In Our Time - Kinetic Theory

Episode Date: May 23, 2019

Melvyn Bragg and guests discuss how scientists sought to understand the properties of gases and the relationship between pressure and volume, and what that search unlocked. Newton theorised that there were static particles in gases that pushed against each other all the harder when volume decreased, hence the increase in pressure. Those who argued that molecules moved, and hit each other, were discredited until James Maxwell and Ludwig Boltzmann used statistics to support this kinetic theory. Ideas about atoms developed in tandem with this, and it came as a surprise to scientists in C20th that the molecules underpinning the theory actually existed and were not simply thought experiments. The image above is of Ludwig Boltzmann from a lithograph by Rudolf Fenzl, 1898With Steven Bramwell Professor of Physics at University College LondonIsobel Falconer Reader in History of Mathematics at the University of St Andrewsand Ted Forgan Emeritus Professor of Physics at the University of BirminghamProducer: Simon Tillotson

BBC Sounds, music, radio, podcasts. Thanks for downloading this episode of In Our Time. There's a reading list to go with it on our website, and you can get news about our programs if you follow us on Twitter at BBC In Our Time. I hope you enjoy the programs. Hello, in 1662, Robert Boyle observed that when the volume of a gas goes up, the pressure goes down, and when the volume goes down, the pressure goes up. The most popular explanation for that, endorsed by Newton,

was that there were tiny static particles in the gas, pushing each other apart, and the more they were squeezed, the higher the pressure. What, though, if the atoms were not static, but moving quickly, what would flow from that? A lot, it's turned out, and those who developed this moving kinetic theory of gases helped unlock much of modern physics,

including temperature, the workings of the sun, and quantum theory. With me to discuss kinetic theory are Isabel Faulkner, reader in the history of mathematics at the University of St. Andrews, Ted Fogan, Emeritus Professor of Physics at the University of Birmingham, and Stephen Bramwell, Professor of Physics at University College London. Steve Bramwell, can you summarise what the kinetic theory of gases is and why it matters? Yes, so the kinetic theory of gases is a very simple model for a gas, the idea that a gas consists of atoms or molecules that fly around in empty space in the vacuum,

they bump into each other, they bump into other objects, and the idea is that using Newton's laws of motion, you can then calculate all the properties of a gas from that picture. The picture to have in mind is a billion balls bouncing around on the table, but there are very many particles in any gas. For example, if you hold your finger up, there may be a trillion trillion molecules per second hitting your finger. So to calculate the properties of that is very difficult. Now, kinetic theory is very important for many reasons. Can I just... Can you ask you?

Kinetic means relating to or resulting from motion. Yes. So kinetic comes from the Greek word for motion. So the key point is that the molecules move through the vacuum. So they move through empty space. And they bump in... They collide with each other and they collide with other objects. And this gives rise to their properties.

So they can exert force through their collisions, for example. So I interrupted you. Yeah, so kinetic theory is important for many reasons. It's important historically because it was the first time that physics really started to embrace the reality of atoms and molecules, started to realize that they were in some sense real objects, as we believe today. Well, there's real objects mean, in your view. Well, I mean, that's a good question, and that was a question that physicists in the late 19th century really, sort of stressed a lot about,

are they real? Are they just things we conveniently believe in? Or are they things we can see, for example? So I think most people would accept that if we can see things with our own eyes, they'd be real. But you can't see atoms and molecules. They're far too small for that. Many orders of magnitude smaller than they need to be to actually be visible.

So we can't see them. Camel do you even see them with the latest gadgets? can now see them. So they started in a sense to become visible in one sense throughout the 20th century. So work by Einstein and others in one sense made them visible, but it's in the last 20 or 30 years that it's become quite common to look at atoms in very powerful electron microscopes, for example. You can't see them in an ordinary optical microscope, but in a device, the electron microscope, you can now see them. and that's fairly normal. So I think most people believe in them as real things, but the atoms of modern physics are very complex things.

They're not like billion balls at all. They don't behave like simple, hard objects. But the kinetic theory was a sort of transient period when it was at the forefront of physics, and you're able to calculate many properties of gases in that way. Can you tell us about Boyle's Law in the late 17th century and why that began to define the idea you've been talking about? Yes, so Boyle's Law came about through a lot of work on pressurizing gases, putting them under pressure. And in turn, that was really stimulated by the revival of a very old debate about whether space was full of matter, plenum,

or whether it was empty, a vacuum and had atoms in it. and that's a debate that goes way back to the ancient Greeks, two schools of thought, one that you have atoms in empty space, coming from philosophers like Democritus and Lucipus, and on the other hand, you have the Aristotelian view, Aristotle's view, that space was full. Now, there was a major event in the 17th century,

the invention of the Mercury Monometer by Torricelli and his discovery of air pressure. and so if you recall the barometer has a column of mercury this column of about 76 centimetres is kept up by the air pressure at the top is a vacuum, the Torricellian vacuum. What about Boyle's theory? So Boyle sort of picked up on that idea. The smaller volume, the greater the pressure.

The greater volume, the smaller. That seems counterintuitive, doesn't it? Well, to people like me, it does. Yeah, not necessarily, though, because we're, what Boyle discovered was that air is like a spring, you know, so the more force you put it under, the smaller it gets. But I suppose Boyle's Law was important and mysterious in the sense. It was the first law that really connected to properties of materials together, the first mathematical statement about properties of materials.

Ted Fogan, how did not play into the beginning of a development over two or three centuries? which led to kinetic theory. So I think we have to go back into a time when a lot less was understood about the nature of physics. So, for instance, heat was entirely uncertain quantity. It was certainly not thought of at the time of boil in terms of the motion of molecules,

which is how we think of it today. In fact, there was a suggestion that heat was a kind of substance, a gas which repelled itself. So if you had a high density of this heat, then things were at a high temperature, and then it would tend to diffuse out into a region where it was low density, and that would explain hot bodies getting colder and warm bodies getting hotter. And so this idea, the idea that heat was a substance, and similarly people didn't understand combustion.

There was the phlogiston theory, which was replaced by the idea of oxidation well after boil. So people were starting at that stage to think, we want to try to explain things into, herbs and substances, but they hadn't got the right substances. Newton figured in the early thing, and the billiard balls are part of his idea of a static universe. What happened to that idea? So Newton wanted to

find an explanation for what Boyle referred to as the spring of the air. That's the actual title of his book about his experiments. We're under an ocean of air. No, no, the idea for instance if you operate a

bicycle pump and you push down on the handle and it feels like you're compressing a spring. So the picture that people wanted to have was somewhere where you had things that were of pushing back like little springs. And this is, this can be used to explain Boyle's law. It is a theory, but it turns out not to be the right theory, but it was, it was supported by Newton. And as a result, it had a lot of popularity. And that was the idea that as you increased, decreased the volume, the springs got compressed. and so the pressure outwards increased. And Newton actually took this a little bit further.

He did a bit of mathematics and said, now let's imagine that each of the individual atoms, so he was believing in atoms, are going to repel each other with a force that varies with distance. It turns out it's not the inverse square law. It was inverse distance law that Newton proved was the right one. And then that was able to explain Blaine Boyle's law. It was a theory.

It was a wrong theory, but it was a widely accepted theory at the time. What did the Swiss physicist, Bernouille, add to the argument? So Benoulli, he was well ahead of his time. He was, well, people... What's the time? Can he give us a date? Oh, the time, I think he was the early 18th century. So he wrote a book in Latin about hydraulics, and that is what he's mainly remembered for today,

that he produced the equation, which accounts for the lifters. of aircraft wings and is well remembered by modern-day physicists as a most important equation. And he was thinking, not in terms of these things like heat as a substance, he was the first person to really express the idea of kinetic and potential energy, the idea that if you raise an object high in the air, then it's got a high potential energy, and if you let it drop, that turns into kinetic energy. So he had that idea, and that was how he explained the motion of fluids and how if you make a hole in the bottom of a barrel, how the water flows out, all these

things were things that Bernoulli was thinking about. So he was thinking very much like a physicist, and he was the first person to actually produce a kinetic theory. He, in his book, I've only seen the picture, I haven't read the Latin, he showed a picture of a cylinder with a piston and a weight on top of the cylinder, and his idea was that the molecules were hitting the bottom of the piston and keeping the weight against the force of gravity. So he really was the introducer of kinetic theory, but against this background, his work just disappeared. It was a chapter in a book on hydraulics. Isabel Faulkner, another man, Robert Brown, made an observation that was relevant in the 19th century as we moved through towards the present day.

What did he add? Yes, that's right. Robert Brown was a, he was a Scottish botanist and microscopist. He became one of the foremost microscopists of his day and did a lot of work. looking at plant pollination, he was one of the first to observe the cell nucleus. He'd been on an expedition with Matthew Flinders to Australia, collected a lot of plant species, and he was trying to classify them. In 1827, he was looking at pollen under a microscope, as part of his experiments on plant pollination.

The pollen was suspended in a glass of water, and the pollen actually burst open into a lot of little grains. And under the microscope, he could see that these grains didn't just sit there in the water. They danced about in a very irregular, jittery manner. Well, his first reaction was to think that this coming from a plant, from pollen, they might actually be live in some way and propelling themselves. So he did more experiments, and he tried to. rock dust, which was definitely inanimate, and very tiny particles of rock, behaved in exactly

the same way if they were suspended in water. They jittered about in the same way. So it clearly wasn't to do with these tiny grains being alive in any sense. And they also, the motion was far too irregular to be explained by some sort of thermal current in the water or any convection current in the water. So what did you conclude? He didn't really know what to conclude and for the next 70 years people followed these experiments up and they still didn't know what to conclude. They tried varying the temperature of the fluid that they were suspended in. They tried varying the nature of the particles. They tried varying what fluid it was so they didn't just use water. They used other fluids. and none of these experiments were decisive.

In the second half of the century, after the beginning of the, as kinetic theory began to be developed, people started to try to make a link between this irregular motion of the particles and the kinetic theory, but it wasn't until pretty much 80 years after Brown had discovered it, that the decisive sort of matching up of by then developed kinetic theory and the explanation of the motion of the particles was made

and they were viewed as a result, Einstein essentially showed that they were, the motion, very irregular motion could be explained as a result of the statistical variation in the speed of molecules. in the gas. She's coming out of kinetic theory. So, and yes. Sorry, interrupt. This is a time when statistics are entering into the discussion. Yes. And some physicists

resented that. They thought statistics were too subjective and fuzzy, whereas their work was clear and very unfuzzy. Yes, I think there are two strands, if you like, to the way statistics entered into physics. And the first was the beginning of the 19th century out of probability theory. Probability theory

having been developed in the 17th and 18th centuries, largely in the context of gambling and a bit in the context of life insurance and annuities. And around the early 1800s, particularly through the work of Gauss and Laplace, these ideas about probability became applied to analysis of errors in physical measurement. Can we come back to that a bit later? Because what I'd like to go to a nasty of Bromel is the laws of thermodynamics and how that changed the discussion. Yes, absolutely. So while this was work of Robert Brown and others was going on, there'd been quite some developments in

understanding what heat was and how it relates to work. So work is lifting a weight, for example, and heat we're all familiar with. As Ted said earlier, people originally thought heat was a fluid, but by about 1850 it was realized that both heat and work were forms of energy or more technically energy transfer. Now, the two laws of thermodynamics were formulated around that time. The first law is the law of energy conservation. So energy comes in different. forms, heat is one of them, but it can be converted to other forms. But the total amount of energy is always the same. It's conserved. Whether it's converted to gas or whatever. Well, whatever it's converted to. So if you rub your hands together, for example, you're to keep them warm. You're starting

off with chemical energy in your muscles. You're converting it to mechanical energy in the motion of your hands and then eventually to heat. But the total amount of energy is always conserved. That's the first law of thermodynamics. The second law of thermodynamics is slightly more mysterious. It's the law of increase of entropy. Now entropy is a slightly mysterious quantity. It relates very much to how much energy spreads out. So if energy starts off in a useful concentrated place, for example, you've got a rock at the top of a hill that you're going to roll down. and take energy out of, it ends up rather spread out, usually as heat. And so there's a sort of feeling among physicists that develops in the sort of 1860s,

particularly clausius, that eventually everything is going to become sort of spread out in energy and you have this so-called heat death of the universe. So this is a very strange thing, yet it's very well supported by experiments, at the time. Ted, Ted Fawn, can you take us on about that? Classius has been mentioned. Can you say what he added in? Can you talk a bit more about entropy?

The word random was introduced in the notes I had. Yes, so entropy actually, so entropy can be thought of in two ways, and I think this represents the two strands of thermodynamics. So there is the kind of things that Steve was talking about, which is heat and work and the operation of heat engines and all that kind of thing. But there's also the idea of thinking about,

this from a microscopic point of view what the atoms and molecules are really doing. And one way of thinking about entropy is to say, well, I know in the, I've got a box of gas, I know it's volume, I know its temperature, I know its pressure, but there's maybe one followed by 20 zeros molecules inside this box. I have no idea what they're doing. So the entropy is a measure of how many different ways those molecules might be moving, all consistent with what I actually know, which is only pressure, volume and temperature. And so that's another way of thinking about entropy.

And so there's a link between the idea of heat spreading out and the heat death of the universe, which is, shall we say, the thermodynamic point of view, and then there's the statistical mechanical point of view, which is looking at the statistics of the molecules, where you concentrate more on what's happening underneath. And Klaus has contributed to both of these. Yes, and I think, just to pick up on Ted's point,

entropy was a mysterious quantity when viewed as something to do with heat. And so there was a great impetus for scientists to want to know what it was. And by that they meant they wanted a microscopic picture of it. So this was a really big impetus for that. So we're a long way from Newton's idea of billion balls. Absolutely. So Clousius, after working on the thermodynamics that Steve's been describing, he then went on to consider kinetic theory.

And he tried to make a disconnection between these two because what he believed, and I think most physicists believe, is that the laws of thermodynamics are entirely independent of the models you put underneath them and what the atoms are doing. What does that mean? The idea that whatever system you have, you will not be able to make a perpetual motion machine. Heat will not pass from a cooler to a hotter body of its own accord

without doing work, etc. These are things that are entirely independent of whether matter is made of atoms or whatever. But then Calcius went on to think about atoms, and he then developed these ideas that have been a hundred or more years before put forward by Bernoulli. And he then estimated the speed of molecules in the air and came out with an amazingly fast speed, several hundred meters per second, nearly a thousand miles an hour. And at this point, it looked as though he'd made a big mistake. Because suppose you're in a big room and someone opens a bottle of perfume at one end, if the molecules really, travel at this speed, then the smell will get to the other end of the room faster than the speed of

sound, but that didn't happen. And this led Clousie is to do one of the things that physicists try not to do, which is to be too simplistic. So people have been thinking of atoms or molecules in a gas as being incredibly small. Indeed, it's a physicist joke about, you know, point masses and weightless beams and all this kind of thing. We go to the extreme in order to get a simple model if it's if it's a good enough model, it doesn't matter for it's simple. But in this case, this was not going to work, because point particles would travel the whole length of the room in next to no time. And what he introduced was the idea of mean-free path,

that the molecules would hit other molecules because they have a finite diameter. And he then took this idea and showed that this would explain the slow speed of diffusion of a smell or any other gas through another gas. And perhaps I should say a bit more about mean-futable. free path because so the path is the distance molecule travels between one collision and the

next one with another molecule where it more or less forgets which direction it was going in and the mean means that not all molecules are going to do exactly the same thing is a bit like radioactivity if you start with a radioactive material and wait one half-life half of the nuclei will have decayed the other half

are still there weight two half-lives and three quarters have decayed the same with molecules if they're travelling in a gas when they've gone along the mean-free path a certain fraction will have hit but the others carry on. But we're beginning to solve them, get to the solution or get to a conclusion about this,

Isabel, through the use of statistics and the idea of not trying to measure individual molecules because there are too many of them moving too quickly and it's impossible with the present technique, maybe always will be, but if we take them en masse, if we talk about the mass of molecules and employ statistics as Maxwell did, then something

is discovered. Yes, that's right. Right, and Maxwell was getting his ideas, not from physics, about statistics, not from physics, but from social science. The ideas about statistics, they'd been used for analysing errors in physics, but they hadn't gone any further than that, whereas the social scientists, with the sort of 19th century love of collecting data about populations, had shown that if you look at, although individual, are variable as a mass, on mass, they have very stable characteristics.

So things like marriage rates, crime rates, suicide rates tend to be fairly stable year on year. And those are the ideas that Maxwell was picking up on when he came to develop Klausia's work on kinetic theory. He was thinking, well, we've got a lot of individual molecules. they're more or less independent of each other. We don't know exactly how any of them behave, but on mass we have this regularity in the properties that's expressed in the gas laws,

the pressure being inversely proportional to the volume. And so, as you outlined, it's just not possible to measure everything sufficiently precisely and do the computation to analyze them, all those molecules. But he took the idea that we could look at their average properties and the variation from the average properties as well. The variation was important. On that they would, the average properties would give the gas laws, but the slight variation that a few molecules would be travelling much faster than the average

or much slower than the average, although most of them would be travelling roughly the average speed. That could also explain some of the other properties of gases. But as I understand it, this gave conclusions which allowed the theory to develop and move on. That gave, yes. And the conclusions were, initially, some of the conclusions were very unexpected.

Indeed, it seems that Max were, when he first published his paper, thought he was likely to be disproving the kinetic theory rather than proving it. Can you take that on, Slee? Why did you think so? Well, I mean, there was some rather strange-looking conclusions like the viscosity of a gas didn't depend on its density.

Meaning what? That means that, you know, the viscosity is maybe how a part, how, let's say, drop a ball in the air, how it's slowed down by interacting with the air. And in fact, you might expect that to depend on the density of a gas, fewer molecules, but actually in terms of Maxwell's equations, it doesn't. And so there were some rather strange predictions, but they all mainly came true. But maybe I could just add one more prediction that also came true.

His theory of velocity involved the mean-free path that Ted mentioned earlier. And meanwhile, while all this physics was going on, the chemists, of course, had been working on their own very. version of the atomic theory, starting way back with Dalton and Averagadro. And they believed in Avigadro's number, the number of molecules in a certain volume. And measurements of diffusion of a gas, giving the mean-free path, and hence the molecular diameter, allowed the first a proper estimate of Avagadro's number. And suddenly, physicists and chemists together could tell you how many molecules they

were in this room, for example. Isabel? Yes, and I think that was really critical. It gave you a measurement. It gave you a measurement not only of the number of molecules, but also you could find out the size of a molecule. And there was a very strong belief among a lot of prominent physicists, including the very influential William Thompson, later Lord Kelvin,

that if you could measure something, then it was real. And Thompson said, you know, this brought atoms and molecules out of the metaphysical into the world of quantitative science. The fact that you could measure it, made it real. I'd like to come back to Steve's remark about the viscosity of a gas being independent of pressure because that immediately says, just a moment,

that can't be true because if you pump all the gas away, then clearly the gas can't have any effect at all. In fact, Maxwell was so worried about this result of his theory that he and his wife did experiments. And I love that. You want to tell people about it. Yeah, so... In his attic.

In his attic with his wife providing the temperature control and him measuring the oscillations of some disks as they... The particularities are wonderful. Controlling the temperature control by shoveling coal under the fire. Absolutely. Yeah, that's right. But that shows you the kind of situation people were in at those days. And the apparatus can be viewed online if you look up the Cavendish Lab Museum,

you can actually see Maxwell's apparatus that he used to measure. And where did this take him? I interrupted. So he then established completely counterintuitively that the viscosity of a gas is independent of pressure, and this was later extended by Boltzmann to show that the thermal conductivity of a gas is independent of pressure. But this must break down at some point,

and this is where the mean-free path comes in. So, because if you pump it all the way, then there can't be any conductivity or viscosity. You know, the Earth would slow down in its orbit in empty space or something like that. So what it turns out is the answer to this is that if you go to sufficiently low pressures, the mean-free path gets very long because the atoms are so far apart. And so the atoms can travel a huge distance. And once they can travel a long, long way, then the result that Maxwell got is no longer applicable. Let me explain it a bit more detail.

To carry heat away from something hot, the molecules have to pick up a little bit of extra energy from the hot object. And that is part of it, but they also have to carry it away, and that depends on the mean-free path. So the amount of heat picked up goes up as the density of molecules, but the mean-free path goes down as the density of molecules, and the two exactly cancel. And this gives this counterintuitive result,

that it doesn't matter about the density, until you pump sufficiently much gas away that the mean-free path goes all the way from the hot object to the cold object and then it can't increase any further. Isabel, please come in first. Now let's go to Isabel first, do you mind? Now, I want to pick up on Boltzman, who has been mentioned.

Would you take up the contribution of Boltzman, please? Yes, okay. When Maxwell had devised his theory, he'd done so on the assumption that the gas was in thermal equilibrium, room. That means essentially that it's the same temperature all the way through. He didn't prove that that state ever really existed or how you got to that state if you weren't already in that state. And that's where Boltzmann came in because Boltzman took Maxwell's ideas and ran with them,

but looked at if you didn't already, weren't already in that state, if you had a gas in a container it was hotter on one side than the other to start with, how it would get to that state. And he showed that it would get to that state so that Maxwell's ideas were right, and he showed that it would almost always get to that state. And the way he reasoned was that he found a way of assigning a probability to each sort of state of the gas, through the concept of entropy. Entropy was increasing. He used the idea that the randomness within the gas of the gas molecules was increasing.

He used the idea that the state of the gas was likely to get more and more probable. And he was able to show that the equilibrium state was the most probable state. So that was where it was likely to end up. And that was how a gas might move from a... initially non-equilibrium state through to the equilibrium state where it would indeed be in the situation that Maxwell had suggested and done the theory for. Steve Bramall, you wanted to come in. I think my point has been made actually, but maybe I could just pick up on that a little bit. So this sort of attractive quality of the kinetic theory was starting to emerge that it was starting to emerge,

that it was starting to explain what entropy was. So Boltzmann believed, to start off with, that he'd basically proved that entropy, the law of increase of entropy, came from Newton's laws. Now he wasn't ultimately right about that, and there was a sort of howl of protest from several different scientists.

And it raised some very interesting questions because Newton's laws are time-reversed, So if you, they run the same forwards in time as backwards in time. But the law of increase of entropy is not time reversible. It only goes one way. No window. Yeah, yes. So, you know, if you smash your window, that happens naturally.

But you never see to unsmash naturally. You know, if you drop your cup of tea into a swimming pool, you're very unlikely to get it out again. This is the one way progress of entropy. but Boltzmann thought initially he'd proved the law of increase of entropy from classical mechanics, Newton's laws, but he hadn't. And Boltzman eventually became a figure sort of under fire from all sides. He did great and amazing things, but also caused a lot of controversy. Ted Foggan, there was a thought experiment in Merger Tram, started by Maxwell. Yes, indeed.

called Maxwell's demon. Indeed, yes, Maxwell's demon. He didn't actually name it a demon. It was named a demon by Kelvin. Now, I think this is a nice example of the way that scientists work, that you don't understand something just by deriving it or learning it. You'd learn about, understand something by playing with it. And a thought experiment is a way of playing with ideas and seeing if they work.

So Maxwell proposed that if you had a box of gas, divided in two by a partition with a very tiny hole in one so small that molecules could go through individually and then you put a small being in there it was actually a sentient being in his plan. He called it the intelligence. Yeah, but I think you could just make an automatic thing that did the same thing.

And that would look around at the gas molecules and every time it saw a hot one coming from the right it would let it through and every time it saw a cold one coming from the left and it would let it through. And it could do this with a little door over the hole, which could be slid sideways so that it could be moved with almost no energy required to move it.

And in this way, if this were to happen, the hot molecules would all move one way, the cold molecules would all move the other way, and you'd establish a temperature difference without doing any work. And that breaks the second law of thermodynamics. You cannot create a temperature difference without doing work. I used the word intelligence I think he used the word

was in intelligence and some people have said this was the God gap that actually it is not susceptible to physics this movement there because it is on its own motion

and it has been called the God gap what do you make of that and that God was operating there or being on a non-physical entity? I think Maxwell

deliberately called it an intelligence his friend William Thompson Kelvin may called it the exercise of free will. So Kelvin made space there for free will, and people subsequently have interpreted it as a Godgap. What I think is most interesting is that Maxwell saw intelligence as outside the laws of physics, and that was a deliberate position taken against

people like John Tyndall, Thomas Huxley, who were pushing scientific naturalism and the idea that deterministic, mechanistic laws could explain mind as well as body. And Maxwell was saying, no, intelligence is outside those laws of physics. There's a sort of physics explanation as to what's going on in Maxwell's demon. If you imagine that you're trying to look for molecules, then you need the light to be on. But if we have the light on, then that's already putting energy into the system, and you then will not be able to break the laws of thermodynamics. Isabel.

The attempts to solve this or understand this problem also acted as a great stimulus to the rise of the development of information science, what we now call information science. And they tried to understand it in terms of the information that the intelligence would need to take in in order to make this decision, storage of that information, and then destroying that information. And in their terms, that destruction of the information actually increases entropy to an extent that counterbalances,

the decrease you get from what the demon is doing. So we arrived at a place in the history of the development of this idea, Steve Romain, Kinetic Theory, is established and accepted. What did it help to reveal? So, for a start, it's... revealed many new properties of gases and allowed a sort of rational basis for the development of chemistry of gases and of atmospheric science and of that sort of thing. It also led on in many different ways to different branches of physics. So a few years after Boltzmann, Max Planck took

the first steps to develop quantum mechanics and he did so by referring back to Boltzman's concept of entropy that had been developed for gases. and now we can sort of, with modern knowledge, we can see the relationship because Plank studied light and light can be thought of as a gas of photons, little particles, if you like, of light. So that was one thing it led to. Another thing, it developed into this major branch of physics called statistical mechanics, which is really the sort of major generalisation of kinetic theory to all sorts of matter and indeed to other systems as well.

And that's really one of the great pillars of modern physics. There are four, not one of them. Well, I think, you know, the others are probably quantum mechanics, relativity, and particle physics. The statistical mechanics has a special property of being relevant to all branches of science, you know, and mathematics as well. And it really has huge relevance. Though it's not as fundamental. Physicists don't think it's as fundamental as particle physics, say, or relativity.

Ted, how does kinetic theory apply to the work you do in your laboratory? Well, I think one of the things that we never got around to mentioning earlier was, and this was discovered way, way back by Bernoulli, is that the kinetic energy of a gas is proportional to temperature. And if you then extrapolate that down to zero kinetic energy, you come up with approximately minus 273 centigrade. And so one of the things that came out of kinetic theory was the prediction of the existence of an absolute zero of temperature,

which took a while to be accepted because no one knew for sure what would happen if they went down to low temperatures. And indeed, a Scottish physicist Dewar, after whom Vacuum Flans were named and Cameling Ones all tried to liquefy the so-called permanent gases. Cameling on is liquefied helium, the lowest temperature one, and thereby discovered superconductivity. And so absolute zero is now much accepted

and is an important part of the work I do, which is mainly to do with superconductors, which have been going up in temperature in recent years, but even if you want to use them, you really need to keep them in liquid helium. And for instance, whenever you have an MRI scan, you'll have a container of liquid helium. The insulation is provided by that vacuum,

which is sufficiently good that Maxwell's, statement that the heat will get through the low pressure gas is no longer true. And so it has an important practical application in the kind of research I'm doing on superconductors. Steve. Of course, we shouldn't forget about Brownian motion. I think we were discussing it earlier. And Einstein in 1905 basically applied kinetic theory to Brownian motion. And rather interestingly...

This is the pollen in the water. This is the pollen jittering around in the water. And basically one of the things Einstein realized really was that the pollen was behaving in a way like a giant molecule interacting with much smaller molecules in the liquid. But that was really kinetic theory made visible. And so a lot of the critics of kinetic theory just melted away at that point. And as we said right at the start, you know, why do we believe in atom as well? people started that process with Einstein and making kinetic theory visible in that way. And actually he didn't need Maxwell's demon for that. He did it directly.

Isabel, would you like to talk of any legacies? We've talked quite a bit about some physical legacies. There's one in mathematics, and that's a godic theory. And this came out of Maxwell and Boltzmann's work. And the way they were thinking about the different, states that a gas could be in. They had the idea that these states were changing through time, and they needed to work out the probabilities. But they suggested that instead of waiting a very long time for a gas to pass through every possible state, actually you could have a very large

number of essentially identical gases and look at the probability of the state that each of them was in. And that's become very powerful in mathematics. Finally, Steve. I think one thing to realise about modern physics is the fundamental physics, that of the smallest possible particles that go way inside an atom, is so far removed from everyday problems that you need to do lots of approximations

to sort of treat normal scientific problems. And so kinetic theory, is now understood as just one of those approximations, but a very important one, because it's the only way we can deal with very large numbers of things, and we're talking truly large numbers. Thank you very much, Isabel Faulkner, Ted Fogan and Steve Bramwell. Next week, the United States President, who aimed to reconstruct America after the civil war.

That was Ulysses S. Grant. Thank you very much for listening. And the In Our Time podcast gets some extra time now with a few minutes of bonus material from Melvin. and his guests. We didn't mention Ernst Mach and his... We didn't mention... The way you go.

So, Ernst Matt, great, very fascinating figure. He was a sort of fine experimentalist, but became more famous as somebody sort of had a genius for picking holes in other people's science, essentially. So his attack on Newton famously inspired Einstein to create his theory of relativity.

But Ernst Mac resisted the kinetic theory, the atomic theory, on the grounds that he said, you know, you shouldn't believe in things that you can't directly confirm. You know, maybe he was talking a bit like we talk about string theory today. Maybe, yes, Isabelle. Yes, he was at a time when there was a, he was a part of the energetist movement, which said, look, we don't actually need these hypotheses about atoms and molecules to explain what we actually see at a macroscopic level.

and they argued very strongly, as Steve has said, for confining your science to what you could actually observe. Now, that went through, so kinetic theory really went through a sort of a low point from about 1880 to about 1900. And as I think it was Ted was saying, Paul Boltzman was really beleaguered. And he, fighting for kinetic theory, he didn't really quite spot that the tide was turning. around 1900 as Plank was supplying ideas from kinetic theory and then Einstein was coming in and poor old Boltzmann committed suicide

who was so unhappy about it in 1906 just ahead and not knowing that he'd just been nominated for the Nobel Prize in 1907 which I always think is... I didn't know that last bit, yes. It sort of goes back to maybe something Ted said earlier that the thermodynamics is such a beautiful thing in itself but it only involves real quantities.

You know, so when you, I don't know about you, Ted, but when I've taught thermodynamics, I start becoming a bit of an energeticist myself, you know, so you don't need to worry about molecules here. I think the idea that just because you can't see something, that it doesn't exist. I was just about to bring that up. There's some molecules going on between us.

Precisely where I was going to bring up. I love that, just because you can't see it, it doesn't exist. I'm all for that. Because, you know, in a court of law, if A committed a crime, you don't actually have to have B seeing A do it. Circumstantial evidence is sufficient, and after a while, the evidence all adds together. I think there's quite a nice analogy of this in particle physics.

Back in the 1960s, people were discovering a whole zoo of subatomic particles, and they produced a theory called a unitary theory, which gave a kind of pattern. And then quarks or quarks, or some people, pronounce them were invented as an explanation of this symmetry and there was absolutely no evidence of that time that they actually existed and it was only about four years later that they by going to higher energies and looking inside a proton they could show that they were quarks inside and actually it's even more extreme than that because even up to today and we think forever

a free quok will never be discovered they can't escape from each other so these are things that you can see indirectly inside other subatomic particles but you can't actually isolate one of them. And so, but if you ask any high-energy physicists, do they believe in them? They say, absolutely, yes. It's coming from that idea of Kelvin's, that if you can measure it, it's real. And if you can construct some sort of an instrument that gives you a measurement for it, then it's real.

I think, to be fair to Mac, of course, you know, people were, well, all this high-brow stuff was going on, you know, sort of ordinary scientists, particularly chemists, were getting very carried away with atoms and molecules at that time. And, you know, he was probably sounding a warning that, you know, maybe we need a bit more evidence for this. And, you know, sometimes those sort of annoying, I mean, it's generally considered that Mac was very unhelpful at this point. You know, he might have shut up for a while. But I think he had a reasonable point to make, you know, that you should at least ask the question, what's your evidence for all these ideas, you know. But modern physics has sort of squared that circle.

we sort of tend to allow hypotheses as long as they predict the right, the experimental answers. Yeah, well, we saw right at the beginning that Newton produced a theory that explained Boyle's law, but it wasn't the right theory. So it's just satisfying experiment is it enough. It has to be a whole lot of evidence adding together, I think, to be sure. I was going to say that I think one of the attractions of kinetic theory, and I've enjoyed teaching it, is that it's the very first theory where you can really start from first principles and explain a property of something.

A gas is, after all, one of the simplest systems. And the molecules are far apart, as we know, because a gas is a thousand times less dense than a liquid or a solid, typically. And so you start from Newton's laws and you can explain its properties. And it provides a nice example of something that, okay, it's slightly idealised,

but you can then use these ideas. And in fact, people use them, for instance, in semiconductors and in metals, people use the idea of mean-free path with the gas of electrons. It's not quite the same statistics because the Pauley Exclusion principle comes in. But nonetheless, the ideas apply there. And Steve and I actually, some of our research involves using beams of neutrons. And the neutrons are produced at very high energy, but then they hit the moderator. And it's like a gas coming into equilibrium with the walls of its container. and they come out with a Maxwell Boltzmann distribution along tubes to the experiment

and we use them for looking aside materials. Absolutely. I was just going to pick up also on that I think as well running through both the whole debate about atoms but also about the kinetic theory, there's a possible, there certainly, as we mentioned before, an issue around indeterminacy, free will, there's also a possible theological, as you indicated, strand that is coming into the work that's done on atoms

by a number of physicists on complex atoms that might explain the chemical properties and things. There's Maxwell's idea that all atoms of an element are identical, and this means they must be in some way, he called the manufactured article, and then you beg the question, well, who did the manufacturing? And that, certainly, again, for some Victorian physicists, was God clearly did the manufacturing.

Is it fair to say that atomic theory suffered for a long time of being thought to be atheistic over the centuries? I'm not sure that it's as simple. Yes, there was a belief, when it was tied to those early Greek ideas, that you were talking about, then yes, yes, but I think they'd lost that by the 19th century. I was just thinking of some other applications of the ideas of gases. And Steve mentioned earlier the idea that radiation, thermal radiation, is a gas,

in this case of photons. And that is actually quite interesting in astrophysics, because if you apply the ideas of kinetic theory, actually photons scarcely interact with each other, so they're more an ideal gas than almost anything else. They differ, though, from the Maxwell Boltzman thing, because they all travel at the same speed, in this case, the speed of light. And also they differ in that their number is not constant.

As the temperature goes up, you get more and more photons. But what they do exactly like a gas is that radiation can exert a pressure. Isabel, last word. And I think that what that's exemplifying is another reason for the kinetic theory was accepted was not particularly because of any experimental evidence, but just that the methods and approaches were

becoming too useful to drop. And Ted's just given us a great example of some of those methods and approaches applied to photons. Well, thank you all very much. Here's our man with the offer you can't refuse.

Tea, please. Tea, I think. Tea, please. In our time with Melvin Bragg, is produced by Simon Tillotson. This is Planet Puffin. There's a fair chance you will get bitten at some point. Planet Puffin is a new podcast coming to you from a tiny island off the east coast of Scotland. Across the summer, we're going to be following the breeding season, no matter what it takes.

Now there's an encouraging piece of poo at the entrance here. There's some nice white guano. So Becky, I'm going to let you take the first game of Puffin roulette. Summer 2019's hearty. Puffin podcast. Well, only Puffin podcast. For BBC Sound.