Nicolas Clément was a noted professor and industrial chemist[24] with many interests besides the theory of heat. He had trained at the *École Polytechnique* with Charles Desormes, who was an assistant in the laboratory of Guyton de Morveau, a renowned chemist and colleague of Lavoisier, Berthollet, and Forcroy[25]. From 1801–1819, Clément and Desormes published numerous papers on topics such as the composition of carbon monoxide, proof that iodine is an element, a value for absolute zero, and a value for the ratio of the specific heats of gases at constant pressure and constant volume that is called γ [24]. The value of γ is important because it provided a means of calculating the mechanical equivalent of heat (Joule's coefficient) [26].

From 1812–1819, Clément and Desormes conducted studies on the nature of heat and derived an algebraic method for calculating the mechanical power that can be obtained from steam. Clément read the paper to the *Académie des Sciences* in August, 1819, more than 20 years before Mayer or Joule took up this subject. Parts of the manuscript were published in the *Bulletin de la Societe' d'Encouragement* in 1819 and later donated to the Royal Society of London[27]. The method for calculating mechanical power was sometimes called the Law of Clément-Desormes. Fox[21, 28] and Lervig[22] state that two key concepts in the paper were the conservation of heat (*calorique*) and adiabatic (rather than isothermal) expansion of steam vapor.

The record shows that Clément not only defined the Calorie but also could calculate the amount of work that could be obtained from steam. Clément taught his students that the energy content of charcoal was 7050 Calories (kcal) per kg, and that 650 Calories was required to convert 1 kg of water to steam. One kg of water vapor could do work as it expanded from 1 L to 1700 L. Clément assumed conservation of energy (or *calorique*) and employed engineering units for work (*Dynamie*) equivalent to lifting 1000 kg to a height of 1 m. Clément noted that steam engines of the day could obtain about 300,000–400,000 kg-m of work from 1 kg of charcoal. Without considering efficiency, this would give a value of less than 57 kg-m/kcal. This is about 13% of the theoretical maximum, but Clément probably did not have a way of calculating absolute thermodynamic efficiency. One of Clément's important contributions was to show that higher operating temperatures and pressures permitted greater efficiencies.

Around 1819, Clément was introduced to Sadi Carnot and gave him a copy of his paper on the motive power of steam. Carnot clearly thought that Clément's approach was not fully satisfactory, and derived an alternative equation with 3 parts that correspond to a production phase, expansion, and release of spent steam. Carnot later gave his colleague an unpublished manuscript, "Recherche d'une formule propre à représenter la puissance motrice de la vapeur d'eau." One equation for motive power, F, was written as follows[

28].

N equals 48.2, and is the ratio P*V/367 where P is the pressure of a 10.4 m column of water and V is 1700 L (the volume of 1 kg of steam). P, p', t and t', respectively, are the vapor pressures and temperatures at the beginning and end of the cycle of operation. Carnot gave an example with p = 760 mm Hg, p' = 9.47 mm Hg, t = 100°C and t' = 10°C. He reported a value of 66,278.5 kg-m but rounded the number to 66,000 because he regarded it as imprecise. Fox[28] states that the correct value of F under these conditions is 66,734.8. By dividing this work by the number of Calories required to heat the kg of water to form steam, the result is 66278/650 = 102 kg-m/Cal.

The maximum amount of work that can be obtained from a perfectly efficient machine using 650 Calories of fuel is found by multiplying the number of Calories times Joule's coefficient, 427 kg-m/kcal. The answer is 277,550 kg-m. This indicates that Carnot's equation gave an answer that represents 23.8% efficiency. Probably, the calculated maximum is not equal to the ideal because perfect efficiency is only obtained if the condenser is operating at absolute zero. William Thompson (Lord Kelvin) later calculated Carnot cycle efficiency from the equation,

where η is efficiency, T_{o} is operating temperature, and T_{c} is condenser temperature (K). At the temperatures stated, efficiency equals 23.5%. This correction would yield a mechanical equivalent of heat equal to 422 kg-m/kcal, which is very close to the modern value. The manuscript that Carnot provided to Clément does not discuss what later became known as Joule's coefficient or the mechanical equivalent of heat. However, Carnot did write a note to himself ([28], p. 191) that "the production of one unit of motive power requires the destruction of 2.70 units of heat." This indicates that he had calculated that 1 Calorie was equivalent to 370 kg-m of work (1000/2.7). This was the same value that Mayer later found, presumably because both men calculated the equivalence using the gas law (the logic is explained in[26], pp. 107–9). Mayer is also the first man known to have used the Calorie in a German publication[29], and he recommended using the kg-m as a common unit of work and energy

The recovered manuscripts demonstrate that the man who invented the Calorie was thinking deeply about heat. He not only defined a Calorie and used it in his calculations, but understood that the energy in fuels was related quantitatively to the amount of work that could be obtained from a heat engine. Clément and Desormes had developed an algebraic method of calculating how much work could be obtained from a steam engine as a function of the temperature and pressure of the piston and the condenser. Carnot solved the same problem using integral calculus and gave Clément a copy of his formula as well as his paper describing what is now called the Carnot cycle. Evidence suggests that Carnot knew that a "mechanical equivalent of heat" existed, but there is no record that he told Clément how to calculate the theoretical maximum. It is stunning that work of this prescience was not published and remained unknown to anyone who had not taken Clément's course. Through his influence on other chemists and engineers, it seems very likely that Nicolas Clément was indirectly responsible for the Calorie entering the French lexicon [30]. However, with no publication other than dictionaries to cite, the origin of the Calorie was unknown to Atwater and other scientists who later used the term.