In the history of thermodynamics, Émile Clapeyron (1799-1864) was a French engineer, a former student of the École Polytechnique, who in 1834 brought French engineer Sadi Carnot’s 1824 paper Reflections on the Motive Power of Fire, into the public light by publishing Memoir on the Motive Power of Heat, an updated graphical analysis of Carnot’s work. [1] This work later caught the attention of Irish physicist William Thomson (Lord Kelvin) who in turn influenced German physicist Rudolf Clausius with his analysis of the subject of Carnot’s work. [2]

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:

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. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX, [1843] 446, 566).
2. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws Which can be Deduced From it for the Theory of Heat." Poggendorff's Annalen der Physik, LXXIX, 368, 500.