Finite-rate thermodynamics of power production in thermal, chemical and electrochemical systems

Power optimization approaches are unified for various energy converters, such like: thermal, solar, chemical, and electrochemical engines. 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, so that 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 so-called idle run voltage is a proper measure of cells imperfection. The voltage losses, called polarization, include three main sources: activation, ohmic and concentration polarization. Examples show power maxima in fuel cells and prove the suitability of the thermal machine theory to chemical and electrochemical systems. The main novelty of the present paper in the FC context consists in introducing the effective or reduced Gibbs free energy change between products p and reactants s which take into account the decrease of voltage and power decrease caused by the incomplete conversion of the overall electrochemical reaction.