Collection: Clausius Statement

The Clausius theorem is a mathematical explanation of the second law of thermodynamics. It was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. Clausius developed this in his efforts to explain entropy and define it quantitatively. In more direct terms, the theorem gives us a way to determine if a cyclical process is reversible or irreversible. The Clausius theorem provides a quantitative formula for understanding the second law.

Clausius was one of the first to work on the idea of entropy and is even responsible for giving it that name. What is now known as the Clausius theorem was first published in 1862 in Clausius’ sixth memoir, “On the Application of the Theorem of the Equivalence of Transformations to Interior Work”. Clausius sought to show a proportional relationship between entropy and the energy flow by heating (δQ) into a system. In a system, this heat energy can be transformed into work, and work can be transformed into heat through a cyclical process. Clausius writes that “The algebraic sum of all the transformations occurring in a cyclical process can only be less than zero, or, as an extreme case, equal to nothing.” In other words, the equation.