Page 185 - Entrophy Analysis in Thermal Engineering Systems

180 Entropy Analysis in Thermal Engineering Systems

On the other hand, if the engine is run by fuel combustion, we find the fol-
lowing relation.

1
¼ H 0 + (11.39)
rev 1 Ψ ch
H
e η
max
Here, H e denotes the enthalpy of the combustion products calculated at
rev
T e , which designates the minimum theoretical temperature of the combus-
rev
tion products exiting the engine. For instance, if methane is used as a fuel,
the minimum exhaust temperature according to Eq. (11.39) is 313.8K. An
exit temperature lower than T e would be in violation of the laws of
rev
thermodynamics.

11.8 Final notes
Before closing this final chapter, there remains to make few remarks
about the limitation of the second law and the application of entropy-based
analysis.

11.8.1 Entropy vs exergy

In principle, there should not be any difference between the design results
obtained from entropy and exergy analyses. It was repeatedly concluded in
Sections 11.2–11.4 that the exergy destruction is equivalent to the total
entropy generation multiplied by the temperature of the coldest reservoir
(Section 11.2) or of the cold reservoir (Sections 11.3 and 11.4). So, minimi-
zation of exergy destruction is identical to minimization of total entropy
generation.
The simplest explanation for the coincidence of the optimum of the two
thermodynamic functions would, perhaps, be: exergy is a consequence of
the first and second laws, but because the first law is an expression of the
conservation of energy, an exergy-based analysis applied to a steady-state
process carries a function whose net value is zero. For a system undergoing
a steady-state process, the first law may be represented with a single function
as F(E i )¼0, where E i denotes all forms of energy that may appear in a first
law equation.
It would then be a matter of preference to employ an entropy- or exergy-
based analysis when modeling the thermodynamic performance of an energy
conversion system. A thermodynamic model is primarily built upon the mass
conservation principle and the first law. If one decides to also include an