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 steadyflow 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
SteadyFlow Work
305
7–11
Minimizing the
Compressor Work
308
7–12
Isentropic Efficiencies of
SteadyFlow Devices
312
7–13
Entropy Balance
319
Summary
332
References and
Suggested Readings
334
Problems
334
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Page 273
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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.
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 Spring '09
 Thermodynamics, Energy, Entropy, entropy change

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