Advanced Thermodynamics for Engineers

D. Winterbone, Ali Turan

• Publisher: Butterworth-Heinemann
• Year: 1996
• eBook ISBN: 9780080523361
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

Although the basic theories of thermodynamics are adequately covered by a number of existing texts, there is little literature that addresses more advanced topics. In this comprehensive work the author redresses this balance, drawing on his twenty-five years of experience of teaching thermodynamics at undergraduate and postgraduate level, to produce a definitive text to cover thoroughly, advanced syllabuses.The book introduces the basic concepts which apply over the whole range of new technologies, considering: a new approach to cycles, enabling their irreversibility to be taken into account; a detailed study of combustion to show how the chemical energy in a fuel is converted into thermal energy and emissions; an analysis of fuel cells to give an understanding of the direct conversion of chemical energy to electrical power; a detailed study of property relationships to enable more sophisticated analyses to be made of both high and low temperature plant and irreversible thermodynamics, whose principles might hold a key to new ways of efficiently covering energy to power (e.g. solar energy, fuel cells). Worked examples are included in most of the chapters, followed by exercises with solutions. By developing thermodynamics from an explicitly equilibrium perspective, showing how all systems attempt to reach a state of equilibrium, and the effects of these systems when they cannot, the result is an unparalleled insight into the more advanced considerations when converting any form of energy into power, that will prove invaluable to students and professional engineers of all disciplines.

1

State of Equilibrium

Most texts on thermodynamics restrict themselves to dealing exclusively with equilibrium thermodynamics. This book will also focus on equilibrium thermodynamics but the effects of making this assumption will be explicitly borne in mind. The majority of processes met by engineers are in thermodynamic equilibrium, but some important processes have to be considered by non-equilibrium thermodynamics. Most of the combustion processes that generate atmospheric pollution include non-equilibrium effects, and carbon monoxide (CO) and oxides of nitrogen (NO_x) are both the result of the inability of the system to reach thermodynamic equilibrium in the time available.

There are four kinds of equilibrium, and these are most easily understood by reference to simple mechanical systems (see Fig 1.1).

Fig. 1.1 States of equilibrium
* The difference between ΔS and dS

Consider Taylor’s theorem

Thus dS is the first term of the Taylor’s series only. Consider a circular bowl at the position where the tangent is horizontal. Then

However

because

etc are not zero.

Hence the following statements can be derived for certain classes of problem

stable equilibrium	(dS)E = 0
	(ΔS)E < 0
neutral equilibrium	(dS)E= 0
	(ΔS)E= 0
unstable equilibrium	(dS)E= 0
	(ΔS)E > 0

(see Hatsopoulos and Keenan, 1972).

1.1 Equilibrium of a thermodynamic system

The type of equilibrium in a mechanical system can be judged by considering the variation in energy due to an infinitesimal disturbance. If the energy (potential energy) increases then the system will return to its previous state, if it decreases it will not return to that state.

A similar method for examining the equilibrium of thermodynamic systems is required. This will be developed from the Second Law of Thermodynamics and the definition of entropy. Consider a system comprising two identical blocks of metal at different temperatures (see Fig 1.2), but connected by a conducting medium. From experience the block at the higher temperature will transfer ‘heat’ to that at the lower temperature. If the two blocks together constitute an isolated system the energy transfers will not affect the total energy in the system. If the high temperature block is at an temperature T₁ and the other at T₂ and if the quantity of energy transferred is δQ then the change in entropy of the high temperature block is

Fig. 1.2 Heat transfer between two blocks

(1.1)

and that of the lower temperature block is

(1.2)

Both eqns (1.1) and (1.2) contain the assumption that the heat transfers from block 1, and into block 2 are reversible. If the transfers were irreversible then eqn (1.1) would become

(1.1a)

and eqn (1.2) would be

(1.2a)

Since the system is isolated the energy transfer to the surroundings is zero, and hence the change of entropy of the surroundings is zero. Hence the change in entropy of the system is equal to the change in entropy of the universe and is, using eqns (1.1) and (1.2),

(1.3)

Since T₁ > T₂, then the change of entropy of both the system and the universe is dS = (δQ/T₂T₁)(T₁ − T₂) > 0. The same solution, namely dS>0, is obtained from eqns (1.1a) and (1.2a).

The previous way of considering the equilibrium condition shows how systems will tend to go towards such a state. A slightly different approach, which is more analogous to the one used to investigate the equilibrium of mechanical systems, is to consider these two blocks of metal to be ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Structure of book
• Symbols
• Chapter 1: State of Equilibrium
• Chapter 2: Availability and Exergy
• Chapter 3: Pinch Technology
• Chapter 4: Rational Efficiency of a Powerplant
• Chapter 5: Efficiency of Heat Engines at Maximum Power
• Chapter 6: General Thermodynamic Relationships: single component systems, or systems of constant composition
• Chapter 7: Equations of State
• Chapter 8: Liquefaction of Gases
• Chapter 9: Thermodynamic Properties of Ideal Gases and Ideal Gas Mixtures of Constant Composition
• Chapter 10: Thermodynamics of Combustion
• Chapter 11: Chemistry of Combustion
• Chapter 12: Chemical Equilibrium and Dissociation
• Chapter 13: Effect of Dissociation on Combustion Parameters
• Chapter 14: Chemical Kinetics
• Chapter 15: Combustion and flames
• Chapter 16: Irreversible Thermodynamics
• Chapter 17: Fuel Cells
• Bibliography
• Index