In schools of thermodynamics, the École Polytechnique is a French engineering school, founded in 1794, associated with a number of connected scientists and founders of thermodynamics as well as various heat/force/work concepts, principles, and theories derived therefrom.

French school of thermodynamics
All-in-all, the the École Polytechnique is the original birthplace or seedling home of thermodynamics, having been founded, in part by, French engineer Lazare Carnot, father to thermodynamics pioneer Sadi Carnot, among numerous other pre-thermodynamics pioneers.

Those of significance to have graduated or taught at the École Polytechnique include Sadi Carnot, a student there in 1812, author of the 1824 Reflections on the Motive Power of Fire (Réflexions sur la puissance motrice du feu), Gustave Coriolis, a tutor there beginning in 1816, first to coin the term “work” as the product of force and distance, and Émile Clapeyron, graduate of the school in 1818, author of the 1834 Motive Power of Heat (Puissance motrice de la chaleur), among others.

The school, originally called the École centrale des travaux publics, was founded in 1794 by French engineer Lazare Carnot, the father of Sadi Carnot, and French mathematician Gaspard Monge, during the French Revolution, at the time of the National Convention.

Coriolis was the first to employ the name work for the quantity fs or force f multiplied by distance s. [2] This was sustained in usage by French engineer and mathematician Jean-Victor Poncelet, a former student (1808-10) and later commandant general (1848) of the École Polytechnique, who adopted the kilogramme-metre as the unit of work. [3]

In the late 1790s, French mathematician and physicist Joseph Fourier was appointed chair of the École Polytechnique. In 1822 he published his Analytical Theory of Heat (Théorie analytique de la chaleur), in which he basing his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures, outlined a mathematical model of heat movement in various directions. [5] In this work Fourier claims that any function of a variable, whether continuous or discontinuous, can be expanded in a series of sines of multiples of the variable.

French physicist Alexis Petit studied at the École Polytechnique, graduating in 1811, later becoming professor of physics from 1815 to 1819. He is known for his 1818 publication on the efficiencies of air-engines and steam-engines and for his discussions with Sadi Carnot on the same subject. One of Petit’s noted students in physics, during the years 1815-16, was Auguste Comte, the French sociologist and philosopher who is generally credited with having coined the term sociology and who first outlined the subject of "social physics".

Thomson’s search for Carnot’s Reflections
See main: Thomson’s search for Carnot’s Reflections
In 1839, at the Royal Belfast Academical Institution of Northern Ireland, where a young 15-year-old student William Thomson (Lord Kelvin) was in attendance, Scottish educator John Nichol, a professor of astronomy, took the chair of natural philosophy. That year, Nichol updated the curriculum, introducing the new mathematical works of Fourier. The mathematical treatment much impressed young Thomson, who became intrigued with Fourier's Théorie analytique de la chaleur and committed himself to study the "Continental" mathematics resisted by a British establishment still working in the shadow of Isaac Newton.

Out of this stimulus, in 1841, at the age of 17, Thomson wrote his first scientific paper on Fourier’s analysis of heat under the pseudonym P.Q.R., which was submitted to the Cambridge Mathematical Journal by his father, titled “On Fourier's expansions of functions in trigonometric series”. [4] Two more papers of similar theme soon followed. [6]

In 1845, after learning of Sadi Carnot’s work through the 1834 paper of Clapeyron, Thomson went to Paris to work with French chemist and physicist Henri Regnault, a former student (1830) and later chair of chemistry (1840) at École Polytechnique, and tried to find a copy of Carnot’s Reflections. To his surprise and disappointment there was no copy in the library of the École Polytechnique, and no Paris bookseller had heard of it or its author. [7]

Mechanical Theory of Heat
By 1850, through Thomson, via Clapeyron, the work of Carnot reached the likes of German physicist Rudolf Clausius. In a footnote to his 1850 paper "On the Motive Power of Heat", Clausius states: [8]

“I have not been able to obtain a copy of this book [Reflections], and am acquainted with it only through the work of Clapeyron and Thomson, from the latter of whom are quoted the extracts afterwards given.”

The supposition, in Carnot’s work, that caught Clausius’ attention was the postulate, expressly stated, that “the quantity of heat remains unchanged” (in the process), which equates to the argument that “no change occurs in the condition of the working body” (during the work cycle). Conversely, according the view of Clausius, as developed in the mechanical equivalence of heat, a certain amount of heat would consumed in the working body during an irreversible passage of heat in the cyclical production of work. These corrections were employed and remolded in Clausius' famous Mechanical Theory of Heat (1850-1875).

References
1. (a) History of the École Polytechnique - Polytechnique.edu
(b) École Polytechnique - Wikipedia.
2. Jammer, Max. (1957). Concepts of Force, (pg. 167). New York: Dover.
3. Cajori, Florian. (1899). A History of Physics in its Elementary Branches, (pg. 52). MacMillan.
4. P.Q.R (1841) "On Fourier's expansions of functions in trigonometric series" Cambridge Mathematical Journal 2, 258-259.
5. Fourier, Joseph. (1878). The Analytical Theory of Heat. Cambridge: At the University Press.
6. (a) P.Q.R (1841). "Note on a passage in Fourier's 'Heat'" Cambridge Mathematical Journal 3, 25-27.
(b) P.Q.R (1842). "On the uniform motion of heat and its connection with the mathematical theory of electricity" Cambridge Mathematical Journal 3, 71-84.
7. Laidler, Keith J. (2002). Energy and the Unexpected, (pg. 31). Oxford University Press.
8. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws Which Can be Deduced from it for the Theory of Heat" (author footnote, pg 1). Poggendorff's Annalen der Physik, LXXIX, 368, 500.