Page 162 - Entrophy Analysis in Thermal Engineering Systems

Entropy and chemical equilibrium 157

Gibbs’s theory is concerned with reversible processes with the surround-
ing temperature assumed to be the same as the system temperature. Setting
T s ¼T in our formulation yields G m ¼G, and Eq. (10.10) is accordingly
expressed in terms of the Gibbs function.

!
1 X X
k
k
f i ΔG
Φ G ¼ G G ¼ (10.13)
j j
j¼1 j¼1
T T
where Φ G is the entropy generation function that is evaluated for the special
condition of G m ¼G, and ΔG denotes the net difference in the Gibbs func-
tion between the initial and final states.
Because real processes are irreversible, we have Φ>0 so the right-hand
side of Eq. (10.10) is always positive. Thus, the change in function G m will
always be negative, i.e., ΔG m <0. Hence,

(10.14)
f i
G < G
m m
In the special case of T s ¼T, one finds G <G . Inequality (10.14) is obtained
f
i
by invoking the second law. It is valid for all thermodynamic processes in the
absence of work, including chemical reactions, which exchange heat with
the surroundings assumed to be at a constant temperature. It states that
for a system undergoing an actual process that is initially at an arbitrary
but known state, the function G m at the final state will always be less than
that in the initial state regardless of whether the transformation from the ini-
tial state to the final state is infinitesimal, the system is initially at equilibrium
or nonequilibrium, or the surrounding temperature, T s , is equal to the sys-
tem temperature. Any other conclusion drawn from inequality (10.14) relat-
ing the state of chemical equilibrium to the minimum of G m (or G in the
special case of T s ¼T) would simply be unjustified.
From the discussion thus far, one may deduce that an application of
Gibbs criterion, Eq. (10.1), may lead to inaccurate predictions of the com-
position of a reactive system because there exists no strong experimental nor
analytical foundation for such criterion. Neither the second law nor the
combined first and second laws suggest that the chemical equilibrium is des-
ignated by setting the differential of the Gibbs function or G m to zero. In a
thermodynamic equilibrium, there is no change in the quantity of any spe-
cies of the system, enthalpy, entropy, etc. The source of mistake is that
“the change in enthalpy or entropy is zero” is often interpreted as
“the differential of enthalpy or entropy is zero.” One is then led to look