# Memoir on the Motive Power of Heat

 Title page to a 1960 English translation of French physicist Emile Clapeyron's 1834 "Memoir on the Motive Power of Heat" by Eric Mendoza. [2]
In famous publications, “Memoir on the Motive Power of Fire” is an 1834 article written by French physicist Emile Clapeyron that expanded on the earlier 1824 booklet Reflections on the Motive Power of Fire, by French physicist Sadi Carnot, via the use of a more rigorous mathematical formulation and the use of the pressure-volume indicator diagram technique, developed in 1796 by James Watt and John Southern, to facilitate a graphical calculation of pressure-volume work. [1] The central function of Clapeyron's Memoir was to introduce other physicists, particularly Thomson and Clausius, to Carnot's Reflections.

Notes
Clapeyron is said to have begun work on his Memoir after returning from Russian in 1830. Clapeyron's Memoir was more widely circulated than was Carnot's book and was translated into English and German. [3]

Indicator diagrams
In 1796, Scottish instrument maker James Watt and his employee John Southern developed a work measurement tool called an "indicator diagram", used to exactly quantify the work produced by a steam engine, which made a chart of the pressure of the steam in a cylinder plotted out against the steam's volume:
Pressure volume work
See main: Pressure volume work
Using data from the indicator diagram, in 1834, Clapeyron the first to employ a graphical analysis of the measure of the work done by the expansion or contraction of the steam, the work of the steam can be determined using calculus:

$W=\int_{V_i}^{V_f} P\,dV$

where W is the work done by the body of steam, Vi is the initial volume, Vf is the final volume, and P is the pressure of the steam. Clapeyron used the phrase "mechanical action" as the measure of this integral.

References
1. (a) Clapeyron, Emile. (1834). “Memoir on the Motive Power of Heat.” Journal de l’Ecole Polytechnique, XIV, 153.
(b) Clapeyron, Emile. (1843). “Memoir on the Motive Power of Heat.” Annalen der Physik, LIX, 446, 566.
2. Carnot, Sadi, Clapeyron, Emile, Clausius, Rudolf, Mendoza, Eric. (1960). Reflections on the Motive Power of Fire and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius, edited with an Introduction by E. Mendoza. Dover.
3. Shachtman, Tom. (1999). Absolute Zero and the Quest for Absolute Cold (pgs. 85-86). Mariner Books.