back to Paris and, out of curiosity, started attending lectures on chemistry and physics. And there, he became especially interested in improving the performance of steam engines. He published his research in a book called Reflections on the Motive Power of Fire, in 1824.

And although his work was largely ignored, it contained a revolutionary idea: a model for the most efficient steam engine possible. Today it’s known as the Carnot engine, and the process by which it works is called the Carnot Cycle. The Carnot cycle is actually a hypothetical process – it’s the most ideal cycle of changing pressures and temperatures in a fluid.

And it’s ideal because it assumes there aren’t any sources of waste, like friction or the conduction of heat between different parts of an engine. So we use this cycle as a standard to judge the performance of heat engines. The Carnot cycle consists of four processes, all of which are reversible – two adiabatic and two isothermal ones.

And it can take place in either a closed or a steady-state system. Let’s look at it in a closed system. Let’s say we have a gas that’s contained in an adiabatic piston-cylinder device.

As we start up our piston, the first process in the Carnot cycle is called reversible isothermal expansion. In this stage, the head of the cylinder starts in close contact with an energy source, or reservoir, at temperature TH. This will transfer heat, which we’ll call QH, to the gas.

As the energy source transfers heat, the gas starts to expand slowly, which does work on the surroundings. As the gas expands, its initial temperature, TH, tends to decrease. But as soon as the temperature drops by a very small, almost negligible amount, some heat is transferred from the reservoir to the gas, which warms it up, bringing it back to its initial temperature.

That means that the temperature of the gas is basically kept constant throughout the process, which will continue until the piston reaches position 2. At this point, we come to the second stage of the Carnot cycle: reversible adiabatic expansion. Here, we’ll make the process adiabatic by replacing the reservoir with insulation.

This means that as the gas expands, it can cool down, since it won’t be heated back up by the reservoir anymore. It will do this until its temperature drops from TH to TL, which brings us to position 3. Halfway there!

Now we just need to go in the opposite direction as we begin the third stage of our cycle: reversible isothermal compression. So now let’s remove the insulation and bring the cylinder into contact with an energy sink at temperature TL. This will cause the gas to transfer heat, which we’ll call QL, to the reservoir.

Now, when some external force pushes the piston inward, which does work on the gas, the gas will compress and its temperature will tend to rise. But as soon as the temperature rises by a very tiny amount, some heat is transferred from the gas to the sink, which cools it down, causing the temperature to drop back down to TL. Now, you’ll notice that this is really similar to what happened in the first stage!

The temperature of the gas will stay the same throughout this process until the piston reaches position 4. Now we’re at the fourth stage of our cycle: reversible adiabatic compression. In this last stage, we’ll put the insulation back on, making the process adiabatic again.

The gas will continue to slowly compress until its temperature rises from TL to TH, which will complete the cycle and bring us back to where we started. And, since we’re back where we started, we have a fully reversible cycle. This makes the Carnot cycle the most efficient cycle that we can have between two different temperatures.

Now, even though we can’t actually achieve it in reality, we can improve the efficiency of our cycles if we try to model them more closely to Carnot’s design. His work shows us that the efficiency of a heat engine is only dependent on the temperatures of its heat reservoirs, rather than the types of fluids that it uses. As such, the maximum attainable efficiency of a heat engine is equal to one minus the temperature of the cold sink divided by the temperature of the heat reservoir.

Now, remember when I said that Carnot was probably more brilliant than we’ll ever know? Well, let me finish his story. Soon after he published his work on the Carnot cycle, he quit his job with the army and was left without an income or any pension.

Diagnosed with “mania” and “general delirium,” he was then sent to an asylum, where he contracted cholera, which was sweeping through Paris at the time. Carnot died at the age of 36. And because all of his personal belongings were considered to be contaminated, they were buried with him, including all of his notebooks and papers.

So, the full scope of his work, and his genius, has been lost to history. Nonetheless, we do know that Carnot discovered the limitation of efficiency, and his work has become foundational to our understanding of wasted energy. But, Carnot’s insights alone don’t fully explain why we can never build the perfect engine.

We still need to understand another property – one that wasn’t even put into words until a few decades after Carnot came up with his cycle. The great mind who gave us this property was Rudolf Clausius. Clausius was a German mathematician and physicist who introduced the concept of entropy around 1850, after he recognized the confusion between Carnot’s work and the conservation of energy.

Entropy is the measure of a system’s thermal energy per unit temperature that’s unavailable for doing work. It’s also the measure of the disorder, or randomness, of a system. Mathematically, if the entropy for a system is 0, then we have a reversible process with no change in entropy, like with a Carnot engine.

Any value over 0, and then the process is irreversible and gains entropy. So, every process results in either no change in entropy or an increase in entropy. It’s impossible to have an overall decrease in entropy.

If you’re only looking at a system itself, it’s possible to have a decrease in entropy. But, and this is very important, the entropy of the system’s surroundings and the universe would have to increase by an amount greater than or equal to the loss of entropy inside the system. Simply put, our universe always tends toward disorder.

It’s just the way of all things. In fact, scary as it may be, entropy and the second law of thermodynamics actually predict the end of the universe as we know it! If everything is tending toward disorder, than the logical conclusion is that all of the usable energy in the universe may one day be converted to heat.

This event is known as the heat death of the universe and, in addition to being a really wonderful band name, it may one day be our fate. I wouldn’t worry about it, though, because while it makes sense in theory, many doubt if it would actually happen. And even if it did, it probably wouldn’t happen for a really long time.

But whether or not entropy will cause the universe to end, it does make it impossible to create a perfect engine with an output of 100% work energy. We can try to get closer than we already are, but no matter how inventive we get as engineers, we always have to follow the rules of the universe – even if it’s one that will lead to our own doom.

So in today’s lesson, we learned about the second law thermodynamics and how we came to understand it. We started by talking about the differences between the first and second law of thermodynamics and how the second law focuses on quality over quantity. Then we talked about the Carnot cycle and how it’s the most efficient form of a heat engine with temperature differences.

We ended our lesson by going over entropy and the randomness that can occur with a system. I’ll see you next week, when we’ll learn more about heat engines and how systems can operate on a cycle. Thank you to CuriosityStream for supporting PBS Digital Studios.

CuriosityStream is a subscription streaming service that offers documentaries and non-fiction titles from a variety of filmmakers, including CuriosityStream originals. For instance, CuriosityStream has a series called “Breakthrough” that’s a deeper look at some major recent developments in physics, astronomy and other sciences. You can learn more at and use the code crashcourse during the sign-up process.

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 The Art Assignment, Deep Look, and It’s Okay to Be Smart. 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.