Boerhaae's law (labeled)
Top: The basic outline of Boerhaave's law, which states that adding heat Q to a body will cause volume expansion and that removal of heat will cause volume contraction, enunciated as a general law of nature in 1720 by Dutch physical chemist Herman Boeraave; a principle that formed the basis of French chemist Antoine Lavoisier's 1787 caloric theory; which, in turn, formed the basis for French physicist Sadi Carnot's 1824 general theory of the operation of heat engines; which, in turn, formed the basis of German physicist Rudolf Clausius' 1865 The Mechanical Theory of Heat, and thus the science of thermodynamics and the two central laws of universal operation, namely energy conservation (first law) and entropy increase (second law). Bottom (right): example of Boerhaave's law in metals: rail length expansion and subsequent rail buckling due to hot weather (heat). Bottom (left): modern tracks use "gaps" to prevent the buckling of tracks during hot weather.
In science, Boerhaave's law states that that every body, whether in the solid, fluid, or gas state, is augmented in all its dimensions by any increase of its sensible heat. [1] The law is named after Dutch physician and chemist Herman Boerhaave who discussed and experimentally demonstrated the law in his 1720s chemistry lectures at Leiden University.

Guericke
In 1663, Otto Guericke, in his Magdeburg Experiments on the Vacuum of Space, stated the following: [7]

Air extends and expands itself more or less according to a greater or lesser intensity of heat. Warm air, consequently, occupies a larger space and cold a smaller.”
Otto Guericke (1663), Magdeburg Experiments on the Vacuum of Space

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Papin's digester
In 1679, French physicist Denis Papin invented the “bone digester” or Papin digester as it later came to be called, a type of high temperature pressure cooker that could liquefy solid bones. Soon thereafter, Papin's digesting device became a standard research tool with which to show that that bodies can be made to change state, from solid to liquid to gas.

Hooke
In 1665, English scientist Robert Hooke, an associate of Papin, so to speak, asserted the principle that thermal expansion and contraction might be a general property of matter: [3]

“The property of expansion with heat, and contraction with cold, is not peculiar to liquors only, but to all kinds of solid bodies, especially metals.”
Robert Hooke (1665), Micrographia (pg. 39); post-dates Otto Guericke equivalent statement; pre-dates Boerhaave’s law (c.1720), which is cited by Antoine Lavoisier (1789) as the basis of his caloric theory

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Papin engine
See main: Papin engine
In 1690, French physicist Denis Papin published his "A New Method to Obtain Very Great Motive Powers at Small Cost" wherein he conceived the view that he could utilize the expansive properties of water by heat to make a piston and cylinder lift weight using fire, the gist idea of which he outlines as follows:

“Since it is a property of water, that a small quantity of it turned into vapor by heat has an elastic force like air, but upon cold supervening is resolved again into water, so that no trace of the said elastic force remains … [thus] I at once saw that machines could be constructed, in which water, by the help of a moderate heat, and a little cost, might produce that perfect vacuum.”

His "New Method" goes into the details of this procedure.

This seems to be the first statement of the outline of the the general property of expansion of bodies by heat and contraction by cold.

Gravesande
Some time in the years 1718 to 1748, Dutch physicist Willem Gravesande, at Leyden university, conducted his classic ball and ring experiment to prove the phenomenon of volume expansion by heat. This research was communicated, shown, or conducted in joint operation (possibly) by Dutch physician and chemist Herman Boerhaave.

Papin engine small (new)Ball and ring experiment
Left: the Papin engine operated via the action of Boerhaave's law. Right: a depiction of the famous "ball and ring experiment" famously performed in circa 1730 by Dutch physicist Willem Gravesande, at Leyden University, to the amazement of crowds in excess of 500, being that the phenomena was contrary to the prevailing theories of matter and heat and their operations.
Boerhaave's lectures
In the 1720 to 1740s,
Dutch physician and chemist Herman Boerhaave (1668-1738), in his his chemistry lectures at the University of Leyden, introduced the the idea of volume expansion by heat as a general law of nature. The main points of Boerhaave’s “law of expansion” or expansion axiom are as follows: [2]

(a) The same degree of fire rarefies fluids sooner, and in greater degree, than it does solids. Without this law, the thermometer would be useless, since the cavity of the tube would then be dilated in the same proportion as the fluid is rarefied.

(b) The lighter the fluid, the more it is dilated by fire. Air, the lightest of fluids known (to Boerhaave), expands the most; after air, spirit of wine.

(c) All the motion in nature arises from fire alone; taking this away, all things become immovable. At the absence of only a certain degree of fire, all oils, waters, spirits, vegetables, and animals, become hard, rigid, and inert. If the greatest degree of cold was arrived at, and all fire was absolutely taken away, all nature would grow into one concrete body, sold as gold and hard as diamond: on the reapplication of fire it would recover its former mobility.

In a modern sense, these statements can be interpreted as being due to the actions of the photon, in the movement of heat in systems of atoms, molecules, and structures, being the force carrier of the electromagnetic force, causes electrons to jump up in atomic orbital making the attached atom more unstable and movable, thus creating the expansion.

Montesquieu
In 1748, French political philosopher Charles Montesquieu, in his The Spirit of the Laws, notes that iron bars tend to contract when cooled (also noted by Carnot in his 1824 Reflections, below), and that by extrapolation such an effect may occur in human nerve endings, thus mediating different personal behaviors in love, sex, courageousness, and passions, etc., of people in lands of different heat. Montesquieu's physics-based theories, according to John Q. Stewart, had a vicarious subtle influential effect on the thinkings of American political theorist James Madison (1751-1836), the fourth US president and so-called “father of the constitution”, who was a student of Montesquieu political philosophy interpreter Scottish-born American John Witherspoon (1723-1794), a signatory of the Declaration of Independence. [6]

Earth (piston view) Boerhaave's lawHuman PV work (f)
Left: a "social volume" piston and cylinder view of society "worked" according to the operation of Boerhaave's law each day when heat from the sun is put into each social system on the surface of the earth, thus causing volume expansion (social volume expansion), otherwise known as daily work. Right: a Mean Girls depiction of Boerhaave's law at work in the operation of human chemical reactions, wherein reaction heat causes volume expansion, when the alpha female walks though the hall of a local high school and the student contract backwards giving her more personal space.
Lavoisier
French chemist Antoine Lavoisier, in his 1787 Elements of Chemistry, cites Papin's digester as experimental proof that stones may be turned to vapor, in other words, in modern terms, that heat can be used to actuate or bring about phase change, and on his opening page credits Boerhaave as establishing principle of the augmentation of the dimension of bodies by heat as a universe rule as follows:

“That every body, whether solid or fluid, is augmented in all its dimensions by any increase of its sensible heat, was long ago fully established as a physical axiom, or universal proposition, by the celebrated Boerhaave.”

In other words, adding heat to a body or system (volume) causes expansion, and this fact is a physical axiom long ago established phenomenon of nature.

Lavoisier then goes on to cite Papin’s digester as the experimental proof that all the solid bodies of the earth, such as “stones, salts, and the greater part of the substances that compose the mass of the earth”, can be “softened and changed into fluids, etc.”.

On this basic, Lavoisier defines three states of matter: solidity, liquidity, and aeriform elasticity. To explain Boerhaave’s law, he then states that caloric particles are what constitute the matter of heat and that caloric is what “communicates a power of repulsion to the particles of bodies”, to the effect that volume is function of the number of caloric particles in a given body. [1]

Carnot's general theory of heat engines
This expansion-by-heat contraction-by-cold principle was used as the basis of French physicist Sadi Carnot’s 1824 general theory of heat engines, particularly in his definition of the working body, and the means by which the working body may be expanded or contracted, in cycle, to produce work.

In utilizing a combination of Boerhaave's law and Lavoisier's caloric theory, Carnot says: [4]

“All substances in nature can be employed for this purpose, all are susceptible of changes of volume, of successive contractions and dilatations, through the alternation of heat and cold. All are capable of overcoming in their changes in volume certain resistances, and of thus developing the impelling power.

A solid body—a metallic bar for example—alternately heated and cooled increases and diminishes in length, and can move bodies fastened to its ends. A liquid alternately heated and cooled increases and diminishes in volume, and can overcome obstacles of greater or less size, opposed to its dilatation.

Phase change diagram for water (500px)
Phase change diagram for water on going from solid-to-liquid-to-vapor, with corresponding increase in volume, according to Boerhaave's law as heat is added; the horizontal sections, enthalpy of fusion Hf and enthalpy of vaporization Hv, to note, correspond to the points at which latent heat is added.
An aeriform fluid is susceptible of considerable change of volume by variations of temperature. If it is enclosed in an expansible space, such as a cylinder provided with a piston, it will produce movements of great extent. Vapors of all substances capable of passing into a gaseous condition, as of alcohol, of mercury, of sulphur, etc., may fulfill the same office as vapor of water.

The latter, alternately heated and cooled, would produce motive power in the shape of permanent gases, that is, without ever returning to a liquid state. Most of these substances have been proposed, many even have been tried, although up to this time perhaps without remarkable success.”

This is the basic operational methodology for what would soon become the science of thermodynamics in his definition of the basic heat cycle of heat engine operation.

References
1. Lavoisier, Antoine. (1789). Elements of Chemistry (pg. 5, 28). London: G.G. and J.J. Robinsons.
2. Dickens, Charles. (1862). All the Year Round, (Section: Fire, pg. 393-95). Jan. 18.
3.
(a) Shachtman, Tom. (1999). Absolute Zero and the Conquest of Cold (pg. 42). Mariner Books.
(b) Quote, supposedly, from lecture by E.N. da C. Andrade before the Royal Society, printed in its Proceedings, 1950.
4. 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.
5. Montesquieu, Charles. (1748). The Spirit of the Laws (XIV: Of Laws in Relation to the Nature of the Climate, pgs. 221-; XV: In what Matter the Laws of Civil Slavery Relate to the Nature of the Climate, pgs. 235-; XVI: How the Laws of Domestic Slavery Bear a Relation to the Nature of Climate, pgs. 251-; XVII: How the Laws of Political Servitude bear a Relation to the Nature of the Climate, pgs. 264-). The Colonial Press, 1900, Edition: 3, Vol. 1. (Translator: Thomas Nugent).
6. Staff. (1955). “Research in Progress: Social Physics”, Princeton Alumni Weekly, 55:17.
7. Guericke, Otto. (1663). The Vacuum of Space (De Spatio Vacuo). Unpublished; New Magdeburg Experiments on the Vacuum of Space (Ottonis De Guericke Experimenta Nova (ut vocantur) Magdeburgica de Vacuo Spatio) (preface, pdf) (pg. 112). Janssonius a Waesberge, 1672.

Further reading
‚óŹ Diemente, Damon. (2000). “Boerhaave on Fire” (abs), J. Chem. Educ. 77(1): 42.

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