Connecting De Donder’s equation with the differential changes of thermodynamic potentials: understanding thermodynamic potentials

The new mathematical connection of De Donder’s differential entropy production with the differential changes of thermodynamic potentials (Helmholtz free energy, enthalpy, and Gibbs free energy) was obtained through the linear sequence of equations (direct, straightforward path), in which we use rigorous thermodynamic definitions of the partial molar thermodynamic properties. This new connection uses a global approach to the problem of reversibility and irreversibility, which is vital to global learners’ view and standardizes the linking procedure for thermodynamic potentials (Helmholtz free energy, enthalpy, and and Gibbs free energy)—preferably to the sensing learners. It is shown that De Donder’s differential entropy production in an isolated composite system is equal to the differential change in total entropy and that De Donder’s equation agrees with Clausius’ inequality. The useful work of the irreversible process is discussed, which with the decrease of irreversibility tends towards the hypothetical maximum useful work of the reversible process.