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3.5 Adiabatic Flame Temperature 85

3.5.1 Constant Pressure Adiabatic Flame Temperature

Considering an adiabatic system with constant pressure complete combustion, the
first law of thermodynamics gives
X X
Q ¼ n i h i ðT a Þ n i h i ðT R Þ ð3:62Þ
P R

where T a is the constant pressure AFT. The temperature of the products of a com-
plete combustion process can be determined for a given combustion reaction where
n i ’s are known for both the mixture of reactants and the combustion products.
The above equation gives Q = 0 for adiabatic flame and

X h i X h i
o o
n i h þ h i ðT R Þ h i ð298KÞÞ ¼ n i h þ h i ðT a Þ h i ð298KÞÞ ð3:63Þ
ð
ð
f ;i f ;i
R P
Considering Eq. (3.57), the above equation becomes

b i 2 2 o
X
n i a i ðT R 298KÞþ ðT ð298KÞ þ h f ;i
R
2
R
ð3:64Þ

X
b i 2 2 o
¼ n i a i ðT a 298KÞþ ðT ð298KÞ þ h f ;i
a
2
P
The values of coefficients a i and b i and the heat of formation, h o in the above
f ;i
equation can be found in Table A.4, and the adiabatic temperature T a can be
determined mathematically. As a common simplification, the temperature of the
air–fuel mixture before combustion is assumed standard temperature, T R = 298 K.
In this case, Eq. (3.64) above is simplified as

X o X b i 2 2 o
n i h f ;i ¼ n i a i ðT a 298KÞþ ðT ð298KÞ þ h f ;i ð3:65Þ
a
R P 2
Example 3.10: Adiabatic Flame Temperature
CH 4 is pre-mixed with air at 298 K at an equivalence ratio of 1.0 and the com-
bustion is complete. Determine the constant pressure AFT.
Solution
First of all, set up stoichiometric combustion reaction equation using the methods
introduced in Sect. 3.4,

ð
CH 4 þ 2O 2 þ 3:76N 2 Þ ! CO 2 þ 2H 2 O þ 7:52N 2
For an adiabatic constant pressure system, with T R = T 0 = 298 K, left hand side
(LHS) of Eq. (3.65)is