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Unformatted text preview: se three before reaction
and after combustion are listed below.
Species
H2
O2
H2O Reactant
0.6667
0.3333
0 Product
0.2915
0.1457
0.5628 As seen in the table, the dissociation is very signiﬁcant; about 30% of the
products is H2. Let’s ﬁnd out how much fuel is not burned by considering the
following stoichiometric reaction:
H2 ðgÞ þ 0:5O2 ðgÞ ! X Á H2 þ 0:5X Á O2 þ ð1 À XÞ Á H2 OðgÞ
The mole fraction of H2 in the products is
xH2 ¼ X
X
¼
:
X þ 0: 5X þ 1 À X 0: 5X þ 1 With xH2 ¼ 0.2915, we get X ¼ 0.3412. If we assume 66% of fuel is burned, a new
^
estimate based on cp at 1,500 K leads to
Tp ¼ 300 K þ 0:66 Á 241:88 kJ=mol
$ 3;700 K
0:047 kJ/mol À K ^
that is in much better agreement with the equilibrium result. If we estimate cp
at 1,800 K we get
Tp ¼ 300 K þ 0:66 Á 241:88 kJ=mole
$ 3;514:7 K:
0:04966 kJ/mole À K 40 2 Thermodynamics of Combustion If we include additional species, H, OH, and O in the products, the predicted
equilibrium temperature drops to 3,076 K. The table below shows the mole fractions of each species in this case.
Species
H2
O2
H2O
OH
O
H Reactant
0.6667
0.3333
0
0
0
0 Product
0.1503
0.0510
0.5809
0.1077
0.0330
0.0771 Evidently, the radicals OH, H, and O take some energy to form; note that their
values for enthalpy of formation are positive. Because the space shuttle engine
operates at 18.94 MPa (2,747 psi, ~186 atm) at 100% power, the pressure needs to
be taken into consideration as the combination of radicals occurs faster at higher
pressures. The predicted equilibrium temperature at 18.94 MPa is 3,832.4 K and the
mole fractions are listed below.
Species
H2
O2
H2O
OH
O
H Reactant
0.6667
0.3333
0
0
0
0 Product
0.1169
0.0336
0.7051
0.1005
0.0143
0.0296 The energy needed to vaporize liquid H2 and O2 and heat them from their boiling
temperatures to 25 C are estimated to be 8.84 kJ/mol and 12.92 kJ/mol (energy ¼
latent heat + sensible energy from boiling point to STP). With H2 þ 0.5O2, the total
energy required is then 8.84 þ 0.5·12.92 or about 15.3 kJ/mol. The temperature
drop due to this process is about ~15.3 kJ/(0.049 kJ/molK) ¼ 148 K. With this, we
estimate the space shuttle main engine temperature is 3,832 À 148 K or ~3,675 K.
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This document was uploaded on 01/20/2014.
 Winter '14
 Physics, Energy, Heat

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