Clausiusegyenlség

Clausiusegyenlség, more commonly known as the Clausius inequality, is a fundamental principle in thermodynamics that states the total change in entropy of an isolated system plus the entropy transfer due to heat exchange with the surroundings is always greater than or equal to zero. Mathematically, this is expressed as dS >= dQ/T, where dS is the change in entropy of the system, dQ is the heat added to the system, and T is the absolute temperature at which the heat transfer occurs.

For a reversible process, the equality holds, meaning the change in entropy is precisely equal to the heat transferred divided by the absolute temperature. In contrast, for irreversible processes, which are ubiquitous in nature, the inequality is strictly greater than zero, indicating that irreversible processes generate entropy within the system or its surroundings.

The Clausius inequality is a direct consequence of the second law of thermodynamics. It provides a criterion for determining the direction of spontaneous processes. A process will spontaneously occur if it leads to an increase in the total entropy of the universe (system + surroundings). The inequality is crucial for understanding the limitations of energy conversion and the concept of entropy generation in real-world thermodynamic systems. It forms the basis for many thermodynamic analyses and calculations, particularly in areas like heat engines, refrigerators, and chemical reactions.