Untitled - Aerobib - Universidad Politécnica de Madrid

26 CHAPTER 1. THERMOCHEMISTRY
of the mixture is the rank of the matrix of coefficients a ij .
The coefficients of a
principal minor of order l ′ of this matrix determine the species that can be adopted
as components of the mixture. A complete system of independent chemical reactions
can now be obtained by expressing each one of the remaining species as a linear
combination of the said components in the form
∑
A j = b ji A i , (j = l ′ + 1, l ′ + 2, . . . , l). (1.110)
l ′
i=1
Here, the first l ′ species are assumed to be the components of the mixture.
For example in the combustion of mixtures of hydrocarbons and some of their
compounds with oxygen and nitrogen, the combustion products are formed by the
species: CO 2 , CO, H 2 O, HO, H 2 , H, O 2 , O, NO, N 2 and N. Therefore, one has:
l = 11; l ′ = 4; and the number of independent chemical reactions is 7. The following
systems of reactions can be adopted (see Ref. [13]) since they are linearly
independent:
C O 2 + H 2 ⇄ C O + H 2 O
1
2 N 2 + H 2 O ⇄ N O + H 2
2 H 2 O ⇄ 2 H 2 + O 2
H 2 O ⇄ O + H 2
N 2 ⇄ 2 N
H 2 ⇄ 2 H
H 2 O ⇄ 1 2 H 2 + O H
(1.111)
The r equations (1.106), together with the l ′ equations which express the conservation
of components in the reactions, determine the equilibrium composition of
the mixture, once its temperature is known. Thus in the preceding example system
(1.111) must be completed with the four equations for the conservation of the number
of atoms of carbon, oxygen, hydrogen and nitrogen. It is not always necessary to consider
all possible reactions since depending on the state of the mixture the fractions of
some of the species may be neglected and the computation simplified.
For the case of adiabatic equilibrium the temperature of the products is unknown.
Hence, trial and error methods become necessary. In applying then, first a
temperature is assumed and the equilibrium composition is determined for it. Once
this is known the corresponding temperature is obtainable through equation (1.10),
h = h 0 , and if this temperature differs from the one previously assumed, the computation
should be reviewed. Gayden and Wolfhard [14] recommend the application of
Damköhler and Edse’s method mentioned in Ref. [15]. The fundamentals and some
of the applications of this method are described in the book by Gayden and Wolfhard.