Clapeyron

Clapeyron refers to Benoît Paul Émile Clapeyron (1799–1864), a French engineer and physicist who made foundational contributions to thermodynamics and the mathematical treatment of gas laws and phase transitions. He helped transform the Carnot cycle into a quantitative framework and established methods for applying pressure–volume diagrams to heat and work processes.

One of Clapeyron’s major achievements was his 1834 memoir, Mémoire sur la théorie générale de la chaleur, in which he derived the equation of state for an ideal gas by combining the empirical gas laws of Boyle, Amontons, and Charles. This work led to the expression PV = nRT, a cornerstone of modern thermodynamics and physical chemistry.

Clapeyron is also remembered for the Clapeyron equation, a relation that links the slope of a phase boundary in a pressure–temperature diagram to the latent heat and the change in molar volume during a phase transition. The equation is commonly written as dP/dT = ΔH/(TΔV) or dP/dT = ΔS/ΔV, and is widely used to estimate latent heat and to analyze phase transitions such as liquid–gas equilibria.

His contributions helped formalize the thermodynamic framework and influenced later developments in statistical thermodynamics and chemical engineering. Clapeyron’s name remains associated with key tools in thermodynamics, including PV diagrams and phase-transition analysis. Clapeyron’s work continues to be taught in thermodynamics.