Kelvin, Boiled Eggs and the Story of Heat

Bath Royal Literary and Scientific Institution, May 2005 (a part of the Einstein Year series)

Speaker's Notes for Talk

This is Einstein year, and the story of heat sounds pretty boring compared to Einstein's dramatic discoveries like the theory of relativity or quantum mechanics. You might be surprised to know that Einstein wouldn't have had a chance of making those discoveries if Kelvin and others before him hadn't asked themselves the question “What is heat exactly?" It's quite a dramatic story, with people being chased from continent to continent, having their honeymoons ruined, and in one case literally losing their head. It told us that the Sun and the Universe will eventually die, it nearly put an end to Darwinism, and even let us calculate how long to boil an egg, but I'll come to that at the end.

A good place to begin is around 200 years ago, with the French chemist Antoine Lavoisier. Here he is:

SLIDE 1  Lavoisier and wife

You can see that he had more than one interest. That's his wife Marie-Anne. She was 13 when he married her. He was also a tax collector, and that's why he was branded as a traitor and had his head cut off during the French revolution. Before he died, though, he produced the very first table of the elements in 1798:

SLIDE 2  Lavoisier's table of elements

Note that he put light and heat as elements. This was no more than common sense. They both seem to flow from place to place. We still talk about heat as “flowing" from hotter to colder places, just like water flowing down hill. It also explained why heated materials expand, because they have to make room for the incoming fluid. It even correctly predicted the ratio of the heat capacities of materials in their solid and liquid form.

So there were very strong reasons to believe in the existence of this fluid, and it even had a name – caloric. There was almost no-one in the eighteenth century who didn't think that heat was this real fluid called caloric, until an American called Benjamin Thompson came along.

This was Thompson with a “p". When we get to Lord Kelvin we'll find that he started life as Thomson without a p, but that comes later – about 50 years later, in fact. Getting back to Thompson with a “p", he had a very interesting life. He was actually on the English side in the American War of Independence. Here he is in uniform:

SLIDE 3  Benjamin Thompson in uniform

He had quite an interest in heat from an early age. One of the things that he did was to design a new type of open fire that is still very popular in America:

SLIDE 4 Rumford stove

You'll notice that it's called a Rumford stove and not a Thompson stove; I'll tell you why in a minute.

He got into quite a bit of strife during the War of Independence. One thing that happened was when troops under his command decided to build themselves a bread oven from the gravestones in a local cemetery.

Bread oven story

That was one of the reasons why he was chased out of America and did a runner to England, but he soon found that the money was better on the continent and he moved to Germany and took charge of the Munich arsenal. By this time he had changed his name and become Count Rumford of the Holy Roman Empire, which is why his stoves are now called Rumford stoves. He still had an interest in heat, and he started wondering why brass cannons got so hot when they were being bored out. At first he thought it might be something to do with the brass being turned into a fine powder as it was removed, so he devised a very clever experiment to check this out:

SLIDE 5  Cannon boring experiment with blunt steel borer

Description of cannon boring experiment

So he concluded that heat could not possibly be a real material, and that it must be motion. That's what we now believe. When we rub our hands together, for example, what we are actually doing is speeding up the vibrations of the molecules in the skin, and we sense this as an increase in temperature.

Rumford published the results of his experiment in 1798 – the same year that Lavoisier published his table of the elements. You'd think that Rumford's experiment would have disposed of the idea of caloric once and for all. That's what students tend to be taught these days, because it makes a neat and tidy story, but it wasn't that way at all. The truth is that the picture of caloric was so deeply imbedded, and made so much sense, that hardly anyone believed Rumford and people carried on believing that heat was a real fluid for another 50 years.

The time we're talking about is well after James Watt had invented his improvements to the steam engine.

SLIDE 6  Watt stationary engine

Watt's inventions were totally pragmatic ones, and it wasn't until 1824 that a Frenchman called Sadi Carnot analysed the performance of heat engines by thinking of it as a series of steps that eventually brought the engine back in a cycle to its original state, ready to start the cycle again. If you think about it, you'll realise that that is how a car engine works, but what Carnot did was to design an idealised engine that could never be quite realised in practice but which was as efficient as any engine could be.

SLIDE 7  Schematic Carnot cycle

I'm not going to attempt to explain this cycle to you. When I was taught thermodynamics this is what they started with, because it's a machine for converting heat into physical work, and the First Law of Thermodynamics

SLIDE 8  First Law of Thermodynamics

First Law of Thermodynamics says that heat and work can be freely converted into each other.

I thought the Carnot cycle was the most boring thing in existence, and it's still pretty high on my list. It was a really terrible way to introduce thermodynamics. The Laws of Thermodynamics hadn't even been thought of when Carnot invented his cycle. Its real significance is that Carnot got it totally wrong, because he still thought that heat was a fluid called caloric, and that caloric couldn't just appear and disappear but had to be preserved at every stage of the cycle. It was another quarter-century before Kelvin and others realised that it was the sum total of (heat + work) – in other words, energy – that had to be conserved, and this had enormous consequences, including the prediction of the heat death of the Universe.

Just to get things in historical perspective, here's how these various discoveries panned out:

SLIDE 9  Dates from Watt to Thermodynamics

You'll see that I've mentioned two laws of thermodynamics, but before I get on to the second I'm going to hand you over to these two to tell you what they are all about:

SLIDE 10  Michael Flanders (wheelchair) and Donald Swan

Flanders and Swann CD Track 6

So how did we come to discover these laws of thermodynamics? The man who gets a lot of the credit was Lord Kelvin. Here he is, complete with magnificent beard, giving a lecture at Glasgow University:

SLIDE 11  Old Kelvin in front of blackboard

He even had the beard when he was a young man:

SLIDE 12  Young Kelvin (early 20s)

In fact, he was only 22 when he became Professor of Natural Philosophy at the University of Glasgow. If you think that's remarkable, you might like to know that he was only 6 when he was first enrolled at the University. He matriculated when he was 10, and passed all of his degree exams when he was 16, but he never actually took the degree because he thought it might prejudice his chances of going on to Cambridge. What he did was to put the letters BATAIAP after his name:

SLIDE 13  BATAIAP

Bachelor of Arts to All Intents and Purposes

He looks serious in his pictures but he had a wicked sense of humour.

Dewdrop story if time

At that stage he was plain William Thomson (that's Thomson without a “p"). He became Lord Kelvin later.

Kelvin was in the audience at a meeting of the British Association for the Advancement of Science in 1847 when a Manchester brewer called James Prescott Joule was giving a talk. Here he is, with his very impressive beard:

SLIDE 14  Joule

In fact, it's a theory of mine that Kelvin and Joule were really the same person. If you don't believe me, have a look at their pictures side by side and see if you can tell the difference:

SLIDE 15  Joule and Kelvin side by side

Be that as it may, Kelvin just couldn't believe what Joule was saying at the British Association meeting, because he was claiming to have proved that heat and mechanical work could be converted into each other in exact proportion. He'd been saying this for years at Association meetings, but Kelvin was the first person to take him sufficiently seriously to start an argument about it. It was one of only two scientific arguments that Kelvin lost during his life.

This is the experiment that they were arguing about:

SLIDE 16  Joule experiment

Describe

Joule tried other experiments along these lines. He even spoiled his honeymoon in the Swiss Alps by insisting on taking a large thermometer and spending his time measuring the temperature at the top and bottom of waterfalls. But this is the experiment that eventually convinced Kelvin and led to his formulation of the First Law of Thermodynamics.

It's quite difficult to disentangle Kelvin's contribution from those of other scientists at the time like Clausius in France and Helmholtz in Germany. This gets especially difficult when it comes to the Second Law of Thermodynamics, because Kelvin and Clausius came up with different formulations which only later turned out to be equivalent. They both got there through worrying about what it was that was really conserved in the Carnot cycle if it wasn't caloric, because by this time pretty well everyone was convinced that heat was motion and not some invisible fluid.

What they eventually concluded was that the sum total of (heat + work) was conserved, and it was given a new name – energy. This was an incredibly revolutionary step, this concept that heat, and subsequently light and magnetism and electricity and radio waves and even motion itself, were all different forms of just the one thing, that could never be created or destroyed, only changed from one form to another. Once they had the concept, they used it to analyse Carnot's ideal heat engine properly, and they came to some amazing conclusions that now form the Second Law of Thermodynamics.

This isn't the place to go into the detailed logic, but what Clausius concluded was that heat could never spontaneously travel from a colder place to a hotter place, while Kelvin concluded that heat could never be entirely converted to work by a heat engine which followed a cycle to return to its original state; there would always be some wasted. In fact, that wasn't quite what he said – what he said was that it would only be possible to get 100% conversion if the material in the engine went to the absolute zero of temperature at some stage of the cycle. Then later a scientist called Nernst came along and showed that it was never possible to attain the absolute zero. This is the Third Law of Thermodynamics.

So here are the three laws:

SLIDE 17  Three Laws of Thermodynamics

Discuss

Everyone's heard of the Second Law and its consequences, even this man:

SLIDE 18  Homer Simpson

There was an episode of The Simpsons where the conversation went like this:

Marge: I'm worried about the kids, Homey. Lisa's becoming very obsessive.
Homer: I know. And this perpetual-motion machine she made today is a joke! It just keeps going faster and faster. Lisa! Get in here. [Lisa walks in] In this house, we OBEY the laws of thermodynamics!

One of the big tests that we do on new theories these days is to test whether they obey the laws of thermodynamics. That means that they can't suddenly introduce new sources of energy, only show how it might be transformed from one form to another. It also means that they have to pass the second law which limits the efficiency with which energy such as heat energy can be converted into useful work. If new theories don't pass both of these tests, out they go. Relativity and quantum mechanics have both passed, incidentally.

C.P.Snow also proposed using the Second Law as another sort of test in his book “The Two Cultures" to find out how much his arts-trained colleagues knew about science. When he asked them to describe the Second Law of Thermodynamics, which he said was the scientific equivalent of ‘Have you read a work of Shakespeare's?' he says: The response was cold. It was also negative.

Yet the Laws of Thermodynamics underpin everything that we understand about the Universe. Life is driven by energy which derives from the Sun, which plants can convert by photosynthesis into chemical energy to drive the chemical reactions that sustain them. When we eat plants we burn them and use the resultant energy to sustain our own processes. But ultimately it all comes from the Sun, and when that runs out, we run out. Current calculations suggest that this will be in about 4.5 billion years.

Story of broadcast

I said earlier that Kelvin got two things wrong in his scientific lifetime. One was when he didn't initially believe Joule. The second was when he tried to calculate the age of the Earth using the rate at which the Earth would lose energy to space. What he did was to go back to the time when the Earth was a molten blob, and calculate how long it would have taken for the Earth to cool down to its present temperature. The equations for the speed at which hot objects lose their heat are well known, and the answer that Kelvin got was around 98 million years.

SLIDE 19  Kelvin and Darwin's age of the Earth

Now Charles Darwin had calculated from fossil evidence that the world was around 300 million years old, and Kelvin launched a campaign to discredit this and to question the whole value of fossil evidence compared to the rigorous equations of physics. He actually used additional information about the structure of the Earth to revise his estimate of its age down to between 20 and 40 million years, while the evolutionists were postulating ages up to 100 times as great. And his equations were rigorous, except that there was one thing that he didn't know, which was that the Earth's core is loaded with radioactive materials, and that these provide heat as they decay and keep the Earth warmer than it would otherwise be. When you take these into account the physics and the fossils disagree nicely, but I should say that some creationists are still quoting Kelvin's original calculations as evidence that Darwinism must be wrong!

Where you can apply Kelvin's calculations is to the subject of boiling an egg, because the equations still work no matter whether heat is leaving an object or entering it. When you apply them, this is what you get:

SLIDE 20  How to Boil an Egg

Brief discuss

Kelvin actually stayed at Glasgow University of for over fifty years, and managed to annex most of the space in the building during that time to turn into laboratories. In fact, he invented the idea of the separate research laboratory, because up until that time lecturers had done all of their research in the same rooms where they taught their classes. He became famous for his application of physics to everyday problems, especially in the design and laying of the first transatlantic cable. When he eventually resigned his Professorship after 53 years, he promptly enrolled himself at the University as a research student at the age of 75! He thus became both the youngest and the oldest student that the university had ever had!

Kelvin's most frightening prediction was that the Universe will gradually become more disordered and eventually die in chaos – the so-called “heat death". It's not going to happen for a while, though, so I'll stop now and give you a chance to get home to your beds – while they're still warm.

Return to Talks