Page 163 - Entrophy Analysis in Thermal Engineering Systems

158 Entropy Analysis in Thermal Engineering Systems

for an extremum that is erroneously believed to represent the state of chemical
equilibrium.

10.5 Reaction advancement

For a reactive system that is at constant temperature T and pressure p,a
change in the state of the system could occur due to a change in its compo-
sition. The entropy generation Φ and function G m may then be described in
terms of the extent of reaction ξ (also called reaction advancement) [19].

Once a chemical equilibrium is established, we have ξ(t eq )¼ξ eq , where ξ eq
denotes the extent of reaction at equilibrium. For t>t eq , both Φ(ξ) and
ΔG m (ξ) will remain unaltered. This, however, should not be confused or
interpreted as Φ(ξ) and G m (ξ) attaint their extremum at the state of
f
equilibrium.
In a chemically reactive system comprising k different species with a
known initial composition, the number of moles of all species participating
in the chemical reaction will change with the reaction advancement and may
be determined using Eq. (10.15).

n ¼ n + a j ξ (10.15)
f
i
j
j
where a j is the stochiometric coefficient of species j that takes part in the
reaction.
Substituting Eq. (10.15) into Eq. (10.6), one obtains
k k
X X
f n + a j ξ
n ¼ n ¼ (10.16)
f
i
j j
j¼1 j¼1
Using Eq. (10.3), one may simplify Eq. (10.16) to derive a relation for the
total moles of the system at the final state.
n ¼ n + aξ (10.17)
f
i
where
k
X
a ¼ a j (10.18)
j¼1
Because the initial state of the system is fixed, a change in function G m solely
depends on its value at the final state, which can be described in terms of the
reaction advancement as