Age of Invention: Counting Caloric

No, that’s not a typo in the title. Caloric was a kind of infinitesimally subtle fluid substance, believed by many prominent scientists in the late eighteenth century to be the source of heat when it flowed. This may sound like just another example of a now-debunked belief that many clever and educated people had in the distant past, to be put up there alongside the longstanding belief that clams spontaneously generated from sand, that geese were born from barnacles, and that peacock flesh did not rot. But I find it interesting because the material theory of heat — that which treated heat as a kind of matter — was believed by some of the key pioneers of modern thermodynamics, both theoretical and applied. Its one of the many energy-related themes I’ve been thinking about lately in my work with Carbon Upcycling.

In this post, let’s start with a theoretical pioneer. One of the founding texts of modern thermodynamics was an 1824 essay by the young French military engineer Sadi Carnot. His father Lazare Carnot, as well as being an important military engineer himself, had been the organiser of the French Revolutionary Army, was one of the five members of the Directorate that ruled France in the latter years of the revolution, and served as minister of war under Napoleon. By the time Sadi wrote his work on thermodynamics, however, Lazare had died in exile and his surname made Sadi a pariah. Sadi’s work, Reflections on the Motive Power of Fire, thus had little immediate impact. It was not recognised until decades later, probably because Sadi himself died only eight years later, aged just 36.

Despite receiving little initial attention, Sadi Carnot’s work nonetheless outlined the theoretical principles for how steam engines — and really all heat-using engines — worked. Carnot laid much of the groundwork for modern thermodynamics, conceiving of a heat engine’s work as being obtained from the flow of heat “from a body in which the temperature is more or less elevated, to another in which it is lower”. It followed that creating heat alone was not enough to “give birth to the impelling power: it is necessary that there should also be cold”. Heat engines derived their motion from the difference in temperature, because the system adjusted to re-establish an equilibrium, where the temperatures would equalise.

Carnot also reasoned that the process could be reversed, with the resulting motion in turn being able to create new and exploitable imbalances in temperature — a fresh “destruction of equilibrium” — such as by raising the temperature of a solid body through friction or collision, or by compressing a gaseous vapour like steam. (Chemical reactions might do the same, but he specifically removed them from the equation, other than noting that burning a fuel usually created the initial imbalance in temperature.)

From his reasoning, Carnot noted that it would be impossible to fully use the motion in the engine to create new temperature imbalances, as that would imply a perpetual motion — something “entirely contrary to … the laws of mechanics and of sound physics”. He thus noted the heat engine’s theoretical maximum efficiency, and from this deduced the ways in which it might lose efficiency. Given that motive power was produced from heat flowing to re-establish an equilibrium, and that same motive power was the only thing within the system capable of disrupting the equilibrium, then “every re-establishment of equilibrium which shall be accomplished without production of this [motive] power should be considered as an actual loss”. From this, Carnot then looked at the relationship of temperature to changes in volume, pressure, and the state of matter, so as to deduce more ways to improve the engine’s efficiency.

This was important theoretical work, and still important today. What’s so striking, however, is that Carnot based all of it on the material theory of heat. Carnot thought in terms of caloric — a substance that literally flowed from higher temperature bodies to lower temperature ones, with the steam of a steam engine “only a means of transporting the caloric”. But it was perhaps because Carnot thought of heat as matter that he was able to come to many of his conclusions.

For a start, caloric was thought to be either containable within a body — known as “latent heat” — or else released from it, to be expressed as “sensible heat” — that which could be sensed, or measured with a thermometer. The idea of latent heat stemmed from the work of the Scottish natural philosopher Joseph Black in the 1770s, who had observed that the temperature of melting ice stayed the same until it had all turned into water (and likewise for water into steam), even though more and more heat was poured into it. The extent to which caloric would be either latent or sensible, however, also depended on volume and pressure — which Carnot used to show how temperature differences could be translated into motive power.

Likewise, Carnot could not yet draw upon a fully-formed idea of what we now call energy, which in all its forms would be conserved. But it was already assumed that there was conservation of the “living” and “dead” forces involved in motion (quite close to what we’d now call kinetic and potential energy). And it had long been assumed that matter, or mass, was also always conserved. Thus, even though motion and heat were not widely thought to be equivalent — an idea that was also ancient, but which by the late eighteenth century had largely gone out of fashion, and would only gain currency again in the 1840s — Carnot’s theories led him to a de facto assumption quite close to the conservation of energy. Caloric was matter, which was always conserved, and it was a substance whose flows either caused or were released by motion, which was also always conserved. He thus implicitly used a kind of version of the first law of thermodynamics, whereby the total motion and flow of caloric together could neither be created nor destroyed within his idealised engine, even if he did not explicitly treat motion and caloric flows as two versions of the same concept.¹

Lastly, and perhaps most importantly, Carnot made a direct analogy between the flow of caloric and the flow of water. Just as the motive power that a waterwheel could capture from a waterfall depended on the quantity of water and the height of its fall, so the motive power of heat depended on the quantity of caloric and “the height of its fall, that is to say, the difference of temperature of the bodies between which the exchange of caloric is made”. The heat engine’s flow from a high temperature to a low temperature reservoir — from furnace to condenser — was in Carnot’s mind just like the flow of water in a river from a higher reservoir to a lower one. It immediately suggested that the theoretical maximum could be worked out in much the same way. Indeed, the early water pioneers, like Antoine de Parcieux, had used the very similar starting point of thinking about what conditions would be needed to get as close as possible to full reversibility, or perpetual motion, and then working back from there.

Caloric theory then, despite being a material theory of heat, still managed to suggest many of the insights that were later formalised in the thermodynamic theories of the 1840s, which treated heat as equivalent to motion. Heat, it seems, did not have to be motion, in order for it to be treated like it in many of the respects that mattered.

As I’ll look into next time, material theories of heat don’t seem to have held back the practical improvement of the steam engine either. Indeed, many of the famous British inventors — such as Robert Stephenson and Isambard Kingdom Brunel — were still speaking in terms of caloric as late as the 1850s.²

1. See e.g. G. Falk, ‘Entropy, a Resurrection of Caloric—a Look at the History of Thermodynamics’, European Journal of Physics 6, no. 2 (April 1985): 108-115, who notes that caloric maps quite neatly onto the later concept of entropy.

2. See, e.g. ‘Discussion. Sir George Cayley’s Hot-Air Engine’, Minutes of the Proceedings of the Institution of Civil Engineers 9, (January 1850): 197–203