# Clapeyron-Clausius equation

The heat of vaporization increases with increasing temperature and vapor pressure.

As we know from molecular kinetic theory, atoms or molecules in liquids and gases are in a state of constant motion. From time to time, individual molecules of a liquid, moving fast enough, can “break away” from its surface. Thus, above any liquid, a certain number of molecules of a given substance will be in the form of vapor. The pressure of these molecules, if there are no foreign impurities, is called the vapor pressure of this substance. Sometimes you can feel this presence of steam above the liquid – remember the characteristic sensation of moisture on the seashore or ocean.

We also know that to convert a substance from a liquid to a gaseous state (cm. Phase transitions) you need to spend some energy. This energy is called heat of evaporation or heat of vaporization… The Clapeyron-Clausius equation precisely describes the relationship between the heat of vaporization H, steam pressure p and temperature T substances:

ln p = H/RT + constant

where ln p Is the natural logarithm taken from the value of the vapor pressure, and R Is Rydberg’s constant. Temperature T measured in kelvin.

The first to bring this dependence in 1834 was the engineer-constructor of steam engines Benoit Clapeyron. Naturally, due to his specialty, Clapeyron was primarily interested in the heat of vaporization, and he used his equation mainly for engineering and applied purposes. For science, the equation for the heat of phase transition was rediscovered almost two decades later by Rudolf Clausius, the author of the formulation of the second law of thermodynamics.

Most often, the Clapeyron-Clausius equation is used for simple calculation or measurement of the heat of vaporization of various substances. By measuring the vapor pressure at different temperatures and plotting it on a graph, along one axis of which the value of ln is plottedp, and on the other – the value 1 / T, scientists from the obtained linear relationship (slope of a straight line) determine the heat of vaporization of a substance.

Benoit Paul Emile CLAPEIRON
Benoît Paul Émile Clapeyron, 1799-1864

French physicist and engineer. Born in Paris. Graduated from the Polytechnic School and the School of Mine Engineering. In the years 1820-1830. worked at the Institute of Railway Engineers in St. Petersburg. Upon returning to France, he became a professor at the School of Bridges and Roads in Paris. He became famous as a designer of railways, a designer of railway bridges and steam locomotives. Proved the “three-point theorem” used to calculate load-bearing structures with three or more support points. However, Clapeyron’s greatest contribution to science was made through the study of thermal processes, for which he was elected a full member of the French Academy of Sciences.

Rudolf Julius Emanuel CLAUSIUS
Rudolf Julius Emanuel Clausius, 1822–88

German physicist. Born in Köslin (now Koszalin, Poland) into a pastor’s family. He studied at a private school, the director of which was his father. In 1848 he graduated from the University of Berlin. After graduating from the university, he preferred physics and mathematics to history, which he initially studied, taught in Berlin and Zurich, held the department of professor of physics at universities in Zurich, Würzburg and Bonn. Since 1884 – Rector of the University of Bonn. The main works of Clausius are devoted to the foundations of thermodynamics and the kinetic theory of gases. Unfortunately, the severe injuries sustained while serving as a volunteer as a medical orderly during the Franco-Prussian War prevented Clausius from realizing his full scientific potential. Nevertheless, after the war and wounds, it was he who formulated the second law of thermodynamics in its modern form.