Polytropic Carnot heat engine

Recent astrophysical datasets have implied that the universe has entered a speedy expansion phase. The Polytropic gas model, which describes a unified formulation of dark contents (matter plus energy), is one of the most reasonable definitions of this mysterious phenomenon. This interesting formulation allows to simulate the dark contents in the cosmic form of the perfect fluid and gives an interesting point of view in the discussion of fundamental theories of physics. In the first step of our investigation, we discuss the thermal equation-of-state (EoS henceforth) and obtain the EoS and deceleration parameters as explicit functions of temperature. Subsequently, we obtain a relation for the thermal efficiency of the Carnot heat engine which depends on free parameters given in the cosmological Polytropic gas description and the limits of maximal and minimal temperatures imposed on the Carnot cycle.