Heat and Thermodynamics

In a workshop with wooden beams, two harnessed horses turn a long bronze cannon lying in a steaming tank of water, watched by a few workmen. — Rumford’s experiment, in 1798: horses turn a cannon against a blunt borer, and the water around it eventually boils. Erosophia illustration, réalisée avec l'aide d'une IA

From the eighteenth century to the middle of the nineteenth, heat was believed to be an invisible fluid.

This idea is wrong. Yet at the time, it was the most cautious and the most rational hypothesis.

This paradox lies at the heart of the story that follows — and it is far more instructive than simply knowing who was right.

First, a kitchen experiment

Before turning to the history, we need to clarify a distinction that everyday language constantly blurs.

A freshly poured cup of tea is hotter than a bathtub of lukewarm water: its temperature is higher. Yet if both are left to cool in the same room, the bathtub will warm the surrounding air far more than the cup. It holds a much greater quantity of heat, simply because there is far more water.

Temperature indicates the degree of agitation, or how hot something is.
Heat measures the quantity of energy transferred from one body to another.¹

A small, very hot object can therefore contain less heat than a large, lukewarm one. Everyone has experienced this.

This distinction is essential for what follows: the theory set out below confused these two notions — and the language we speak still bears its trace.

Caloric

As it was taught for more than a century, the theory ran as follows.

Heat was supposed to be a substance: an invisible fluid, whose molecules repel one another, and which flows naturally from hot bodies to cold bodies. It was called caloric. Temperature, in this model, simply represented its density — the quantity of caloric per unit of volume.²

The idea may seem far-fetched today. Yet this model accounted well for many observations of the time, and it even made it possible to calculate how heat spreads through solids, with results that still hold today.³

Why it was the most cautious theory

This is the heart of the matter.

The rival theory held that heat is motion: the particles that make up matter are agitated, and the more vigorous this agitation, the higher the temperature.

But this hypothesis, a much older one, lacked the quantitative successes of its rival.⁴

Caloric, by contrast, drew on the most recent chemistry — it was pictured as a gas of indestructible atoms — and it explained combustion and calorimetry very well. Its calculations gave most of the right results.⁵

In 1800, which approach was the more scientific? The one that gave figures that could be checked, or the one that stopped at an intuition?

The wrong model was the more rigorous one. A related debate, about what one may accept without seeing it, appears on the page devoted to atoms (4.2), where eminent scientists still refused to believe in them at the end of the nineteenth century.⁶

The experiment of 1798

Benjamin Thompson, known as Count Rumford, was supervising the boring of cannon at the Munich arsenal — an operation that consisted of hollowing out solid bronze cylinders.⁷

He noticed that the friction of the tool produced an apparently inexhaustible supply of heat. But if heat were a fluid stored in the metal, this reservoir would eventually run dry.

To prove it, he surrounded the end of the cannon with a box filled with water and pressed a deliberately blunt borer against it while the cannon was turned: the borer rubbed without cutting into the material. Then he measured the rise in temperature.⁸

The water eventually boiled.

But the experiment would only be conclusive if Rumford ruled out the other explanations, and this is where it became exemplary. He collected the chips torn from the metal, and showed that they could not be the source of the heat. In the same way he ruled out the air, then the water surrounding the machine.⁹

Finally, he made a decisive observation: friction seemed able to produce heat endlessly, without ever being exhausted. But a substance exists in a limited quantity: it cannot be produced indefinitely out of nothing.¹⁰

Rumford concluded that heat was not a substance contained in the metal, but the manifestation of motion.

A qualification is needed, however. Rumford associated heat with motion, but there is no evidence that he subscribed to a precise theory of agitated particles. He showed what heat was not far more clearly than what it was.¹¹

The reversal

One last twist illustrates the complexity of scientific progress.

In 1800, the astronomer William Herschel discovered the existence of thermal radiation lying beyond the red in the light spectrum: infrared. This advance is described in detail on the page devoted to the electromagnetic spectrum (4.14).¹²

This experiment is taught today as proof that our senses perceive only a fraction of reality. That is true — today.

But at the time, it had the opposite effect: it seemed to confirm the caloric theory.¹³

In that period, light was seen as a stream of corpuscles. Since Herschel had just shown that heat crossed empty space exactly as light did, physicists concluded that heat too was made up of particles: molecules of caloric.¹⁴

It was only in the 1820s, when the wave nature of light became established, that this argument lost its footing.¹⁵

An accurate observation and a rigorous measurement thus served to consolidate a false theory for more than twenty years.

Facts never interpret themselves: a fact speaks only in the theoretical language its era lends it.

We still speak the language of caloric

Caloric was abandoned more than a hundred and fifty years ago, but our everyday language still bears its stamp.

We still say that heat “flows”, that it “passes” from one body to another, or that it “escapes” from a poorly insulated house. More striking still: the unit of energy shown on our food packaging is still called the calorie — a word that appeared in lectures given in Paris between 1819 and 1824, at the height of caloric’s reign.¹⁶

This is the vocabulary of a fluid. It has outlived the theory that gave rise to it. Physicists are well aware of these nuances and carry out rigorous calculations, but these terms remain linguistic ghosts of obsolete ideas.

The direction of time

Thermodynamics introduces a concept that is unique in physics, and unsettling.

If you film the collision of two billiard balls and play the sequence backwards, the scene remains perfectly believable. Almost all the laws of classical mechanics are reversible with respect to time.

Heat is the exception. A cup of hot tea cools spontaneously in a lukewarm room; a lukewarm cup will never warm up of its own accord by cooling the air around it. Heat transfer always takes place from hot to cold, and never in the opposite direction without an external input of energy.¹⁷

With one exception known only to particle physicists, this is the only fundamental law of physics that distinguishes the past from the future — and it is this law that explains why energy inexorably degrades, as described on the page devoted to energy (4.8).¹⁸

Note 1

We also saw in Temperature, Kinetic Theory, and the Gas Laws that temperature is proportional to the (average) kinetic energy of atoms and molecules. […] Heat is the spontaneous transfer of energy due to a temperature difference.

Urone, Paul Peter and Hinrichs, Roger, College Physics 2e, OpenStax (Rice University), 2022, section 14.1 “Heat”