Optimal configuration of a class of irreversible heat engines. II

In a previous paper we analyzed a class of irreversible cyclic heat engines to find their optimal operating configuration for specific performance goals. In that paper the thermodynamic variables of the working fluid were not treated as dynamical variables, instead the dynamics was replaced by an integral constraint. In this paper we reanalyze the same class of heat engines treating the thermodynamic variables of the working fluid as dynamical variables, and we obtain the optimal configuration of the engine when the performance goal is to maximize the average power output per cycle or, alternatively, to maximize the efficiency of the engine. To carry through this program it is necessary to use mathematical techniques from optimal-control theory. Since this subject is unfamiliar to most physicists and chemists, we briefly introduce some of the central ideas of the theory.