First and Second-Law Efficiencies in a New Thermodynamical Diagram

Abstract

Graphical representations of the first and second-law effciencies of heat engines, refrigerators and heat-pumps are used to compare these real devices with their corresponding reversible counterparts. Other representations, such as the temperature-energy diagram, also known as the Bejan/Bucher diagram, illustrate the conservation nature of the first and second-law of thermodynamics. This work intends to combine the major benefits of these thermodynamical representations by means of a dimensionless approach and using the concepts behind the Bejan/Bucher diagram into a new diagram. The proposed chart allows a direct reading of the first and second law effciencies and of the entropy generation. It may be used as well to compare different thermal machines among them, with the available thermodynamical models and with the observed performance of state of the art devices, from both first and second-law viewpoints. Using simple geometrical concepts, a number of thermodynamical principles can also be easily deduced. This is illustrated, in Appendix A, through the derivation of the Curzon-Ahlborn formula for the efficiency of endoreversible engines; the most complex case of the Curzon-Ahlborn engine–different cold and hot thermal resistances–is considered.