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8/6/2019 Combustion Ch 1 Lecture 04Mar10
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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
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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
/
/
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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
Ent ha lpy o f format ion
Consider the formation of H2O at Pref, Tref
Chapter 1 45
Ent ha lpy o f format ion
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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
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