## On the Motive Power of Intuition

I’m sure that most of you were taught thermodynamics in high school. You’ll probably remember listening to things like “…thermodynamics is the branch of physics that studies heat and work…”, or “…thermodynamics is concerned with large objects, like heat engines…”. For most people thermodynamics was indeed a pleasant subject to study. Its math was simple. At least, simple compared to those horrible vectors and scary integrals from electromagnetism or mechanics. And the theory was fairly easy too: You just had to memorise a couple of formulas and those good old Three Laws.
(Or were there four of them?)
There’s no doubt that some may have liked thermodynamics better than others, but we all understood it.

In my case, I later started a physics degree and had to take yet another “Basic Thermodynamics” course. While electromagnetism and mechanics had become considerably more scary in the first year of the degree, thermodynamics still looked pretty much the same.
(Nothing to worry about. Piece of cake)
However, some things got me thinking. I started to ask myself about basic concepts that had never troubled me before. For instance, the ‘state variable’ T stands for ‘temperature’ and appears all over the place in thermodynamics but, did I really understand what temperature was?

“You must be kidding. Everyone knows what temperature is!”, you may say.

“Really? Then tell me what is it”, I would reply defiantly.

Temperature is what you measure with a thermometer. It tells you how hot things are“, you could answer.

“So you’d say that temperature is a measure of the ‘hotness’ of things. What is that hotness then?”, I would continue impassively.

“I mean the amount of heat that things carry”, you could reply. And maybe you’d like to add here: “For God’s sake! And you say you finished that physics degree of yours?”

I concede that heat and temperature can be easily confused. Top scientists of the 18th century made such mistake by developing the now obsoleted ‘caloric theory’. Everyone knows that when a hot object is placed next to a cold object, they exchange heat until their temperatures level off. However, temperature is not a measure of the heat contained in either of the bodies. As a matter of fact, bodies carry no heat at all. They carry energy. Heat is more of a currency for trading energy.
“What is temperature then?“
It seems that the question is not as silly as it sounds. Is it?

This sense of perpetual wonder is quintessential to thermodynamics. We are so used to concepts like heat, energy, power or temperature that we rarely stop to think about them.

“Who cares how temperature is rigorously defined?”, you could object. “Other than a first-year physics student, that is… As I said, as long as I have a thermometer I can measure temperature. I don’t really need to know what I’m measuring. All I need to know is that 37 °C is a normal body temperature, or that it takes 30 minutes at 180 °C to bake a carrot cake“.

That’s not just a fair point. It’s actually brilliant: Historically, it was not the theory of thermodynamics that we know today (with its elegant axioms and all) which drove the Industrial Revolution during the 18th and 19th centuries. Instead, progress was possible thanks to the intuition of engineers, solidly built on the experiences of a lifetime dealing with temperature, heat, and work.

For instance, let’s talk about temperature. Its existence was promoted to the level of postulate or Law of Thermodynamics (the Zeroth Law) only in the 1930s. The statement goes like this:

If a body A is in thermal equilibrium with two other bodies B and C, then B and C are in thermal equilibrium with each other. Hence, systems can be sorted into equivalence classes. We may label these classes with a parameter T, called temperature.

For A and B, being in thermal equilibrium simply means that nothing happens if they are brought into contact with one another. The Zeroth Law certainty is a useless truism, with no bearing in practical thermometry. Ancient physicians definitely knew about fever, and felt the urge to measure the temperature of their patients (whatever that was) as early as the second century A.D. In the late 1590s Galileo and his students pioneered in the thermometer-manufacturing business, and after a few centuries, people got pretty good at it: Better designs were conceived, reference points were established, and temperature scales were defined, allowing for the comparability of measurements. By the 18th century, thermometers were customarily found in the streets and homes and had many different uses. However, nobody was aware of what they were measuring!

Another good example of the value of intuition in scientific progress is the backstory of Carnot’s Great Theorem. In 1824 young Sadi Carnot published a scientific paper (or “memoir”, as they used to call them) on the motive power of fire. Nowadays Carnot’s memoir is acknowledged as the ‘birth certificate’ of thermodynamics and one of the biggest milestones in the history of physics. Let us quote here his main result:

The driving force of heat is independent of the agents chosen to produce it; it’s amount is solely determined by the temperatures of the bodies between which ‘caloric’ is transferred.

“And what is that supposed to mean?”, you may ask.

“Well, it means that if you came up with a fancy design for a new heat engine tomorrow, no matter how many smart tweaks you had included in it, its energy-efficiency would always be less than a universal quantity (determined by the external temperatures). A more efficient heat engine would simply be against the laws of nature”, would be my answer.

Carnot’s statement is equivalent to the Second Law of thermodynamics, which was not established until thirty years later. He phrased it in very practical terms. Thanks to his theorem, engineers could benchmark their newest designs not against the best existing engines, but against the best engines possible.

However, as shocking as it may sound, the line of reasoning that led Carnot to his Great Theorem was completely flawed. As a nostalgic supporter of the old-fashioned caloric theory, he thought that bodies carried “caloric fluid”, which was supposed to flow downstream from hotter bodies to colder bodies (the overall caloric being conserved). In Carnot’s view, that stream of heat could then be utilised to generate motive power in the same way in which electricity is produced by the turbines of an hydroelectric power plant.

“Then, how could he get that theorem right?”, you’d probably wonder.

Undoubtedly it was not because he had a correct understanding of heat, temperature and work (which he hadn’t), but because of his right intuitions about them. We must bear in mind that in Carnot’s time, engineers had been designing and building engines for over a century. In all those years they were completely unaware of the Second Law or any other legal requirement that their designs had to comply with. They didn’t need to know such things. They just did their job.
(And I can tell you that they were damn good at it)
Carnot, who was an engineer himself, must have also developed some kind of thermodynamic instinct.

Sadly, poor Carnot’s extraordinary achievement went mostly unnoticed during his lifetime. He got his memoir rejected by the editor of “Annalen der Physik”, which was the leading physical journal of the time, and had to publish it as a standalone little book. By the time he died (of cholera, aged 36), nobody seemed to have read it. Nobody except the mining engineer Benoît Clapeyron. He liked it so much than he even reprinted a revised version of the memoir in the journal of the Polytechnical School of Paris in 1834, two years after Carnot’s death. Clapeyron’s revision attracted the attention of Johann Poggendorff, who published it in “Annalen der Physik” in 1843. Ironically, that was the same Poggendorff that had rejected Carnot’s original 19 years earlier! In this unlikely way, Carnot’s ideas made it to William Thomson (later promoted to ‘Lord Kelvin’), who wrote “An Account of Carnot’s Theory of the Motive Power of Heat” (1849). There, the word “thermo-dynamic” was used for the very first time. As you can see, thermodynamics works in mysterious ways.

In conclusion, it would be historically inaccurate to claim that the Industrial Revolution was fueled by the advancements in thermodynamics. Instead, both the Industrial Revolution and thermodynamics were a result of the daring ingenuity of a legion of reckless engineers that insisted in pushing technology beyond the boundaries of physics. Such feat was only possible because of their intuitive understanding of energy transformations and their everyday familiarity with the elements of thermodynamics.
(And because rich fellows decided to spend quite a bit in science back in the day)

Today, there’s another technological revolution going on: the “Quantum Revolution”. For instance, we have developed the technology to grab a single atom, manipulate it, move it around, put it close to other atoms, and make them interact. These technical capabilities bring all sorts of sci-fi gadgets a step closer to reality. Some prophesize that the Quantum Revolution will be as life-changing in the coming decades as the Industrial Revolution was in the 18th century.
(Provided that rich fellows decide to put some good money on that too)
For instance, how about building a heat engine made up of a single atom? Or even better, how about building an atom-sized refrigerator? Or hundreds of thousands of them? That definitely sounds like a lot of fun but, before we can start to play with our atoms, quantum engineers must solve a serious problem: The problem is that our classical intuitions about temperature, heat and work are worth nothing in the quantum world. And that’s because classical and quantum physics are usually very different.
(That makes everything much harder, doesn’t it?)
This is why still today I ask myself things like:

“Can you measure temperature with a thermometer made up of a single atom?”

“What is the heat that two atoms can exchange?”

“What is the work done by a single atom?“

I wonder…