Accumulation Function for the Ideal Air-Standard Brayton Cycle Based on Serrin’s Thermodynamics

Serrin's works provided a new perspective on classical thermodynamics through his statements of the first law and the accumulation function, and of the second law and the accumulation theorem, as well as the subsequent result by Huilgol that the work accomplished in a thermal cycle implies an inequality where the important temperatures of the thermal cycle and an integral similar to that of Clausius appears. Based on these pioneering works, explicit forms of the accumulation function have been derived for the Otto, Diesel, Stirling and Ericsson cycles. In this paper, a more straightforward derivation than that made by Huilgol is presented to obtain the inequality for the work accomplished in a cycle, following the theoretical framework of Serrin and Huilgol, and explicitly introducing that the temperature ranges in which the system exchanges heat are finite. This paper clearly shows the natural physical fact that heat exchange processes in a system have two defined extreme temperatures, corresponding to the beginning and end of the process, which can be equal in the isothermal limiting case. The derivation of the accumulation function for the ideal air-standard Brayton cycle is provided for the first time, extending Serrin's thermodynamic framework, where the temperature constraints of the adiabatic compression and expansion processes under which it operates are analyzed. Finally, a practical example is included to illustrate the behavior of the accumulation function of the ideal air-standard Brayton cycle.