292
5 – Applications
R
1 T H
S
th
r T
r T
Δ
Δ
= −
The oxidation reactions for the various fuels is
H 2(g) + 2
1
O 2(g) m H 2 O (g)
(1)
.
.
R
247 9
192 6
th1 = −
−
. %
R
77 7
th1 =
CH 4(g) + 2O 2(g) m CO 2(g) + 2H 2 O (g)
(2)
.
.
R
800 5
800 2
th2 = −
−
. %
R
99 9
th2 =
5. The power density P of the cell depends on the emf ΔU under current when
the cell carries a load and on the current density i,
P
U i
S
U I
Δ
Δ
=
=
#
#
where S is the active surface area of the electrodes.
When the cell delivers current, the emf diminishes because of the ohmic
drop across the electrolyte (R el I) and the overpotentials η a and η c at the
anode and cathode, respectively.
ΔU = ΔE − | η c | − η a − R el I
The electrolyte resistance R el is determined based on the ionic conductivity
of YSZ taken from figure 98 (1.3 # 10
−2
S cm
−1
at 1 000 K) and the cell
dimensions according to
R
1 S
el
,
σ
=
#
R
1.3 10
1
5
0.01
9.8 10
el
2
5
3
π
Ω
=
=
−
−
#
#
#
#
Consequently, ΔU = 1.132 − 0.2 − 0.02 − 9.8 # 10
−3 # 23.5
ΔU = 0.682 V
which gives a power density of
P
5
0.682 23.5
5
π
=
#
#
P 0.205 W cm
2
=
−