Page 160 - Entrophy Analysis in Thermal Engineering Systems

Entropy and chemical equilibrium 155

k

X
i
ð
i
S ¼ n j s j T, pÞ (10.5)
j¼1
where h is the specific molar enthalpy, and s denotes the specific molar
entropy.
If the system undergoes a chemical reaction, its composition at the final
state will be different than the initial composition. Hence,
k
X
f f f f
f
n ¼ n + n + … + n ¼ n j (10.6)
2
1
k
j¼1
10.4.1 Exothermic reaction
In this case, the reaction leads to a release of thermal energy. If the process
takes place adiabatically, the temperature of the system will increase. Sup-
pose that the heat Q is transferred from the system to the surrounding that
is at temperature T s . The amount of Q sufficient to reduce the temperature
of the system to the initial temperature is obtained by applying the first law.
Hence,

k k
X
X
n j h j TðÞ ¼ Q + n j h j TðÞ f (10.7)
i
j¼1 j¼1
The total entropy generation is determined as
k k
X Q
X
f i
ð
Φ ¼ n j s j T, pÞ n j s j T, pÞ + (10.8)
ð
j¼1 j¼1 T s
The first two bracketed terms on the right-hand side of Eq. (10.8) account
for the change in the entropy of the system, whereas the last term is the net
increase in the entropy of the surrounding. A combination of Eqs. (10.7) and
(10.8) yields
( )
1 X X
k
k
f f i i
ð
Φ ¼ n h j TðÞ T s s j T, pÞ n h j TðÞ T s s j T, pÞ
ð
j
j
j¼1 j¼1
T s
(10.9)
Introducing a new function g m ¼h(T) T s s(T,p), Eq. (10.9) may be repre-
sented as