Page 113 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

3.5 Adiabatic Flame Temperature 87

3.5.2 Constant Volume Adiabatic Flame Temperature

For an adiabatic constant volume combustion process the work done is zero to the
surroundings. The first law of thermodynamics gives
X X
Q ¼ n i U i ðT a Þ n i U i ðT R Þ¼ 0 ð3:66Þ
P R

From h = U + PV = U +RT, one can get U = h − RT. And the above equation
becomes

X X
n i ðh i ðT a Þ RT a Þ¼ n i ðh i ðT R Þ RT R Þ ð3:67Þ
P R
or

X h i X h i
o o
n i h þ h i ðT a Þ h i ðT 0 Þ RT a ¼ ð
ð
f ;i
f ;i n i h þ h i ðT R Þ h i ðT 0 ÞÞ RT R
P R
ð3:68Þ
Reorganizing the formula leads to
" # " #
X X X X
o o
ð
n i h i ðT a Þ¼ n i h i ðT R Þ h i ðT 0 Þ n i h n i h f ;i
f ;i
P R P R
ð3:69Þ
" # " #
X X X
þ n i h i ðT 0 Þ þ n i RT a n i RT R
P p R
There is an extra term in the last bracket compared to the formula for constant
pressure AFT. This term is positive because the flame temperature is always greater
than that of the reactants. Therefore, mathematically it shows that the constant
volume AFT is greater than the constant pressure one. The AFT is lower for
constant pressure process since there is work done on the surroundings.

3.6 Practice Problems

1. Determine the stoichiometric air/fuel mass ratio and product gas composition
for combustion of heptane (C 7 H 16 ) in dry air.
2. Determine the stoichiometric air required for the combustion of butane in kg of
air per kg of fuel.