Efficiency of Energy Conversion Cycles in Finite Time Thermodynamics: The Case of Nuclear-Driven Carnot Cycle

Abstract

This paper aims to clarify the conditions required to derive, within the framework of Finite Time Thermodynamics, the efficiency of "endoreversible cycles" (Eq. (1) of this paper). It is shown that the steady-state enthalpy and entropy balances of the working fluid at maximum power, the finite time thermodynamics optimum, lead to this efficiency. This result is obtained without introducing the "finite time" of the cycle, the most usual approach. To compute this efficiency for real systems, the heat source and sink temperatures must be clearly defined. In complex systems such as nuclear reactors, several choices of the upper temperature are possible. For a rational choice - using the steam generator as the heat source - these temperatures are relatively low, and the finite time thermodynamics optimum corresponds to unrealistic operating conditions, slightly underestimating actual efficiencies. Conversely, higher upper temperature values yield more realistic conditions but overestimate efficiency. The finite time thermodynamics limits are revealed by computing all thermodynamic cycle parameters and introducing irreversibilities in the working fluid. The cycle specific net work (MJ/kg) appears to be a more relevant optimisation criterion for real systems. This supports the idea that acceptable predictions from finite time thermodynamics efficiency result from compensating errors: low maximum temperatures balanced by the ideal cycle assumption. A general efficiency equation better illustrates why actual efficiency remains below Carnot's, clarifying optimisation issues in energy conversion systems and the trade-off between reducing irreversibilities and maximising average heat source temperature.