Surely it Breaks The 2nd Law

When I blow air into this device, it separates the air into cold molecules that come out of this end and hot molecules that come out of this end. See how the hot end can melt gallium? It doesn't use electricity and there are no moving parts. Isn't that crazy? Maybe you've seen one of these things before. It's called a vortex tube, but look, I managed to get one made of glass so that we can see what's going on inside. And I cut one in half. So, we really should be able to figure out how these things work. I love vortex tubes because straight away it feels like we must be violating some law of thermodynamics. You know what I mean? Like obviously fridges do it. They make the inside cold and the outside hot, but that's like a whole complicated machine. This thing just separates air into hot and cold. How is that possible? Well, a famous scientist called James Clark Maxwell also thought about separating hot and cold molecules. He imagined a little demon at the opening between two containers of gas. Like a bouncer, the demon only lets hot molecules pass through in this direction and cold molecules in this direction until eventually all the hot and cold molecules are separated. But that would violate the second law of thermodynamics. You can't just sort hot and cold like that without expending a whole load of energy in the process. That's why your fridge stops working when you unplug it from the mains. But this thing isn't plugged in anywhere. It feels like this is Maxwell's demon in mechanical form. But it can't be, can it? If we can get our heads around the working principle of a vortex tube, we should be able to answer that question. The first thing you'll notice is that the inlet tube is off center. So when the air enters the main tube here, it forms a vortex spinning counterclockwise. This wall here prevents that spiraling air going in this direction. So you end up with this twisting corkcrew motion in this direction. You can see it for real here where we've added particles into the stream. When this vortex of air reaches this end, there's a tiny gap around the outside edge and some of the air escapes. The rest is forced into the middle of the tube. Angular momentum is conserved, so it's still spinning. So, you've got this second vortex traveling back down the tube through the middle. This inner vortex lines up with the hole in the wall. So, you have another stream of air coming out this end. This is the cold end and this is the hot end. But how? Well, I mentioned earlier that angular momentum is conserved when some of the air moves into the center of the tube. And you might know from ice skaters that they spin faster when they pull mass into the middle. And the same thing happens here. When the spinning air is forced into the middle of the tube, all that angular momentum is concentrated into a smaller space and so it spins faster. So you've got an outer vortex and an inner vortex, but one of them is spinning faster than the other. That's the first important thing. The second important thing is that with all this air spinning around, we've basically got a centrifuge. With a centriuge, the gas feels like it's being flung outwards. So, you have high pressure around the outside and low pressure in the middle. I've made a little animation here of what's going on. Let's spin the camera at the same rate as the vortex. So, we're now in the rotating reference frame. And so, we have centrifugal force that points outwards like this. In this animation, I'm holding the gas molecules back with a barrier. Let's remove the barrier to see what happens. Well, because some of the molecules are whizzing around in all different directions because of the thermal energy they have, some of them will move up into the middle of the tube, and some molecules will get assists off other molecules further down, kicking them into the middle. In other words, the gas expands into the middle. But because of that centrifugal force, when they move into the middle, they're moving against a force. It's a bit like throwing a tennis ball directly up in the air against gravity. The kinetic energy you give the ball at the beginning turns into gravitational potential energy. In other words, the ball slows down. And the same thing happens with these gas molecules. They lose kinetic energy as they climb into the middle against that centrifugal force. And kinetic energy at the molecular level is just thermal energy. So the gas cools down. So those are the two important differences. The inner vortex is spinning faster and it's colder. And so, I mean, that's great. We've got cool air now. We did it. The end. Except unfortunately, it's not that simple. Because actually, we have to worry about the total energy of that inner vortex. Because here's the thing, the gas has actually got two types of energy. It's got thermal energy, which is that random chaotic jiggle of the molecules, but it also has bulk kinetic energy, which is like the overall flow of the gas, like the movement you can see with your eyes at the microscopic level. This is what a gas with just bulk kinetic energy looks like. And this is a gas with just thermal energy. And this is a gas with both. But here's the thing about gases. That bulk kinetic energy will always become thermal energy eventually. That's called dissipation. See how any kind of bulk movement of the gas molecules eventually just becomes random chaotic jiggle. So, if we could capture this fastmoving jet of cold air going through the center of the tube and allow it to settle, well, it would come back up to room temperature because all of that bulk kinetic energy would be converted back to thermal energy. So, you've got these kind of energy bank accounts. Thermal energy and bulk kinetic energy. Think about this animation from earlier. For example, this shows thermal energy being turned into centrifugal potential energy. But actually, that's not quite right because in this animation, I forgot to model the corololis force. In this more accurate simulation, when the particles move towards the middle, the corololis force causes the gas to rotate. So, actually, thermal energy is being converted to bulk kinetic energy when the gas enters the middle of the tube. In the same way that my muscles had to do work to pull these weights closer to my body and that work was converted into the kinetic energy of my increased spin. The thermal energy of the gas does work as it expands into the middle and that's turned into the kinetic energy of the gas spinning faster. And of course, this bulk kinetic energy would very quickly dissipate back to thermal energy. Except that the vortex tube does something really clever. It steals some of that bulk kinetic energy before it has time to dissipate back into thermal energy. In other words, it slows down the spin of that central vortex. But how does it do that? Well, remember the inner vortex is spinning faster than the outer vortex. And air has a bit of viscosity, which you can think of like a bit of friction between the two vortices. Just like if you had a fast spinning disc with a slow spinning ring around it, if you introduced some kind of viscous fluid between the two, well, the spinning disc would drag the outer ring around, causing it to speed up. And conversely, the outer ring would drag on the inner disc, slowing it down, so their rotations equalize. So, let's rewind a little bit. When the gas first enters the center of the tube, some of its thermal energy is converted into bulk kinetic energy. In other words, it gets colder, but then some of that bulk kinetic energy is transferred into the outer vortex, leaving just a cold, slowmoving gas, and that's how we get the cold end. But let's think about the bulk kinetic energy we just transferred to the outer vortex. Remember that in a gas bulk kinetic energy will always eventually turn into thermal energy. That happens in the outer vortex as well. And so that gas gets hotter and that's how we get the hot end. As it goes, this glass vortex tube isn't amazing at separating hot and cold. It's not the most efficient vortex tube in the world. Whereas this one that you can buy has been optimized in lots of ways. I got one cut in half so you can see the differences. The most important one probably is that the air is injected at several points around the tube instead of just one point in the case of the glass vortex tube. I'm not exactly sure why that makes it more efficient, but it does. I didn't realize this until I cut it in half, but look, you can actually adjust the amount of space that the hot vortex can escape through. And that's going to change the balance between like how much cold air comes out and how cold it is. And then there's a diffuser on this end which I think promotes that dissipation that we talked about. But I got the glass one made with the simplest possible geometry for clarity. Just one inlet and two outlets. And even that works though there are a number of optimizations that you have to make even for that. Like what's the optimum ratio between this area and this area or this length and this length for example. I ended up printing out about five or six prototypes before eventually getting the right spec to send to my glass blower. And that cone-shaped valve is just something that I then 3D printed because I needed to finesse that. I think it's come out really well. So, do we now have everything we need to be able to explain why this thing doesn't violate the second law of thermodynamics? Well, maybe you already know that the second law of thermodynamics tells us that entropy always increases. And you might have an idea of what entropy is. But my preferred definition is that entropy is a measure of how spread out the energy in a system is. In fact, I made a whole video about that years ago, link in the description. But in summary, this is low entropy and this is high entropy. And this is low entropy and this is high entropy. So on the surface, if you take all the thermal energy of a load of molecules and you concentrate that into just half of those molecules, in other words, the hot jet, well then entropy must have gone down because the energy is less spread out. It's more concentrated among fewer molecules. So if we don't want to violate the second law of thermodynamics, entropy needs to be going up somewhere else. And actually, we don't have to look far to see where that is. So, the transfer of energy between the two vortices only happens because the vortices are spinning really fast relative to each other. And they're only spinning really fast because we're injecting air into the system at high pressure. And the air is under pressure because it's being supplied by this air compressor. In other words, we've got a load of energetic molecules all clumped together inside the air compressor. But when these molecules leave the compressor via the vortex tube, they return to atmospheric pressure. And so they spread out. And so we have clumped up energy spreading out. In other words, entropy goes up. And if you do the maths, the entropy goes up more because of that than the entropy went down because of the separation of hot and cold. And actually, if you want to go even further back, like I had to plug this thing in for it to be able to compress the air in the first place. So, we're using energy in the process just like a fridge. And just like a fridge or an AC unit, what we have here is a heat pump. Though, actually, the vortex tube works in quite a different way to those heat pumps. And in fact, it turns out that a vortex tube is an incredibly inefficient heat pump. A bog standard fridge might have an efficiency of say four, whereas a vortex tube is more like 0.1. So, if they're so inefficient, why do people ever use them in the first place? Well, for several reasons. Like, if you're already in a workshop and you have access to compressed air or shop air, then it's really convenient. Especially if you want to do localized cooling and you just point the vortex tube at the thing you want to be cold. It's even used for personal cooling, like if you're working in a hot environment, like welding, for example. You get these special vests. They've got these little holes on the inside and there's a vortex tube attached to it. You just plug that in and it squirts cold air at you from under the vest. And you know, unlike a fridge, there are no moving parts. So, it never breaks. Like, there's no maintenance at all. It lasts forever. So, you know, usually people who make heat pumps, they're obsessed with efficiency, quite rightly. But sometimes the form factor is just as important, if not more. So the Vortex tube, it isn't Maxwell's demon, and you'll probably never need to use one, but I mean, who cares? It's just really cool. So many people sent me the Vortex Tube as an idea for a video because I guess just for a certain type of person, the Vortex Tube, you just have to know how it works. And the sponsor of this video, Jane Street, is really interested in people like that. Jane Street is a quantitative trading firm, so they're always on the lookout for intellectually curious people, which is why they run programs like the Academy of Maths and Programming, which is accepting applications now for their summer program. The Academy of Maths and Programming is an educational program for recent high school graduates interested in maths and computer science and have experienced barriers to accessing advanced STEM educational opportunities. The program runs from the 29th of June to the 31st of July in New York City. It focuses on mathematics, computer science, game theory, and much more. Accommodation, travel, and food are all covered, and you get a $5,000 scholarship to put towards your future education. You don't need any previous experience in finance or coding. You just need to be you, someone who's interested in how vortex tubes work. Just like me, Jane Street love sharing the things that they've discovered. So, you'll be surrounded by a community of like-minded people sharing their knowledge and passion for maths and computers. Applications close on the 11th of March, so click the link in the description today to apply for your place on the program. I hope you enjoyed this video. If you did, don't forget to hit subscribe. And the algorithm thinks you'll enjoy this video next. that we'll have to do.

If you’d like to learn more about AMP visit: https://jane-st.co/SM-AMP-2026 A vortex tube splits a stream of air into hot and cold! This is how it works and why it doesn't violate the second law of thermodynamics. You can buy my books here: https://stevemould.com/books You can support me on Patreon and get access to the exclusive Discord: https://www.patreon.com/stevemould Twitter: http://twitter.com/moulds Instagram: https://www.instagram.com/stevemouldscience/ Facebook: https://www.facebook.com/stevemouldscience/ TikTok: https://www.tiktok.com/stevemould Buy nerdy maths things: http://mathsgear.co.uk