Page 177 - Entrophy Analysis in Thermal Engineering Systems

172 Entropy Analysis in Thermal Engineering Systems

(11.10)
W net ¼ H H e
The total entropy generation associated with the engine is

Φ ¼ S e Sð Þ + Q e + S 0 S e (11.11)
T 0
where the first bracket denotes the change in the entropy of the hot stream
within the engine, and the second bracket is the entropy generation due to
cooling the exhaust stream from T e to T 0 . Also,

Q e ¼ H e H 0 (11.12)
From Eqs. (11.10) and (11.12), we conclude
(11.13)
W net ¼ H Q e H 0
Eliminating Q e between Eqs. (11.11) and (11.13), we get

ð
T 0 Φ + W net ¼ H H 0 T 0 S S 0 Þ (11.14)
The right-hand side of Eq. (11.14) denotes the flow exergy, so it can alter-
natively be expressed as
Ψ de + W net ¼ Ψ fl (11.15)

In the reversible limit Ψ de ¼0, so Ψ would represent the maximum theo-
fl
retical work extractable from the hot stream. On the other hand, for a
known initial state of the hot stream, the flow exergy in Eq. (11.15) is fixed.
Thus, maximization of work would be identical to minimization of exergy
destruction or of entropy generation.
In general, if the engine is operated using the thermal energy of multiple
hot streams (Fig. 11.2B), Eq. (11.15) is expressed as
Ψ de + W net ¼ Ψ + Ψ + … + Ψ fl (11.16)
fl
fl
2
1
n
where Ψ i denotes the flow exergy of the ith stream and i¼1, 2, …, n.
fl
11.4 Chemical exergy
The chemical exergy is referred to the maximum theoretical work
extractable from the oxidation of a fuel. We investigated the combustion
of a hydrocarbon fuel in air in Chapter 8 and showed that the maximum
work per unit mole of fuel, which was denoted by w rev , is nearly constant.
In practical power-generating systems driven by combustion of fuel in air