Irreversible entropy production in low- and high-dissipation heat engines and the problem of the Curzon-Ahlborn...

Heat engines performing finite time Carnot cycles are described by positive irreversible entropy functions added to the ideal reversible entropy part. The model applies for macroscopic and microscopic (quantum mechanical) engines. The mathematical and physical conditions for the solution of the power maximization problem are discussed. For entropy models which have no reversible limit, the usual "linear response regime" is not mathematically feasible; i.e., the efficiency at maximum power cannot be expanded in powers of the Carnot efficiency. Instead, a physically less intuitive expansion in powers of the ratio of heat-reservoir temperatures holds under conditions that will be inferred. Exact solutions for generalized entropy models are presented, and results are compared. For entropy generation in endoreversible models, it is proved for all heat transfer laws with general temperature-dependent heat resistances, that minimum entropy production is achieved when the temperature of the working substance remains constant in the isothermal processes. For isothermal transition time t, entropy production then is of the form a/[tf(t)±c] and not just equal to a/t for the low-dissipation limit. The cold side endoreversible entropy as a function of transition times inevitably experiences singularities. For Newtonian heat transfer with temperature-independent heat conductances, the Curzon-Ahlborn efficiency is exactly confirmed, which-only in this unique case-shows "universality" in the sense of independence from dissipation ratios of the hot and cold sides with coinciding lower and upper efficiency bounds for opposite dissipation ratios. Extended exact solutions for inclusion of adiabatic transition times are presented.