Page 193 - Entrophy Analysis in Thermal Engineering Systems

190 Appendices

Table B.1 Comparison of the heating value and the minimum specific entropy
generation of a gas turbine cycle (TIT¼1100K) for five different fuels.
Minimum SEG
Fuel HV (kJ/mol) (J/molK)

H 2 241.8 536
CH 3 OH 675.9 1676
CH 4 802.3 1956
C 2 H 5 OH 1277.5 3187
2043.9 5075
C 3 H 8

hydrogen with the highest heating value (measured in kJ/g) among the five
fuels would yield the greatest specific entropy generation, whereas methanol
with the least heating value would lead to the lowest SEG.

f
Appendix C: Determination of ξ at minimum G m
An equation can be derived for the reaction advancement that min-
imizes the function G m but maximizes the entropy generation, see
f
Eq. (10.10), for a mixture of k ideal gases, i.e., Eq. (10.19). Substituting
the relation

0
s j T, pð Þ ¼ s + s T, j R lny f (C.1)
j j
for the entropy of species j in Eq. (10.19) yields

k
X h i
0
G ξðÞ ¼ n + a j ξ h j TðÞ T s s + s T, j R lny R lnp (C.2)
f
i
f
m j j j
j¼1
0
where s denotes the specific entropy at the standard temperature and pres-
sure, and s T is the entropy change due to the difference between the tem-
perature T and the standard temperature.
The model fraction of species j is defined as
f n + a j ξ
i
n
f j j
y ¼ ¼ (C.3)
j n + aξ
f i
n
where n j and n are substituted from Eqs. (10.15) and (10.17), respectively.
f
f
Substituting Eq. (C.3) into Eq. (C.2), G m can be described as a function
f
of ξ only.