aula 3

Prévia do material em texto

Revision of basic concepts
New Terminology
1. Concentrations
2. Mole fractions
3. Mass fractions
Mixture of species (gases) 
– Average Thermodynamic Properties
P, T, V, h, s, … 
Fuel-air mixture, most common.
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Fuel-air mixture:
• Air to Fuel Ratio
• Fuel to air ration
FARAFR /1
air
fuel
m
m
FAR 
fuel
air
m
m
AFR 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Fuel-air mixture:
• Air to Fuel Ratio
• Fuel to air ratio
• Stoichiometry
no fuel & no oxidizer in the products
• Lambda
st
AFR
AFR

stfuelair
fuelair
mm
mm
)/(
)/(

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Fuel-air mixture
Equivalence Ratio
trystoichiome - 1
fuel pure- 
air pure- 0
(fuel) lean- 1
(fuel) rich- 1








stairfuel
airfuel
fuelair
stfuelair
mm
mm
mm
mm
)/(
)/(
)/(
)/(

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Hydrocarbon Combustion
4/yxa 
22222
21.0
79.0
221.0
79.0
( N
a
OH
y
xCONOaHC
yx


 
fuel
NO
st
MW
MWMWa
AFR 22
)21.0/79.0(

AFRst???
methane
octane
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Hydrocarbon Combustion 
225242322122
21.0
79.0
)
21.0
79.0
( N
a
OaHaOHaCOaCOaNO
a
HC
yx


 
1 1 1  
air excess - 1
trystoichiome - 1
 /)1( ,2/ , balance atomic
0
531
42


aayaxa
aa
 )/-(1air excess 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Hydrocarbon Combustion 
225242322122
21.0
79.0
)
21.0
79.0
( N
a
OaHaOHaCOaCOaNO
a
HC
yx


 
1
products theinexist e 
2
HCO
?????????????????
Additional equations are needed –
Chemical Equilibrium
Combustion – Prof. Gurgel
1 1 1  
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction
• Concentration 
tot
i
i
n
n
x 
kmol ni
kmol ntot
prodreac
kmolkmol 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration 
tot
i
i
m
m
Y 
kg species i 
kg of mixture
prodreac
kgkg 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration 
1
11
 

N
i
i
N
i
i
xY
mix
i
ii
MW
MW
xY 
1
1 1

 
  







N
i
N
i i
i
iimix
MW
Y
MWxMW
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration 
   3
4
/ mkmol
Vol
n
CH i
V
nx
V
n
C totii
i

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration (Ci) 
TR
P
x
PTRn
nx
C
u
i
utot
toti
i

/
TRnPV
utot

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration (Ci) 
i
i
ui
mixi
i
MW
Y
TR
P
MW
MWY
C





N
i
ii
N
i u
ii
u
mix x
TR
MWPx
TR
PMW
11

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Gaseous Mixture
• Mole Fraction (xi)
• Mass Fraction (Yi)
• Concentration (Ci) 
 
 smkmol
dt
dC
dt
CHd
i 34 /
Conservation equation  mass fractions, Yi
Chemical reaction rate
Gas analysers, flow meters  volume fractions, xi
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)



N
i
ii
hYh
1
)kJ/kg(



N
i
ii
hxh
1
)kJ/kmol(
)kg/kmol()kJ/kg()kJ/kmol(
mix
MWhh 
?????
i
h
?????
i
h
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)
?????
i
h ?????
i
h
hreact hprod
heat
T = 298 K
P = 1 atm
T = 298 K
P = 1 atm
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)
hreact hprod
Heat – where it comes from?
No sensible enthalpy
Tprod = Treac
T = 298 K
P = 1 atm
T = 298 K
P = 1 atm
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)
Reactants
T = 298 K
P = 1 atm
CxHy
O2 + 3.76 N2
Products
T = 298 K
P = 1 atm
CO2, H2O, 
…
Gas composition alters significantly
Enthalpy of FORMATION
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)
The standard enthalpy of formation or 
"standard heat of formation" of a compound is the 
change of enthalpy that accompanies the 
formation of 1 mole of a substance in its standard 
state from its constituent elements in their 
standard states (the most stable form of the 
element at 100 kPa of pressure and the specified 
temperature, usually 298 K or 25 degrees 
Celsius).
Its symbol is ΔHof. 
(ref.: Wikipedia)
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Intensive Mixture Properties
• Thermodynamic property – mixture enthalpy (h)
(1) Standard - this means a very specific temperature and pressure: one atmosphere 
and 25 °C (or 298 K). If a solution is being discussed, then everything in solution 
will be at a 1.00-molar concentration. 
(2) Formation - this word means a substance, written as the product of a chemical 
equation, is formed DIRECTLY from the elements involved. The substance in 
question is always written with a coefficient of one. Here are some examples:
C (s) + O2 (g)  CO2 (g)
C (s) + (1/2) O2 (g)  CO (g)
H2 (g) + O2 (g)  H2O2 (l)
H2 (g) + (1/2) O2 (g)  H2O (l)
C (s) + 2 H2 (g) + (1/2) O2 (g)  CH3OH (l) 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Enthalpy of formation
Three Points:
(1) Every substance is shown in its standard state. This is the physical state 
(solid, liquid, or gas) that a substance would be in under standard conditions. 
Thus, the standard state for carbon is solid, for water is liquid and for hydrogen 
is gas. Why? Because at 1.00 atm. and 25 °C, these substances are in the 
physical state specified. 
(2) There is never a compound on the reactant side, only elements. What is 
being written is a formation reaction. Look again at the definition of formation. 
Here is an example of a chemical reaction that IS NOT a formation reaction:
6 CO2 + 6 H2O  C6H12O6 + 6 O2
Here is the formation reaction for C6H12O6 : 
6 C (s) + 6 H2 (g) + 3 O2 (g)  C6H12O6 (s) 
Combustion – Prof. Gurgel
(3) Formation reactions sometimes are "fake" reactions, in that they cannot 
possibly happen as written. For example: 
H2 (g) + O2 (g)  H2O2 (l) 
is simply not possible.You can't make hydrogen peroxide by reacting hydrogen 
and oxygen directly. When you do that, you ALWAYS get water. Hydrogen 
peroxide is made a different way, but you can still write the formation reaction. 
Revision of basic concepts
New Terminology
Enthalpy of formation
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Enthalpy of formation
Exothermic chemical reactions will have a negative ∆H and endothermic reactions 
have a positive ∆H . The reason for the sign convention has to do with system and 
surroundings, in thermodynamics. What all this means is that EACH formation 
reaction has an enthalpy change value associated with it. (Notice- enthalpy changes, 
since absolute enthalpy values cannot be measured.) For example, here is the 
formation reaction for carbon dioxide: 
C (s) + O2 (g)  CO2 (g) 
The product (s) have some unknown absolute enthalpy value (call it H2) and the 
reactant (s) have another value (also unknown), called H1. Even though those two 
values cannot be measured, we can measure the difference (H2 minus H1 is called 
∆H) in an experiment using a calorimeter. 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Enthalpy of formation
Heat/work flow out of 
system – change sigh 
on enthalpy is negative
exothermic
Heat/work flow into the 
system – change sign 
on enthalpy is positive
endothermic
Thermodynamic System
C + O2  CO2 
surroundings
Combustion – Prof. Gurgel
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology - Enthalpy of formation
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology - Enthalpy of formation
http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=1
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Enthalpy of formation
The standard enthalpy of formation for an element in its standard state is ZERO!!!! 
Elements in their standard state are not formed, they just are. 
So, ∆H°f for C (s, graphite) is zero, but the ∆H°f for C (s, diamond) is 2 kJ/mol. 
That is because graphite is the standard state for carbon, not diamond. 
∆H°f O2 = 0
∆H°f N2 = 0
∆H°f C(s) = 0
W=498390 kJ / kmolO2
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Absolute Enthalpy
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THTHTH
isref
o
ifi

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,
KHTHTH
is




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i
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,,
1
THTHYH
isref
o
if
N
i
ireac
 

Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Absolute Enthalpy
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isref
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


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i
iimix
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1
)()(
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Enthalpy o Combustion



N
i
iimix
ThxTh
1
)()(
)()()(
,,
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isref
o
ifi

reagprodcomb
hhh 
Combustion – Prof. Gurgel
Revision of basic concepts
New Terminology
Entropy



N
i
iiimix
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ref
i
refiii
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RPTsPTs ln),(),( 
ref
i
urefiii
P
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RPTsPTs ln),(),( 
Combustion – Prof. Gurgel
Revision of basic concepts
Chemical Equilibrium
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

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i
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ref
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ref
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processes natural and actualfor 0
universe
S
process reversiblefor 0
universo
S
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
systisolated
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Classification of Equilibrium States
Stable Unstable
Neutral
Right barrier removed. Unstable for 
small perturbations
Metastable
Barrier
Barrier
Stable with respect to 
small perturbations
Maximum and Minimum Principia (Extremes) 
S
Proposed variations
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Revision of basic concepts
Chemical Equilibrium
Revision of basic concepts
Chemical Equilibrium
Revision of basic concepts
Chemical Equilibrium
Revision of basic concepts
Chemical Equilibrium
Revision of basic concepts
Chemical Equilibrium
Revision of basic concepts
Chemical Equilibrium