Clapeyrons

Clapeyrons refers to concepts and results named after Benoît Paul Émile Clapeyron, a French engineer and physicist who lived from 1799 to 1864. Clapeyron made foundational contributions to thermodynamics in the early 19th century and helped formalize the modern treatment of heat engines, phase transitions, and the behavior of gases. His work bridged earlier empirical gas laws and Carnot’s theory, culminating in a more systematic, mathematical framework for thermodynamics.

The most widely known Clapeyron concept is the Clapeyron equation, also called the Clausius–Clapeyron equation. This relation describes how the pressure and temperature of a substance at phase equilibrium change along a coexistence curve. In its common form for a phase transition, the slope of the boundary in a P–T diagram is dP/dT = ΔS_trans/ΔV_trans, or equivalently dP/dT = ΔH_trans/(T ΔV_trans). For liquid–gas transitions, this becomes dP/dT = L/(T ΔV_trans), where L is the latent heat. The equation is used to estimate how vapor pressure varies with temperature and to infer latent heats from experimental data.

Clapeyron’s 1834 Mémoire sur la puissance motrice de la chaleur presented a rigorous synthesis of Carnot’s ideas with the ideal gas law, contributing to the development of the concept of an equation of state for gases and the quantitative basis of thermodynamics. The term Clapeyrons thus encompasses the equation bearing his name and his broader role in shaping early thermodynamic theory. In modern usage, the Clausius–Clapeyron equation remains a standard tool in physical chemistry and meteorology.