Page 106 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

80 3 Basics of Gas Combustion

where DU ¼ increase in the internal energy of the system (J), Q ¼ heat added to the
system (J), and W ¼ work done by the system on the surroundings (J).
Since combustion takes place in a relatively short period of time, it allows us to
conduct a simplified analysis without complex integration, considering a combus-
tion reaction starting with reactants at state 1 (pressure P 1 and temperature T 1 ).
After a constant pressure combustion the products are at state 2 (P 2 ; T 2 ). The system
is at constant pressure (P 1 ¼ P 2 ¼ P), therefore, work is done by the system on the
surroundings, where W ¼ PðV 2 V 1 Þ. Applying first law of thermodynamics,

U 2 U 1 ¼ Q PðV 2 V 1 Þ ð3:47Þ

which leads to the heat produced by the combustion process as

ð
ð
Q ¼ U 2 þ PV 2 Þ U 1 þ PV 1 Þ ð3:48Þ
Note that the enthalpy of a system at certain status is defined as
H ¼ U þ PV ð3:49Þ

where H = the total enthalpy of the system (J), U ¼ the internal energy of the
system (J), and V ¼ the volume of the system.
Therefore, the heat added to the system is the total enthalpy difference

Q ¼ H 2 H 1 ð3:50Þ

The total enthalpy at status j ¼ 1 or 2 is the summarization of the enthalpy of all
the compounds,

X
H j ¼ n i h i ðT j Þ ð3:51Þ

Then Eq. (3.50) becomes

X X
ðÞ
Q ¼ n i h i T 2 n i h i T 1 ð3:52Þ
ðÞ
P R
where n ¼ mole amount of the component in fuel–air mixture or the product,
hðTÞ¼ enthalpy of a component at temperature T in J/mole. Subscripts i; P and R
stand for the ith component, product, and reactant, respectively.
The combustion system can be defined as exothermic, isothermal or endothermic
based on the heat of reaction as follows:

8
Q \ 0 exothermic reaction
<
Q ¼ 0 isothermal reaction
:
Q [ 0 endothermic reaction