An Unified Approach to Thermodynamics of Power Yield in Thermal, Chemical and Electrochemical Systems

This paper unifies power optimization approaches in various energy converters, such as: thermal, solar, chemical, and electrochemical engines, in particular fuel cells. Thermodynamics leads to converter’s efficiency and limiting power. Efficiency equations serve to solve problems of upgrading and downgrading of resources. While optimization of steady systems applies the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting systems chemical affinity constitutes a prevailing component of an overall efficiency, thus the power is analyzed in terms of an active part of chemical affinity. The main novelty of the present paper in the energy yield context consists in showing that the generalized heat flux Q (involving the traditional heat flux q plus the product of temperature and the sum products of partial entropies and fluxes of species) plays in complex cases (solar, chemical and electrochemical) the same role as the traditional heat q in pure heat engines. The presented methodology is also applied to power limits in fuel cells as to systems which are electrochemical flow engines propelled by chemical reactions. The performance of fuel cells is determined by magnitudes and directions of participating streams and mechanism of electric current generation. Voltage lowering below the reversible voltage is a proper measure of cells imperfection. The voltage losses, called polarization, include the contributions of three main sources: activation, ohmic and concentration. Examples show power maxima in fuel cells and prove the relevance of the extension of the thermal machine theory to chemical and electrochemical systems. The main novelty of the present paper in the FC context consists in introducing an effective or reduced Gibbs free energy change between products p and reactants s which take into account the decrease of voltage and power caused by the incomplete conversion of the overall reaction. Keywords— Power yield, entropy production, chemical engines, fuel cells, exergy.