Page 174 - Entrophy Analysis in Thermal Engineering Systems

CHAPTER ELEVEN

Exergy

11.1 Introduction

The mechanical theory of heat, as stated by Clausius in his last memoir
[1], rests on the equivalence of heat and work (first law) and the equivalence
of transformations (second law). A combination of the two laws leads to a
relationship between the work and the uncompensated transformation
(i.e., entropy production). It was indeed Clausius who initiated utilization
of the combined first and second laws. Concepts like availability and exergy
(equivalent in principle) are deduced from the combined laws. They refer to
the maximum work extractable from a source of heat energy, e.g., thermal
reservoir, a hot stream, fuel combustion. Often, exergy-based analysis is
erroneously attributed to the second law only. In this chapter, we show
where exergy is originated from and that conclusions drawn from both
exergy and entropy analyses should in principle be identical.

11.2 Thermal exergy
Fig. 11.1 depicts schematically an engine that operates in a closed cycle
while communicating with n+1 thermal reservoirs. The first and second
laws may analytically be expressed as

n
X
W net ¼ Q i (11.1)
i¼0
n
X
Φ ¼ Q i (11.2)
i¼0 T i
where T i denotes the temperature of the ith reservoir. Also, note that the
usual sign convention is applied, i.e., the heat imparted to the engine is pos-
itive whereas the heat rejected by the engine is negative.

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Entropy Analysis in Thermal Engineering Systems 169
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