Page 85 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

62 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

cumulative volume of the reactants. But the cumulative volume of the reactants
and of the products of the oxidation reaction of methane is the same. This is also
apparent by the values of the activity K (In( 1) = 0). Thus there is theoretically no
change of the entropy in the last case and the real change of the measured values
at the standard state 0 is very limited as indicated in Table 3.1. This is the reason
for the very small dependence on temperature of the free enthalpy or the
reversible cell voltage of the oxidation reaction of methane, the idealised
pressure dependence of the entropy yields no change in the cell voltage caused by
the system pressure. The reversible cell voltage of the hydrogen and the carbon
monoxide oxidation decreases with increasing system temperature and
increases with increasing system pressure.

3.3. Voltage losses by Ohmic Resistance and by Mixing Effects by
Fuel Utilisation
The thermodynamic relevance of the voltage can be understood by
considering Eqs. (13) and (16). The voltage is a measure of the exergetic quality
similar to the work of a thermodynamic process. The exergy is defined as the
potential of the reversible work of a system related to the ambient state 0 [l].
Thus it is clear that the voltage loss AV due to the electric resistance R is
connected with an additional irreversible production of entropy. We get for
the voltage loss

AV=I*R (30)
and for the power loss

Pioss = AV + I = I2 . R = Tsopc . Uf . ~FI Asirr. (31)
*
Equation (3 1) shows that the irreversible entropy production of an ohmic loss
Ploss in a SOFC is smaller than that in another fuel cell operating at a lower
temperature and a generalised form of Eq. (13) yields the irreversible entropy
production

Equation (1 3) was generalised here as

I = -ne' . Uf . hFI . E. (33)

It has already been mentioned that the mixing effects during fuel utilisation
within a SOFC do not allow a reversible SOFC operation. These influences and the
voltage reduction can be easily calculated by considering the fuel utilisation
connected with a change of the partial pressures of the components within the
system [2].