**Entropy Analysis in Thermal Engineering Systems**

by Yousef Haseli

**Preface**

It was about two centuries ago that Nicolas L_eonard Sadi Carnot, a French military engineer, presented an influential treatise. Although remained unappreciated for a decade, it provided a profound basis for investigations of his successors and the advancement of the Science of Thermodynamics. Carnot’s research on the theory of heat engines was itself founded upon the caloric theory, empirical findings of his predecessors, and philosophical reasoning. The invalidity of the notion of heat as an indestructible matter had become obvious among the pioneers by the mid-19th century. There were compelling experimental evidences supporting the equivalence of heat and work, the first main principle of the Mechanical Theory of Heat, according to which heat can be produced by expenditure of work and vice versa. Unlike the first main principle whose statement and formulation can readily be understood by a student of an average intelligence, concepts like entropy originated from the second main principle of the Mechanical Theory of Heat appear to be challenging, perhaps, for everyone who has undertaken an introductory class on the subject. Such concepts are invented through a formulation of the second law of Thermodynamics. However, the analytical formulation of the second law is not a mere expression of the experimental observations—that heat cannot be converted completely into work, or heat cannot spontaneously transfer from a cooler to a warmer body. It involves a hypothetical concept, reversibility, which may only be realized in an imaginary process; which may be regarded as a preliminary source of difficulty in understanding the entropy-related concepts.

Today, after over 150 years of invention of entropy by Clausius, still there remain confusions surrounding the concept of entropy and the phenomenon of entropy increase. One may find a variety of interpretations or descriptions for entropy such as arrow of time, measure of disorder, chaos, wastefulness, and energy dispersal. On the other hand, some argue that understanding of entropy is only possible through statistical mechanics. The first question may cross a curious mind is: Why is not there a universally agreed interpretation for entropy yet? It has a simple definition dS¼dQ/T, a differential of S (entropy) is equal to the differential of Q (heat) divided by T (temperature of body). The explanation given by Clausius as the inventor of entropy is that S represents the transformational content of a body like U that denotes its (internal) energy content. All we know nowadays about Clausius is his inequality with no adequate mention of what he meant by entropy and how he discovered it.

Despite entropy remains as a gray area (it is not as clear as many other concepts deduced from natural laws), today entropy-based analysis has frequently been employed as a design tool in a wide range of applications. Often, second law-based studies present entropy calculations but without any constructive use of such calculations. It is natural to ask: What is the goal of entropy-related calculations? Is entropy generation always an indication of losses, for instance, in a power cycle, fluidized bed, boiler, hydrogen production plant, chemical reaction, condenser? Do we need to be always concerned about the growth of entropy? Are there specific circumstances where entropy-related calculations may yield meaningful results? The primary objective of this book is to highlight the limitations of the application of entropy in engineering and clarify when a second law analysis may lead to rewarding results.

The journey of the present book begins with an overview of the fundamental thermodynamic concepts in the opening chapter. It is then followed by a brief historical sketch of Thermodynamics in Chapter 2, which illuminates its evolution as well as the contributions of many ingenious men to the advancement of the subject during the 19th century. More importantly, a careful examination of several sources reveals that the tutorial method of the second law and entropy could be much easier had it followed the same path as it was discovered and presented by the founders. The current method of teaching the second law, inherited not from the original founders but those authors who developed first textbooks on Thermodynamics in the late 19th and early 20th century, skips important steps, for instance the role of the ideal gas law in the investigation of Carnot, Thomson, and Clausius.

A detailed discussion on the shortcomings of the common tutorial method of entropy is presented in Chapter 3. Specifically, the demonstration technique of the Carnot’s corollaries that rests on philosophical reasoning is shown to suffer from certain issues. The common derivation method of Carnot efficiency and introduction of the absolute temperature scale without a proper background is critically reviewed. A simple but effective method is then proposed to ease understanding the connection between the chain of concepts like Carnot efficiency, entropy, reversibility, and absolute temperature. The discussion will advance in Chapter 4 where the main task is to clarify the phenomenon of entropy increase and to show the direct connection between the phenomena of heat transfer and entropy generation.

Chapter 5 presents a comparative assessment of the efficiency of common heat engines. The chief goal is to illuminate that determination of the most efficient engine is contingent on specific assumptions. For example, the Carnot engine along with the Stirling and Ericsson engines are said to possess the highest efficiency among all heat engines subject to an assumption that the highest and the lowest temperatures are the same for all the engines. If, however, the engines are constrained to experience the same degree of compression, the Carnot engine is no longer the most efficient design.

Our investigation continues by applying entropy analysis to simple and advanced power cycles. The objective is to show that entropy production may become equivalent to an efficiency loss under specific conditions. We will see in Chapter 6 that in endoreversible heat engines, a class of theoretical heat engines which experience external irreversibility only, the thermal efficiency happens to inversely correlate with the entropy production. Nevertheless, in practice, engines do also experience internal irreversibilities. It will be shown in Chapter 7 that a design based on minimum entropy production rate in irreversible engines operating in closed cycles is not equivalent to either of maximum power and maximum efficiency designs.

The three designs may, however, become identical if, for instance, the thermal energy supplied to an irreversible engine operating between a heat source and a heat sink, or the power output is treated as a fixed parameter. In Chapter 8, we investigate the applicability of a second law-based analysis in conventional thermal power plants such as gas turbine and combined gas/steam cycles, which are usually driven by fuel combustion. In this chapter, the concept of specific entropy generation (SEG) is introduced, a new parameter that measures the entropy production of a power cycle per unit of fuel burned. It will be shown that SEG unconditionally correlates with the inverse of the cycle efficiency, and it can be viewed as a measure of efficiency losses in combustion-driven power generating systems. An application of the SEG concept to typical thermal power plants is explored.

An investigation on the application of entropy analysis to fuel cells is presented in Chapter 9. The primary objective is to show that the theoretical efficiency of a fuel cell is not bound by the efficiency of a Carnot cycle operating between the same low and high temperatures. Chapter 10 examines possibility of any connection between entropy and chemical equilibrium. A careful assessment of the Gibbs criterion of equilibrium reveals that the characterization of a chemical equilibrium by minimum Gibbs function is simply a postulation without a strong experimental evidence or theoretical proof. The last chapter explains the exergy concept and describes how it is originated by combining the first and the second laws. It is shown that a conclusion drawn from an exergy analysis may often be obtained from an entropy analysis.

It is hoped that this book will help readers to improve their knowledge and comprehension of the second law-related concepts and to have a clearer understanding of the applicability area of entropy-based analysis.