This Tiny Engine Explains Entropy

I have some marbles in a test tube. If I just plug up one end of it and connect to a syringe and then heat the test tube, something amazing happens. It starts moving like an engine. It takes heat and turns it into work. This is another engine that does the same thing. It takes heat from my hand or a cup and turns it into a flywheel that we can use to do work. Both of these devices are doing the same thing. They're taking disorganized energy like heat and turning it into organized energy like work. But here's the important question. If you have heat energy in a hot object and you let it flow to a cold object, what's the maximum amount of work you can get out of it? Well, it turns out there's a very strict limit and it has nothing to do with friction or bad engineering. So let's look at how one of these engines works. But before we continue, I want to thank the sponsor for this video, Anker. Why can't my charger be high power, compact, and stay cool at the same time? If you increase the power, you usually get more heat. — If you try to reduce the heat, you need bigger components. But Anker has been trying to solve this problem by pushing past what seems like hard limits. By using gallium nitride instead of traditional silicon, they can make chargers much more compact while still delivering the high power. In 2025, they introduced MBuck topology driven by proprietary algorithms. Traditional chargers hit a bottleneck with the inductor. The higher the power, the bigger it must be. But MBuck combined with Anker's algorithm drastically reduces the current impact on the inductor and increases its switching frequency, shrinking the inductor to just a fourth of its traditional size. At the same time, they're tackling the heat issue with systems like Active Shield, which performs over 10 million temperature checks every single day. They've also implemented a molded potting compound for thermal equalization combined with an L-shaped graphene layer to keep things running efficiently. Instead of just pushing power into whatever it's plugged in, it uses intelligent power distribution, what they call power cube. It relocates idle power every 2 minutes, and a 160 W charger is equivalent to three original chargers totaling 210 W. So, with Anker, instead of choosing between fast, small, or cool, you're starting to get all three at once. So, if you want to check out how Anker is continuing to push past these limits and solve real engineering problems in charging, you can check them out in the link below in the description. Now, let's get back to our experiment. This is something called a Stirling engine. A Stirling engine is a type of heat engine that converts heat into mechanical work. So, in my marble device, at its resting state, if I heat up the air on this side, the marbles aren't airtight, so the total volume of air inside expands and pushes on the syringe. This increases the overall volume and pushes up the syringe that pushes on the test tube, so now the marbles eventually fall due to gravity to the other side. Now, this small volume of air here gets moved to the other side now, but the other side's much colder. So, the air cools down and contracts. This decreases the total volume and pulls the syringe back down, and then the marbles fall back to the other side, and the process repeats over and over again. So, this is an engine, and we could use it to do work both on the down stroke and the up stroke. The same thing's happening with the other Stirling engine as well. It's just a little bit harder to see. This black piece in the middle is like our marbles. It isn't airtight, but when it moves, it shifts where the large volume of air is, moving it from the hot side to the cold side. And when it's on the hot side, the air expands, moving this driving piston. And when it's on the cold side, it contracts, sucking the piston down the other way. So, Stirling engines don't just need heat, they need a difference in temperature in order to work. So, I could even make it work a different way by cooling the cold side down instead of heating the hot side, and it still works the same way. Stirling engines are actually some of the most efficient engines that exist, but there's another engine that's even more efficient than the Stirling engine that's one of the most important engines in physics called the Carnot engine. Carnot was an engineer who wanted to figure out the most efficient engine possible. So, instead of building one, he imagined the perfect engine by doing a thought experiment that avoids every possible loss. And what he discovered are something really surprising. The main thing that limits how much work you can do isn't friction, it's entropy. The enemy of work is entropy. Work is organized energy, but entropy is energy becoming more spread out. So, the more entropy you create, the less work you can get out. So, let's start with the worst possible engine where we get no work and just create entropy. If you just take a hot piece of metal and a cold touch them together, you get zero work out of it. All that happens is heat spreads out and entropy increases. We can quantify this with a simple relationship. The change in entropy is equal to the heat transferred divided by the temperature. So, if we put some numbers to this

suppose we take 100 J of heat out of a hot block at 400 K, the entropy change of the hot block would be that heat divided by 400, which gets -0. 25 J per K. Now, we take that same 100 J and put it into a colder block at 300 K. The entropy change of the cold block would be that same heat divided by 300 now, which is about +0. 33 J per K. Now, if we add those together, we get a positive increase in entropy. So, even though the same energy moved, adding heat to the colder object increases entropy more than removing it from the hotter object decreases it. So, the disorder doesn't cancel, it increases. This is happening because of the lower temperature. If you were able to just take heat from a hot block and somehow add it to another hot block at the same temperature, this would be an overall change of zero entropy. But is this possible to exchange heat with no temperature difference? Well, in theory, yes. This is part of the Carnot cycle that aims to exchange heat without increasing entropy. In theory, you could have a gas at the exact same temperature as the hot source and add heat to it while it's able to expand and push on a piston. If everything is perfectly controlled with no friction and perfect heat transfer, then this step creates zero entropy and only produces work. Then you remove the gas from the heat source and let it expand further without any heat transfer. This changes its temperature, but still creates no entropy. Then you compress it back down and attach it to a cold source at the same temperature doing the reverse process. So now you've taken heat from the hot side and moved it to the cold side and extracted work without creating any entropy. That's the Carnot engine, a perfect engine with no creation of entropy. So it seems like this would be really efficient, but here's the surprising part. — Even though we created zero entropy, we still don't get 100% efficiency. The efficiency is equal to 1 minus the heat you have to dump into the cold side divided by the heat you took from the hot side. And since heat is equal to temperature times entropy, the heat coming from the hot side is the hot temperature multiplied by that entropy. And the heat dumped into the cold side is the cold temperature multiplied by that same entropy. — So when you take the ratio, the entropy cancels out and you're left with efficiency being equal to 1 minus the cold temperature divided by the hot temperature. So if we plug in real numbers, if the hot side's 573 K and the cold side's 373 K, then the efficiency is about 35%. That means if we put in 100 J of heat, we only get 35 J of work. So this is We're not even talking about friction losses. Even with perfect insulation and perfect heat transfer in a perfect engine, we're still only 35% efficient. This limit is called the Carnot efficiency, and it applies to every heat engine you could possibly come up with, including real car engines. And it also sets the fundamental limit for devices like Peltier plates that transfer heat from a hot side to a cold side. So, this is frustrating. The energy is there in heat, but when we try to use it to do anything, we run into this Carnot efficiency limit. But that limit actually tells us something really important. The greater the temperature difference between the hot and cold side, the more that heat can be turned into work. I used to think it was just because it gives you a stronger driving force, but in reality, it's because a larger temperature difference means less entropy has to be carried to the cold side per unit of energy. So, more of that energy can be converted into useful work. Now, some of you might be wondering about the efficiency of electric motors. Electric motors can be super efficient, approaching 100% with some of the best lab-grade motors at around 99% efficiency. So, how can these motors be so efficient when I just showed you the impossibility of approaching 100% in the Carnot engine? Well, the difference is with electricity, you're going from an ordered energy state like electricity to another work. And that can be done in a really efficient way. But in reality, in order to achieve that high ordered initial electric state, you had to first have done something that was inefficient, like change heat into work. So, every very efficient electric motor is hiding the fact that beforehand, there was some inefficient process that got it to that state to start with. So, it's not that we're running out of energy, it's that we're constantly turning useful energy into less useful forms. And once that happens, you can't get it back. So, the point is use your energy wisely. Make a picture of me giving Isaac Newton a high five. And thanks for watching another episode of the Action Lab, and we'll see you next time.