# The Second Law of Thermodynamics

## Abstract

Clausius was one of the principle architects of the science of thermodynamics. In 1850 he published a groundbreaking paper entitled *On the Moving Force of Heat and the Laws of Heat which May Be Deduced Therefrom*. In this paper he criticized the caloric theory of heat—upon which Carnot’s work had been founded—on the grounds that it violated the first law of thermodynamics. Heat, Clausius argued, was not an indestructible substance, but rather a form of energy which could be transformed into work, and *vice versa*. The conversion of mechanical work into heat (*via* friction) had been explored as early as 1798 by Count Rumford while boring canons, and more recently by Julius Mayer and James Joule in the 1840s. Indeed, when proposing his general principle of the conservation of energy in 1847, Hermann Helmholtz recounts the careful experiments of Joule, who had measured the heating of a bath of water stirred by a descending weight (see Fig. 6.1).

By 1854, Clausius had expanded these ideas into what is today known as the second law of thermodynamics. In so doing, he provided the first mathematical definition of *entropy*, a term which he himself coined. In addition, Clausius’ study of phase transitions led to what is now known as the Clausius-Clapeyron equation. And his work on the kinetic theory of gasses led him to develop a mathematical formula for the *mean free path*—the average distance which a particle travels within a gas before striking a neighboring particle. The reading selection included in this chapter is from an 1867 collection of Clausius’ memoirs translated into English by T. Archer Hirst. It was originally published in Poggendorff’s *Annalen* in May 1862, as well as in the *Philosophical* Magazine and the *Journal des Mathématiques* of Paris.