Page 184 - Entrophy Analysis in Thermal Engineering Systems

Exergy 179

power-generating systems. It reveals that the efficiency of a Carnot cycle
constrained to operate between the same highest and lowest temperatures
of a combustion-driven cycle is not an accurate efficiency bound.
Based on this argument, it would be inappropriate to define the second
law efficiency of a heat engine as the ratio of the actual thermal efficiency (η a )
to the efficiency of the corresponding Carnot engine. It should rather be
defined as the ratio of η a to η max . Hence,
η
η ¼ a (11.35)
SL η
max
The second law efficiency defined in Eq. (11.35) accounts for the heat
source type because as discussed, the maximum theoretical work production
of a heat engine may vary depending on whether the thermal energy
requirement of the engine is supplied from thermal reservoir(s), hot
stream(s), or fuel.

11.7 Minimum exhaust temperature
According to the second law, a portion of the thermal energy supplied
to a heat engine must be rejected to the surroundings, even at fully reversible
operation where entropy generation is zero. From this principle, we may
define a minimum exhaust temperature for an engine that is run by a hot
stream or fuel combustion. In this case, the amount of heat rejected by
the engine is obtained using Eq. (11.12). If the heat is supplied by a hot
stream (Fig. 11.2A), the heat rejected at the reversible limit can also be deter-
mined by

rev
fl
Q ¼ H H 0 Þ Ψ ¼ T 0 S S 0 Þ (11.36)
ð
ð
e
Comparing Eq. (11.12) with Eq. (11.36), one obtains
H H 0 ¼ T 0 S S 0 Þ (11.37)
ð
rev
e
Notice that H e denotes the enthalpy of the hot stream at the engine exit, and
S is the entropy of the stream at the inlet of the engine. Assume that the hot
steam is an ideal gas with a uniform pressure. The minimum exhaust tem-
perature or the exhaust temperature at reversible operation may be deter-
mined by

¼ T 0 1+ ln (11.38)
rev T
T
e
T 0