Page 82 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Therrnodynnrnics 59

In Eq. (13) we introduced the elementary charge e

e = (1,60217733 & 0,00000049). lO-I9C. (14)
and the Faraday constant F

F = e. NA = (96485,309 & O,029)C/moI (15)

as the product of the elementary charge and the Avogadro constant NA. Equations
(1 3) and (1 5) show that the electric current Iis a measure of the fuel spent. Thus
a current measurement is a very simple method to measure the fuel spent. The
matching between thermodynamic and electrical quantities can be done by the
power but not by the work. The reversible power can be written as a product of
the reversible voltage VFcrP,, and the current I as well as a product of the molar
flow of the fuel hH2 and the free enthalpy A'G of the oxidation reaction

PFCrel, = VFCrev * I = hH2 * M'tFCrev = nH2 * A'G. (16)

The reversible voltage Vpcrev results from Eqs. (1 3) and (1 6)

-&2. ArG
VFCrev =
k1.F .
Equation (12) shows the ratio between the molar flow of the electrons and the
spent hydrogen as 2. This can be generalised and net is the number of the
electrons that are released during the ionisation process of one utilised fuel
molecule, related on the molar flows we get with Eq. (1 1)

and finally for the reversible voltage VFcrev of the oxidation of any fuel gas
-A'G
VFCrev = -
ne2 . F .
It has already been mentioned that the mixing effects during fuel utilisation
within a SOFC do not allow a reversible SOFC operation. These effects and the
voltage reduction can be calculated by considering the fuel utilisation connected
with a change of the partial pressures of the components within the system [2].
We can write Eq. (4) more precisely as

ArG(T,p) ArH(T,p) - T-A'S(T,p). (20)
Using the common assumption of the ideal gas we get

ArG(T. p) = ArH(T) - 7'. ArS(T, p) (21)

and we can write, with dS = (dH - v.dp)/T , for the entropy S, of any component j