Chapter 7 - cen54261_ch07.qxd 9:57 AM Page 273 CHAPTER...

ENTROPY
I
n Chap. 6, we introduced the second law of thermodynamics and applied
it to cycles and cyclic devices. In this chapter, we apply the second law to
processes. The first law of thermodynamics deals with the property energy
and the conservation of it. The second law leads to the definition of a new
property called entropy. Entropy is a somewhat abstract property, and it is dif-
ficult to give a physical description of it without considering the microscopic
state of the system. Entropy is best understood and appreciated by studying its
uses in commonly encountered engineering processes, and this is what we in-
tend to do.
This chapter starts with a discussion of the Clausius inequality, which forms
the basis for the definition of entropy, and continues with the increase of
entropy principle. Unlike energy, entropy is a nonconserved property,
and there is no such thing as a conservation of entropy principle. Next, the
entropy changes that take place during processes for pure substances, in-
compressible substances, and ideal gases are discussed, and a special class of
idealized processes, called isentropic processes, is examined. Then, the re-
versible steady-flow work and the isentropic efficiencies of various engineer-
ing devices such as turbines and compressors are considered. Finally, entropy
balance is introduced and applied to various systems.
273
CHAPTER
7
CONTENTS
7–1 Entropy 274
7–2 The Increase of
Entropy Principle 277
7–3 Entropy Change of
Pure Substances 281
7–4 Isentropic Processes 285
7–5 Property Diagrams
Involving Entropy 286
7–6 What Is Entropy? 288
7–7 The T ds Relations 291
7–8 Entropy Change of
Liquids and Solids 293
7–9 The Entropy Change
of Ideal Gases 296
7–10 Reversible
Steady-Flow Work 305
7–11 Minimizing the
Compressor Work 308
7–12 Isentropic Efficiencies of
Steady-Flow Devices 312
7–13 Entropy Balance 319
Summary 332
References and
Suggested Readings 334
Problems 334
cen54261_ch07.qxd 11/18/03 9:57 AM Page 273

7–1 ENTROPY
The second law of thermodynamics often leads to expressions that involve in-
equalities. An irreversible (i.e., actual) heat engine, for example, is less effi-
cient than a reversible one operating between the same two thermal energy
reservoirs. Likewise, an irreversible refrigerator or a heat pump has a lower
coefficient of performance (COP) than a reversible one operating between the
same temperature limits. Another important inequality that has major conse-
quences in thermodynamics is the Clausius inequality. It was first stated by
the German physicist R. J. E. Clausius (1822–1888), one of the founders of
thermodynamics, and is expressed as
0
That is, the cyclic integral of d Q / T is always less than or equal to zero. This
inequality is valid for all cycles, reversible or irreversible. The symbol (in-
tegral symbol with a circle in the middle) is used to indicate that the integra-
tion is to be performed over the entire cycle. Any heat transfer to or from a
system can be considered to consist of differential amounts of heat transfer.