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CHAPTER SIX
Endoreversible heat engines
6.1 Introduction
The statement of the second law, unlike many physical laws, is not an
explicit equality. It is based on the observation that while heat can flow
spontaneously from a hot body to a clod body, it cannot flow back from
the cold to the hot body without external expenditure. Also, while work
can be completely converted into heat, it is impossible to convert all the heat
back into work. The second law is a general observation that the thermal
processes may proceed in certain directions. Nevertheless, it does not pro-
vide a quantitative measure on what amount of a given quantity of heat is
convertible into work, or conversely, how much external work would be
needed to transfer a unit of heat from a cold reservoir to a hot reservoir.
As discussed in Chapter 2, it was Sadi Carnot [1] who first investigated max-
imum theoretical work that could be extracted from a given amount of heat.
This investigation led him to come up with the design of an engine that
would operate on a cycle comprising two adiabatic and two isothermal
processes.
The significance of the Carnot cycle is that it played a key role in the
formulation of the second law and the invention of entropy. Clausius [2]
remarkable conclusion was that a Carnot-like (reversible) engine com-
municating with any number of heat reservoirs would yield no entropy
production—see the discussion of Section 3.3.2. Clausius also concluded
that the real heat engines would result in uncompensated transformation,or
entropy generation.
It is natural to question whether there is any relation between the
entropy produced by a heat engine and its thermal efficiency or power out-
put. In 1975, Leff and Jones [3] discussed by means of an analytical argument
that an increase in the thermal efficiency of an irreversible heat engine would
not necessarily result in a decrease in its entropy production. Salamon et al.
[4] showed that the maximum work and the minimum entropy production
in heat engines might become equivalent under certain design conditions.
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Entropy Analysis in Thermal Engineering Systems 67
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