The enthalpy balance of the reaction is
h
0
f
C 8 H 18 l
ð Þ
þ 0 ¼ 8 h
0
f
CO 2
þ 9 h
0
f
H 2 O l
ð Þ
þ 0 þ HHV
Here, the fuel heating value is the higher heating value (HHV) because water in the
product is in the liquid form. The balance in numerical terms
À249; 950 ¼ 8 Â À393; 520
ð
Þþ9 Â À285; 830
ð
ÞþHHV
gives the n-Octane (liquid) HHV
HHV ¼ 5; 470; 680 kJ/kmol ¼ 47; 891 kJ/kg
Repeat the same fuel–air mixture now with water in the product in the vapor
form. The heating value, in this case, is called the lower heating value (LHV),
C 8 H 18 l
ð Þ þ 17:5 O 2 þ 3:76N 2
ð
Þ!8CO 2 þ 9H 2 O g
ð Þ þ 5O 2 þ 65:8 N 2
The enthalpy balance of the reaction is
h
0
f
C 8 H 18 l
ð Þ
þ 0 ¼ 8 h
0
f
CO 2
þ 9 h
0
f
H 2 O g
ð Þ
þ 0 þ LHV
Correspondingly,
À249; 950 ¼ 8 Â À393; 520
ð
Þþ9 Â À241; 820
ð
ÞþLHV
i.e.,
LHV ¼ 5; 074; 590 kJ/kmol C 8 H 18 l
ð Þ
¼ 44; 424 kJ/kg C 8 H 18 l
ð Þ
The corresponding LHV based on one kg of working fluid of a stoichiometric
octane–air mixture is
LHV ¼ 44; 424 Â
F = A
1 þ
F
A
¼ 2771:3 kJ/kg workingfluid
266
9 Applications to Special States of Thermodynamic Equilibrium …