Modern Engineering Thermodynamics

CHAPTER 10
Availability Analysis
CONTENTS
10.1 What is Availability? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
10.2 Fun with Scalar, Vector, and Conservative Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
10.2.1 Scalar and Vector Fields . .....................................................320
10.2.2 Conservative Fields. .........................................................321
10.3 What Are Conservative Forces? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
10.4 Maximum Reversible Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
10.5 Local Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
10.6 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
10.7 Closed System Availability Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
10.8 Flow Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
10.9 Open System Availability Rate Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
10.10 Modified Availability Rate Balance (MARB) Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
10.11 Energy Efficiency Based on the Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
10.11.1 First Law (Energy) Efficiency .................................................339
10.11.2 Second Law (Availability) Efficiency . . . .........................................340
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
10.1 WHAT IS AVAILABILITY?
Availability 1 is a measure of how useful the energy within a system can be. It is the name given to the amount of
energy within a system that is “available” to do useful work, and consequently, it is a measure of the “quality”
of the energy present within a system. Some forms of energy within a system are more available to do useful
work than others. Consequently, these energy forms have a higher value, or availability, than the others. In addition,
a system may contain forms of energy that cannot do any useful work at all because they do not have a
high enough potential, so they are called unavailable energy. Figure 10.1 illustrates how a system can have available
and unavailable energy.
For example, one gallon of gasoline contains about 158 MJ (150,000 Btu) of energy and currently sells for about
$2–$4 dollars. Yet, if you purchase 158 MJ of electrical energy from your local electrical power company, it costs
you about $5. Why does electrical energy cost more than an equivalent amount of chemical energy? The answer
is simply that electrical energy is more available to do useful work than chemical fuel. An electric motor can
convert about 90% of the electrical energy supplied to it into useful output work, whereas an internal
1 Availability is called exergy and essergy (essence of energy) in European textbooks. The term exergy was coined to be similar in form to
the words energy and entropy, and the term essergy is a contraction of “essence of energy.” Both terms lack any obvious connotation
and consequently are not used here.
Modern Engineering Thermodynamics. DOI: 10.1016/B978-0-12-374996-3.00010-5
© 2011 Elsevier Inc. All rights reserved. 319