J. Non-Equilib. Thermodyn. ;  ():– Research Article Ricardo T. Páez-Hernández*, Pedro Portillo-Díaz, Delno Ladino-Luna, Alejandro Ramírez-Rojas and Juan C. Pacheco-Paez An analytical study of the endoreversible Curzon–Ahlborn cycle for a non-linear heat transfer law DOI: ./jnet-- Received June , ; revised October , ; accepted October ,  Abstract: In the present article, an endoreversible Curzon–Ahlborn engine is studied by considering a non- linear heat transfer law, particularly the Dulong–Petit heat transfer law, using the ‘componendo and divi- dendo’ rule as well as a simple dierentiation to obtain the Curzon–Ahlborn eciency as proposed by Agrawal in . This rule is actually a change of variable that simplies a two-variable problem to a one-variable problem. From elemental calculus, we obtain an analytical expression of eciency and the power output. The eciency is given only in terms of the temperatures of the reservoirs, such as both Carnot and Curzon– Ahlborn cycles. We make a comparison between eciencies measured in real power plants and theoretical values from analytical expressions obtained in this article and others found in literature from several other authors. This comparison shows that the theoretical values of eciency are close to real eciency, and in some cases, they are exactly the same. Therefore, we can say that the Agrawal method is good in calculating thermal engine eciencies approximately. Keywords: Curzon–Ahlborn, Dulong–Petit, eciency, endoreversible, Newton, power output  Introduction In , Curzon and Ahlborn [] studied a Carnot-like thermal engine in which there was no thermal equi- librium between working uids and thermal reservoirs during the isothermal branches of the cycle. Curzon and Ahlborn showed that such an engine delivers non-zero at maximum power output, unlike the Carnot engine. Moreover, the eciency of this engine, given by η CA =  - T  /T  and η CA , is now called Curzon– Ahlborn (CA) eciency at maximum power output, where T  and T  are the temperatures of the external heat reservoirs (T  > T  ). This pioneering work led to the establishment of a new branch of irreversible thermo- dynamics, known as nite-time thermodynamics (FTT), which considers a macroscopic system as a network of systems working in cycles and exchanging energy in an irreversible fashion. To study the CA engine, many authors consider the heat uxes governed by the Newton heat transfer law in the isothermal branches. Nevertheless, in , Angulo-Brown and Páez-Hernández [] used a non-linear heat transfer law, partic- ularly the Dulong–Petit heat transfer law, because it takes into account the principal forms of heat transfer, *Corresponding author: Ricardo T. Páez-Hernández: Área de Física de Procesos Irreversibles, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo , Col. Reynosa, CP  México, DF, Mexico, e-mail: phrt@correo.azc.uam.mx Pedro Portillo-Díaz: Departamento Ciencias Básicas, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo , Col. Reynosa, CP  México, DF, Mexico, e-mail: ppd@correo.azc.uam.mx Delno Ladino-Luna, Alejandro Ramírez-Rojas: Área de Física de Procesos Irreversibles, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo , Col. Reynosa, CP  México, DF, Mexico, e-mail: dll@correo.azc.uam.mx, arr@correo.azc.uam.mx Juan C. Pacheco-Paez: Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edicio , ° Piso, UP Zacatenco, CP  México, DF, Mexico, e-mail: jcpacheco@esfm.ipn.mx