Abstract
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.
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The differential change of Helmholtz free energy is: \(dF=-SdT-pdV+\sum_{i=1}^{C}{\mu }_{i}d{n}_{i}\); while at \(V,T=const.\) is: \(dF=\sum_{i=1}^{C}{\mu }_{i}d{n}_{i}\).
Differential change of entropy in the primary system (which is a closed system to the environment, i.e., to the reservoir of the corresponding intensive parameter) is the sum of differential change of entropy due to irreversible process within the primary system (\(d{S}_{i}\)) and differential change of entropy due to energy and particle exchange with the environment (\(d{S}_{e}\)): \(dS= d{S}_{i}+d{S}_{e}\).
The reversible work source (RWS) is a system of the conservative force ($${F}_{CF}$$), then virtually the $${W}_{P,T}^{max}$$ work can be viewed as the energy that is transformed into the potential energy of conservative force ($${W}_{P,T}^{max}=\Delta {U}_{CF}$$). Therefore, the $${W}_{P,T}^{max}$$ work (energy from a thermodynamic process) is virtually stored in a reversible work source as potential energy:
$$\Delta {U}_{CF}={W}_{P,T}^{max}={\int }_{i}^{f}Fdr=-{\int }_{i}^{f}{F}_{CF}dr$$In real fuel cells \(\sum_{i=1}^{C}{{\nu }_{i}\mu }_{i}\) (6) is no longer constant, or in real galvanic cells where the electrochemical reaction progresses to an equilibrium state during the work potential decreases due to increased irreversibility—in equilibrium, the work potential of the galvanic cell is zero.
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Poša, M. Connecting De Donder’s equation with the differential changes of thermodynamic potentials: understanding thermodynamic potentials. Found Chem (2024). https://doi.org/10.1007/s10698-024-09507-z
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DOI: https://doi.org/10.1007/s10698-024-09507-z