# Introduction

The Kelvin-Planck statement of the Second Law of Thermodynamics says that it is impossible to construct a heat engine to receive heat and to convert is completely into work. However, it does not indicate how much of heat is convertible into a useful form of energy; i.e. work. The first mathematical formulation of the second law is credited to Clausius, who showed that in a reversible Carnot cycle operating with an ideal gas QL/QH equals TL/TH. This conclusion led him to invent thermodynamic property Entropy defined as S = Q/T. Clausius implied that if the Carnot engine is the most efficient engine among all engines operating between the same thermal reservoirs, QL/QH would be greater than the temperature ratio TL/TH in other types of engine, hence expressing his well-known inequality; i.e., ∫(∂Q/T) ≤ 0. Clausius therefore concluded that the real heat engines would result in production of entropy.

It is natural to question: does minimization of entropy produced by a heat engine result in a design with a highest efficiency? In other words, is there any relationship between the entropy produced by an engine and its efficiency? The objective of the present article is to address these questions. We will examine a variety of heat engines by investigating the efficiency and work output of typical endoreversible models of power plants as well as irreversible gas turbine engines at the condition of minimum entropy production. We aim to find out whether there is any relationship between entropy production and efficiency of a heat engine, and to identify the conditions at which these two parameters may correlate.

Despite a large volume of published articles, which have used entropy-based analyses of various energy systems; e.g., heat exchanger, power cycles, fuel cells, etc., few authors have investigated the applicability of an entropy generation analysis in engineering systems. In 1975, Leff and Jones [1] discussed by means of analytical argument that an increase in the thermal efficiency of an irreversible heat engine would not necessarily result in a decrease in its entropy production. Salamon et al. [2,3] argued in early 1980s that maximum work and minimum entropy production are two different designs in the optimization of heat engines. Around two decades later, Salamon et al. [4] showed that the equivalence of maximum work and minimum entropy production in heat engines might occur under certain design conditions. Shah and Skiepko [5], Qian and Li [6], Qun et al. [7], and Cheng [8] have argued that minimization of entropy production is not a useful tool for analyzing heat exchangers.

Numerous articles have appeared in the literature claiming a direct relationship between the entropy produced by a power producing system with its thermal efficiency. To the best of my knowledge, there has not been any work, except those presented in Refs [1, 9, 10], to pursue any possible connection between the entropy production and the thermal efficiency. In some cases, a relation between maximum work production and minimum entropy has been observed; see Ref. [7, 11-13]. None of the analyses presented by previous, yet, few authors; i.e., Ref. [1-4, 7, 11-13] have dealt with the models of power plants which are currently in use for the purpose of power generation. In practice, the inefficiencies of power plant components such as compressors, turbines, pumps, are unavoidable. So, any realistic analysis should account for the imperfectness of the components of a power generating device. This article aims to address the previously posed question; whether there is any relationship between the thermal efficiency of a power plant and the entropy produced due to the operation of that plant.

We will analyze two classes of power generating systems: endoreversible power plants, and irreversible power cycles. The first group includes some simplest models of power plant, which are the models of Curzon-Ahlborn [14], Novikov [15], and Carnot vapor cycle. The second group includes irreversible Otto, Diesel and Brayton cycles. The main idea is to find the thermal efficiency and the work output of these power cycles at the operational regime of minimum entropy generation.