Non-unique detailed constructions of Curzon-Ahlborn cycle on thermodynamic plane

The Curzon-Ahlborn (CA) cycle is a paradigmatic model of endoreversible heat engines, which yields the so-called CA efficiency as the efficiency at maximum power. Due to the arbitrariness of the relationship between the steady temperature and the time taken for the isothermal process of the CA cycle, the constructions of the CA cycle on the thermodynamic plane are not unique. Here, we give some of the detailed constructions of the CA cycle on the thermodynamic plane, using an ideal gas as a working substance. It is shown that these constructions are equal to each other in the maximum power regime in the sense that they achieve the best trade-off between the work and the inverse cycle-time, known as the Pareto front in multi-objective optimization problems.