Combustion Ch 1 Lecture 04Mar10

8/6/2019 Combustion Ch 1 Lecture 04Mar10

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1

Theory of Com bust ion

Stoichiometry & Heat offormation

HW #1 Due 3/9

3/4/2010

Chapter 1 23

St o ich iom et ry : exam ple (1 /2)

Stoichiometric CxHyOz - air



2

Chapter 1 24

St o ich iom et ry : exam ple (2 /2)

Chapter 1 25

Equiva lence ra t io

Equivalence ratio Φ: Quantitatively indicate that if a fuel-oxidizermixture is rich, lean, or stoichiometric

• Φ = 1

• Φ < 1

• Φ > 1

==Φ

st OF

OF

/

/



3

Chapter 1 26

Other w ays fo r de fin ing s to ic h iomet ry

Percent of stoichiometric air

% stoichiometric air = 100 % / Φ

Percent excess air

% excess air = 100% * (1 – Φ)/ Φ

Chapter 1 27

Global react ion for Φ ≠ 1



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Chapter 1 28

Approaches for Φ > 1

More complicated if fuel left over is allowed

Simple approach:

• No left-over O2

• Fuel breaks down into CO and H2

Chapter 1 29

Ex t ensive and in tensive proper t ies

The numerical value of an extensive propertydepends on the amount (mass or number ofmoles) of the substance considered.• usu. Denoted with CAPITAL letters.

• e.g. V (m3) for volume, U (J) for internal energy, H (J)

(=U+PV) for enthalpy The numerical value of an intensive property is

independent of the amount of substancepresent.• Mass-based intensive properties are generally

denoted with lower-case letters.

• e.g., v (m3 /kg) for specific volume, u (J/kg) for specificinternal energy, h (J/kg) (=u+Pv) for specific enthalpy.



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Chapter 1 30

Equat ion o f Sta t e

An equation of state provides the relationship among thepressure, P, temperature, T, and volume V (or specificvolume v) of substance.

For ideal gas (single component)

Ideal gas: a model treat molecules as point particlesexchanging momentum in elastic collisions, neglecting

both molecular size and intermolecular attractions,.• Low density (pressure)

• High temperatures

Chapter 1 31

Ot her form s of equat ion o f s ta t e

For ideal gas, mole fraction is equivalent to volumefraction.



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Chapter 1 32

Calor i f ic equat ions of s ta t e (1/2)

For pure substance at thermodynamic equilibrium,independent intensive properties define the state.

Chapter 1 33

Calor i f ic equat ions of s ta t e (2/2)



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Chapter 1 34

Mix tures

Consider a system of i = 1, 2, … Nsp chemicalspecies occupying a volume V

Mass fractions Yi

Chapter 1 35

Mole f rac t ions

Mole fractions xi



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Chapter 1 36

Idea l -gas mix t ures

Molar concentration

Chapter 1 37

Ideal-gas m ix t ures (2/2)

Partial pressure Pi



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Chapter 1 38

Latent heat o f vapor izat ion

Latent heat of vaporization (also known as the enthalpy ofvaporization, denoted as hfg): the heat required in aconstant-pressure process to completely vaporize a unitmass of liquid at a given temperature

hfg(T,P)=hvapor(T,P)-hliquid(T,P)

where T and P are the corresponding saturationtemperature and pressure, respectively.

Clausius-Clapeyron equation can be used with the latentheat of vaporization to estimate saturation pressurevariation with temperature:

Chapter 1 39

Fi rs t law o f thermodynamic s

First law – fixed mass



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Chapter 1 40

Fi rs t law o f thermodynamic s

First law – control volume

Chapter 1 41

Enthalpy

For any species i

Absolute enthalpy at temperature T = Enthalpy offormation at Tref, P

0 + Sensible enthalpy change in goingfrom Tref to T

Enthalpy of formation (hf): an enthalpy that takes intoaccount the energy associated with chemical bonds.

Sensible enthalpy (Δhs): An enthalpy that is associatedonly with temperature.



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Chapter 1 42

Ent ha lpy a t Reference St at e

At Pref and Tref, enthalpy of elements intheir “natural state” is zero.

Reference state• Pref=P0=

• T

Elements in natural state• Oxygen

• Hydrogen• Carbon

• Nitrogen

Chapter 1 43

Ent ha lpy o f format ion

To form oxygen atomsat the standard staterequires the breaking ofthe covalent bond ofoxygen

The dissociation energyfor O2 at 298 K is498390 kJ/kmolO2

Thus, the enthalpy offormation for atomicoxygen is



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Chapter 1 44


Consider the formation of H2O at Pref, Tref

Chapter 1 45




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Chapter 1 46

Chapter 1 47

Enthalpy o f

fo rmat ion

The enthalpy offormation chartfrom high to low

Similar to apotential energychart

As species atthe top react toform species atthe bottom, heatis ,and ansystem exists



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Chapter 1 48

Relat ionsh ip betw een bond energ ies

and heat o f format ion

The bond energy for dissociation D0(R-X), is also know as the strengthof a chemical bond between R and X of the molecule RX

The energy required to break the R-X bond at 298.15 K, RX->R+X, isrelated to the enthalpy of formation

D0298(R-X)=Δh0

f,R+Δh0f,X-Δh0

f,RX (per mole) Bond and resonance energies can be used to estimate heats of

formation for some molecules and heats of combustion for certainreactions.

Ex:Bond energies (kcal/mol)H-H 104.20C-H 80.88+- 0.29

H-O 102.20

C-O >= 141.97C=O 173

N≡N 225.94+-0.14O=O 119.11C=C 145.08 +- 5.02

Chapter 1 49

Ex am ple 1 (1/4)

A gas stream at 1 atm contains a mixtureof CO, CO2, and N2 in which the COmole fraction is 0.10 and the CO2 mole

fraction is 0.20. The gas-streamtemperature is 1200 K. Determine theabsolute enthalpy of the mixture on botha mole basis (kJ/kmol) and a mass basis(kJ/kg). Also determine the massfractions of the three component gases.



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Chapter 1 50

Ex am ple 1 (2/4)

Chapter 1 51

Ex am ple 1 (3/4)



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Chapter 1 52

Ex am ple 1 (4/4)

Chapter 1 53

Ent ha lpy o f react ion

Heat released by complete combustionof a specific fuel at specified P and T



Chapter 1 54

Ent ha lpy o f react ion

StoichiometricCH4 /air

Per mass of fuel

Combustion Ch 1 Lecture 04Mar10

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