
French physicist Sadi Carnot's 1824 so-called re-establishment of equilibrium in the caloric, namely his model of a body being able to "reestablish" its equilibrium amount of caloric, a then considered a conserved particle, following expansion to one volume and state, followed by contraction to its original volume and state.

re-establishment of equilibrium in the caloric 2

French physicist Sadi Carnot's 1824 so-called re-establishment of equilibrium in the caloric, namely his model of a body being able to "reestablish" its equilibrium amount of caloric, a then considered a conserved particle, following expansion to one volume and state, followed by contraction to its original volume and state.

In thermodynamics, re-establishment of equilibrium in the caloric is a view professed by French physicist Sadi Carnot, in his 1824 Reflections on the Motive Power of Fire, that the production of motion in steam-engines is always accompanied by a circumstance on which we should fix our attention. This circumstance, according to Carnot, is the:

“re-establishing of equilibrium in the caloric; that is, its passage from a body in which the temperature is more or less elevated (hot body), to another in which it lower (cold body).”

This view originated from the descriptions, by French chemist Antoine Lavoisier in the 1780s, of combustion, as a process that sets free or releases heat or "caloric" particles and light, otherwise known as caloric theory, which became the predominant view of what heat was, lasting well into the 1830s. In more detail, to describe the operation of the steam engine, Carnot states that:

“The caloric developed in the furnace by the effect of the combustion traverses the walls of the boiler, produces steam, and in some way incorporates itself with it. The latter carrying it away, takes it first into the cylinder, where it performs some function, and from thence into the condenser, where it is liquefied by contact with the cold water which it encounters there. Then, as a final result, the cold water of the condenser takes possession of the caloric developed by the combustion … the steam (working substance) is here only a means of transporting the caloric.”

Caloric flow
The caloric, described here, and first defined in the 1787 publication Method of Chemical Nomenclature, written by Guyton de Morveau, Antoine Lavoisier, Antoine-Francois de Fourcroy, and Claude Berthollet, was thought of as an indestructible, fluid-like, massless particle of heat that could travel though the pores of bodes, liquids, and gases acting as the repulsive force balancing the attractive force of the particles (atoms) of bodies towards each other. This view was initially described in French chemist Antoine Lavoisier’s 1780 memoir “On Combustion in General”. In this memoir, Lavoisier lays out six points:

(a) In combustion, there is a disengagement of the matter of fire (caloric) or light.

(b) A body can burn only in pure air [oxygen gas].
(c) In combustion, there is a destruction or decomposition of pure air and the increase in weight of the body burnt is exactly equal to the weight of the air destroyed or decomposed.
(d) The body burnt changes into an acid by addition of the substance which increases its weight.
(f) Pure air is a compound of the matter of fire (caloric) or of light (possibly caloric) with a base.
(g) In combustion, the burning body removes the base, which it attracts more strongly than does the matter of heat, and sets free the combined matter of heat (caloric), which appears as flame, heat, and light.

In his famed 1789 Elements of Chemistry, Lavoisier elaborates further on the nature and action of caloric by devoting his entire opening chapter to the subject. To begin, he enunciates Herman Boerhaave’s law of separation of particles by heat, which states that “every body, whether sold or fluid, is augmented in all its dimensions by any increase in its sensible heat.” Lavoisier states that the term caloric, “while we are not obliged to suppose this to be a real substance”, is used to distinguish “the cause of heat, or that exquisitely elastic fluid which produces it.” He states that the caloric be “considered as the repulsive cause, whatever that may be, which separates the particle of matter from each other”. In respect to radiant heat, Lavoisier concludes:

“in the present state of our knowledge, we are unable to determine whether light be a modification of caloric, or if caloric be, on the other contrary, a modification of light.”

In relation to expansion or contraction of bodies by heat, Lavoisier states that “bodies become solid, or fluid, or aeriform, according to the quantity of caloric by which it is penetrated; or, to speak more strictly, according as the repulsive force exerted by the caloric is equal to, stronger, or weaker, than the attraction of the particles of the body it acts upon.” He also points out, in addition to these attractive and repulsive powers, that a “third power”, that of the pressure of the weight of the atmosphere, acts to give us states of liquid and solid, whereas otherwise the caloric would cause everything to be in a state of unstable melting. In relation to equilibrium, Lavoisier tells us:

“The particles of every substance in nature exist in a certain state of equilibrium, between that attraction which tends to unite and keep the particles together, and the effects of the caloric, which tends to separate them.”

After giving definitions for “free caloric”, “combined caloric”, “specific caloric”, and the “capacity of bodies for containing caloric”, he then goes on to define heat as something considered as a sensation, i.e. sensible heat, as the effect produced upon our sentient organs, by the motion or passage of caloric, disengaged from the surrounding bodies.” To elaborate on this definition, he states, in relation to the sensations of heat and cold, that:

“When we touch a cold body, the caloric which always tends to become in equilibrio in all bodies, passes from our hand into the body we touch, which gives us the feeling or sensation of cold. The direct contrary happens, when we touch a warm body, the caloric then passes from the body into our hands, producing the sensation of heat. If the hand and the body touched be of the same temperature, or very nearly so, we receive no impression, either of heat or of cold, because there is no motion or passage of the caloric.”

It seems that Carnot, in spite of Lavoisier admonition of "not be obliged to to suppose this to be a real substance”, took the caloric to be a real entity that could pass from body to body until it found equilibrium. In particular, the model that Carnot seems to base his analysis on is the 1890 Papin steam engine, on which all other steam engines, in principle, are built (depicted above).

Papin's steam engine model
In the original steam engine design by Denis Papin, depicted above, as described in his 1690 memoir "A New Method to Obtain Very Great Motive Powers at Small Cost", on which all others were built, a body of water (working substance) contained in a cylinder, closed at the bottom, but topped by a air-tight movable piston, was taken through a process of steps in which one engine cycle, designed to produce the “intended effect”, i.e. the downward forceful thrust of the piston, to which a pulley and heavy weight were attached, was described as such:

1. The cylinder of water was put in contact with a fire.
2. The fire caused the water to be converted into steam, thus forcing the piston up.
3. The fire was removed.
4. The cylinder, now being in contact with cooler surrounding air, condensed, thus causing a vacuum to form.
5. The piston was then forced downward, as the vacuum could not hold up the weight of the atmosphere.

In later engine designs, such as made by Savery and Watt, the body of the cool surrounding air was replaced with the body of cool flowing water, which was thus able to remove the heat from the cylinder faster. In a sense, to produce the “intended effect”, the particles of heat, deemed indestructible, an hypothesis originating with the 5th century atomic theory of Greek philosopher Leucippus, would flow from the fire, due to their release via combustion, into the water of the cylinder, cause the water to expand, then flow out into the cold body in the final step, thus letting the water, now having been rid of the caloric particles, to condense or contract in volume.

Thermodynamics
In 1798, American-born English physicist Benjamin Thomson showed, in his now-famous cannon boring experiment, that heat could be generated continuously by turning a dull boring bit inside of a cannon. [2] This laid question to Lavoisier’s caloric theory. In other words, heat particles were seemingly being created here, not due to combustion, or a passage from a hot to a cold body, but by friction. This was a mystery to many. Soon, similar types of experiments were being done, such as British chemist and physicist Humphry Davy's 1799 “ice-rubbing experiments”, where in a room colder than the freezing point of water, he generated heat or made ice melt by the mechanical rubbing of cubes together. These efforts, among others, led to the establishment of the mechanical equivalent of heat in about 1842, a set of experimental results which showed that quantities of heat could be converted into work and, conversely, that quantities of work could be converted into heat:

Heat ↔ Work

This equates to the equivalence of caloric particles being converted, as they flow through the working substance, into "internal work" or the motions of atoms of bodies:

Caloric ↔ Movement of atomic bodies under the influence of force

In other words, in the terminology of caloric particles, newer experiments began to show that a certain portion of the caloric particles that went into cooler bodies were transformed into an equivalent amount of internal atom work and that these “transformed” caloric particles could not be recovered, as Carnot had supposed. Using the above diagram, as an example, if say five caloric particles went in, modern experiments would show that less than five would come out.

To correct this deficit in theory, beginning in 1850, German physician Rudolf Clausius spent 15-years writing the monumental Mechanical Theory of Heat, which introduced the quantity of entropy, in place of caloric, to correct Carnot’s theory, thus laying out the foundations for the new science of thermodynamics, as we know it now. [3]

References
1. Carnot, Sadi. (1824). Reflections on the Motive Power of Fire - and on Machines Fitted to Develop that Power. Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.
2. (a) Thomson, Benjamin. (1798). “An Inquiry Concerning the Source of Heat which is Excited by Friction”. Philosophical Transactions. Vol. XVIII, pg. 286.
(b) Thomson, Benjamin. (1798). “An Inquiry Concerning the Source of Heat which is Excited by Friction” in The Complete Works of Count Rumford, (pgs. 469+). Oxford University Press, 1870.
3. (a) Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. (Google Books). London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
(b) Clausius, Rudolf. (1879). The Mechanical Theory of Heat, (2nd ed). London: Macmillan & Co.