Application of Extremes in Internal Energy and Entropy for Defining Loss of Working Capacity

In physical chemistry textbooks, it is explained that thermodynamic processes in isolated systems (with constant internal energy) evolve until the total entropy reaches a maximum value; irreversible processes, or those in closed systems (at a constant entropy value of the system), evolve until the total internal energy reaches a minimum value; and in quasi-static processes, the maximum work is obtained under the given conditions. However, if the maximum useful work is not obtained from the system, the thermodynamic process is usually described using the Clausius inequality. Assuming that the internal energy and entropy are first-order homogeneous functions (according to Euler’s relation and additivity over system elements) and that they are state functions based on the principle of local equilibrium, the principle of maximum entropy and minimum internal energy can be applied not only to entire isolated or closed systems but to any volume element of the system. From this follows a unique discussion of the transition of a closed system (with a quasi-static isentropic process) to an isolated (irreversible) system, along with the thermodynamic process that occurs when the system remains closed and does not achieve the maximum useful work, some of which is dissipated.