1. Heat of Reaction 1st Law Analysis of Combustion Systems
Lecture 37
Heat of Reaction
1st Law Analysis of Combustion Systems

2. Combustion System Analysis
Consider the complete combustion of octane in 150% theoretical air,
C8H18
Combustion Chamber
Products (p)
PTA = 150%
In the previous lecture, we found the balanced reaction,
The First Law applied to the system identified above is,

3. Combustion System Analysis
C8H18
Combustion Chamber
Products (p)
PTA = 150%
reactants
(air and fuel)
combustion products
Potential issue: There are no Dh values (except for O2 and N2). This has the potential to cause a datum state problem.

4. Resolving the Datum State Problem
In combustion calculations, the enthalpy of all stable* elements is defined as zero at the standard reference state (SRS),
*‘Stable’ means chemically stable at the SRS. For example, diatomic oxygen (O2) is stable at the SRS. Monatomic oxygen (O) is not stable at the SRS.

5. Enthalpy of Formation
The enthalpy of a compound at the standard reference state
Heat released in an exothermic reaction (or absorbed in an endothermic reaction) when a compound is formed from its elements. (Elements and compound at the SRS)
Example – Methane C CH 25 C 4
1 atm 25 C 2H
1 atm 2

7. Enthalpy of Formation Values
Using EES* …
*Unit setting = molar

8. Enthalpy of Formation Values
Results ...
Conclusion: EES uses the SRS as the datum state for enthalpy for the ideal gases! Therefore, enthalpy of formation values can be calculated from EES using the ideal gas substances (except AIR)

9. Enthalpy Values in Combustion
What do we know so far?
The enthalpy of a stable element at the SRS is 0
The SRS is 25°C, 0.1 MPa
The enthalpy of a compound at the SRS is the enthalpy of formation (Table 15.1 or from EES)

10. Enthalpy Values at Other States
The enthalpy of a component at any temperature in a combustion process can be evaluated by,
Accounts for the enthalpy difference relative to the SRS
How is the enthalpy difference in brackets determined??

11. Enthalpy Values at Other States
Three possibilities ...
If the heat capacity of the component can be assumed constant,
If the constant heat capacity assumption is not accurate enough, then use the ideal gas tables (Table C.16c). In this case the datum state for the table does not have to match the enthalpy of formation.
Use a set of property tables for all components that has all enthalpy values referenced to the SRS. Does such a thing exist?

12. Enthalpy Values at Other States
Exploring Option 3 from the previous slide ...
If a thermodynamically consistent set of tables exists, then
Therefore the enthalpy of the component could simply be looked up in a table at the given temperature,
If something like this were available ... combustion calculations would be EESy! 

13. Enthalpy Values at Other States
ALL of the ideal gas enthalpy reference states (except for the ideal gas ‘AIR’) in EES are referenced to the SRS!
This is from the EES Help Menu for the ideal gas CO2 ...
All other ideal gases in EES (except AIR) say the same thing!
Significance: Combustion calculations just became EESy!

14. Heat of Reaction
Consider an aergonic combustion process as shown below
Fuel
Products (P)
Combustion Chamber
Reactants (R)
Air
The First Law applied to this system results in,
Dividing by the molar flow rate of the fuel,

15. Heat of Reaction
The molar flow rate ratios are the molar coefficients from the balanced combustion reaction! Therefore,
This is known as the molar heat of reaction.

16. Heating Values of Fuels
Given: Gaseous octane (C8H18) is burned completely in 100% theoretical air. The reactants and the products are at the SRS.
Find: The heat released during this combustion process per mole of fuel for the following cases,
the water in the products is all vapor
the water in the products is all liquid

17. Heating Values
The system boundary is drawn around the combustion chamber. Applying the First Law results in,
Dividing both sides of this equation by the molar flow rate of the fuel,
Number of moles of reactant per mole of fuel
Number of moles of product species per mole of fuel
How are these found?

18. Heating Values
The molar flow rate ratios on the previous slide are the molar coefficients from the balanced combustion reaction (for one mole of fuel)! Therefore,
Notice: PTA = 100% means stoichiometric combustion
Observations ...
The importance of being able to balance the combustion reaction is evident!
As long as the combustion process is aergonic, the First Law will be as written above, independent of the conditions in and out of the combustion chamber!

19. Heating Values
For the complete combustion of normal octane in 100% theoretical air, we previously found,
Applying the First Law to the system,

20. Heating Values
Now we have an interesting problem. Is the water liquid or gas (or both)?

21. Heating Values
Let’s consider both extremes (1) the H2O is all vapor and (2) the H2O is all liquid.
All vapor water ...
All liquid water ...

22. Heating Values All vapor water ... Lower Heating Value (LHV)
All liquid water ...
Higher Heating Value (HHV)
Observations ...
The reactants and products are at the SRS
The reaction occurs with PTA = 100% (xi = ni )
The difference between the HHV and the LHV is the enthalpy of vaporization of water!

23. Heating Values 1 mol fuel TSRS Products TSRS, PSRS PSRS
(vapor H2O)
TSRS, PSRS
Stoichiometric air
Products
(liquid H2O)

24. Heating Values
The heating values represent the maximum possible heat transfer that can occur per mole of fuel.
The reactants and products are at the SRS
The HHV represents fully condensed water vapor
The LHV represents all water vapor
These values provide a basis for the combustion efficiency,

25. Example
Back to our problem ... Is there liquid water in the products at the SRS? If so, how much?
Will water condense?
Since TSRS < Tdp, water will condense

26. Example
How much water will condense? At TSRS = 25°C, the mole fraction of water vapor in the products is,
The mole fraction of the water vapor at 25°C can be found,