Benoît Paul Émile Clapeyron

Benoît Paul Émile Clapeyron was born in Paris in 1799 and trained as an engineer at the École Polytechnique and the École des Mines. He spent the 1820s in Russia teaching and building infrastructure, then returned to France, where he became a leading railway engineer, designing locomotives and bridges and helping build some of the country's first rail lines.

In 1834 Clapeyron rescued the work of Sadi Carnot from obscurity. Carnot's 1824 treatise on the motive power of heat had been almost entirely ignored; Clapeyron restated its reasoning analytically and, crucially, in graphical form, introducing the pressure–volume diagram to represent the Carnot cycle. This gave thermodynamics its first piece of enduring graphic notation and made Carnot's ideas accessible to Clausius and Kelvin, who built the second law upon them.

From the analysis of phase equilibria came the relation now called the Clausius–Clapeyron equation, which links the slope of a coexistence curve to the latent heat of the transition and the volume change across it. Clapeyron derived an early form; Clausius later put it on a firm thermodynamic footing.

Clapeyron was elected to the Académie des sciences in 1858 and remained active in engineering and the theory of elastic structures until his death in Paris in 1864.