Page 83 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

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

where C, is the temperature dependent heat capacity of the component j.
The pressure dependence of Cpj can be neglected in this common assumption,
Eq. (21). Using Eq. (22), we can write for the reaction entropy A'S(T,p)
A'S@, p) = A'S(T) - R, . ln(K) (23)

with the equilibrium constant K(see, e.g., [l])

vi is the fuel-related quantity of the component j in the equation of the oxidation
reaction andpo is the standard pressure (1 bar):

po = lbar. (25)

Using Eqs. (21)-(24) weget
A'G(T,p) = ArG(T)+T.Rm.ln(K).

This use of the assumption of an ideal gas allows one to express the Nernst
potentialor theNernstvoltage VNbyusingEqs. (18), (19) and(26) as

-ArG(T) R, . T ln(K)
v, = - (2 7)
ne! . F ne! . F

The following reversible oxidation of hydrogen (Hl), of carbon monoxide CO
and of methane (CH4) can be analysed as examples by using Eq. (2 7):

1
H2 f-02 -+ H20.
2
1
co + -02 -+ c02.
2
CH4 + 202 4 2H20 + c02. (29)
The equations (7), (28), and (29) determine the reaction enthalpy, the
reaction entropy and thus the free enthalpy and the voltage of the reversible
oxidation as formulated in Eqs. (5) and (19) with the thermodynamic data of the
reactions at the standard conditions 0 (25"C, 1 bar) as collected in e.g. [1,4]. A
variation of the thermodynamic state of the environment of the reversible cell