Optimum work in real systems with a class of finite thermal capacity reservoirs

The optimum work in real systems with two finite thermal capacity reservoirs is determined. It is obtained by using optimal control theory. It is shown that the temperature of external working fluid changes exponentially with respect to flow velocity and process duration. The analysis proves that the optimum work is different for heat engine mode and heat pump mode. The recently obtained results are compared with those obtained previously. The models and results in this paper provide an approach to improve calculations of energy limits in real systems.