Energy and Entropy

Abstract

In his Sixth Memoir on The Mechanical Theory of Heat, Clausius explained how the internal energy of a body ($U$), consists of both thermal content ($H$) and ergonal content ($Z$). These represent the energy associated with the motion and the configuration of the body’s particles, respectively. According to the first fundamental theorem of the mechanical theory of heat—now known as the first law of thermodynamics—the internal energy of a body may be changed by either adding heat ($Q$) to the body, or doing external work ($w$) on the body. But the first law of thermodynamics alone is not sufficient to explain the types of processes which tend to occur in nature. Rather, only those processes, or transformations, occur which are characterized by positive (or at best, zero) equivalence-values; any process which has a negative equivalence value must be compensated by another process having an equal or greater positive equivalence value. This is Clausius’ second fundamental theorem of the mechanical theory of heat. Today, it is known as the second law of thermodynamics. In the reading selection below, taken from his Ninth Memoir, Clausius clarifies these ideas by writing them in a succinct mathematical form. Perhaps most notably, he introduces the concept of entropy, denoted by the letter $S$. What is meant by this term? From where was it derived? And what is the connection between entropy and the second law of thermodynamics?

The entropy of the universe tends to a maximum.

—Rudolph Clausius