Optimal decisions for chemical and electrochemical reactors 365 9.19. FINAL REMARKS By applying generalized kinetics and optimization for steady chemical units and fuel cells, we evaluated static and dynamic energy limits, the latter being linked with the notion of a generalized exergy. The generalized work function obtained via optimization can be regarded as an extension of the standard thermodynamic exergy for finite rates, this extension including imperfect battery systems with an overvoltage. In processes departing from equilibrium this generalized work function is larger than in processes approaching the equilibrium. Importantly, bounds for the mechanical energy yield or its consumption provided by such a performance function are stronger than those defined by classical exergies (that provide only restrictive, reversible bounds). The enhanced bounds obtained here are useful in the performance analysis and design of fuel cell systems. The dynamic fuel cell system has been outlined as a multistage thermodynamic device that converts the energy of chemical reaction directly into electricity and heat, thus producing power efficiently at a finite rate and in an irreversible way. Dynamic programming has been the main tool applied in computations. In the thermodynamic analysis of a dynamical fuel cell system the performance criterion may be its entropy production S in a form that describes a real stack from which the power delivery takes place at a finite rate. The functional S in the form of a sum over stages constitutes a discrete performance criterion of the operation occurring due to the chemical reactions and mass transfer coupled with transfer of heat. The minimization of S eliminates all controls from S , thus generating a potential function R (X A , X B , B - A ) = min S which depends only on initial and final states and the extensive transport parameter called the number of the transfer units. Yet, in the fuel cell case, a more practical criterion is usually applied instead of S : the criterion of the total work produced in a given time, W. The optimizations of S and W are related by the familiar Gouy­Stodola law which links the lost work with the entropy production. Due to a finite S the actual cell voltage U and finite-rate work W are smaller than those in an ideal cell (because of the losses associated with cell polarization and Ohmic losses). In general, no simple rule exists for the optimal control of the unsteady state system subject to external adjustable decisions. Yet, the optimal solution for total work W often implies a nearly constant intensity of the entropy production along an optimal dynamical path. Such a simple strategy is, however, valid only when no constraints are imposed on the control variables. Post-quadratic terms and non-linearities in kinetic equations usually cause the violation of this strategy. Nonetheless, minimal inevitable losses of power and reduction of the cell voltage are determined. With thermodynamic knowledge, enhanced limits are estimated for the optimal work function, W max , that generalizes the familiar reversible work W E for the realm of finite rates. There is an abundance of research papers on fuel cell systems, in particular solid oxide fuel cell (SOFC) power systems (Campanari, 2001; Roy-Aikins, 2002; ´ Lema nski, 2003; Li and Chyu, 2004; Ordonez et al., 2007). Zero-dimensional