Environmental Engineering Reference
In-Depth Information
Table 3.1 Free energy,
enthalpy (higher heating
value), and entropy for the
reaction (
3.13
) at different
temperatures in the range
298-373 K [
4
]
T (K)
DG (kJ/mol)
DH
HHV
(kJ/mol)
DS (kJ/mol/K)
298
-237.3
-286.0
-0.163
333
-231.6
-284.8
-0.160
353
-228.4
-284.2
-0.158
373
-225.2
-283.5
-0.156
where DS is the difference between entropies of products and reactants in reaction
(
3.13
), and the product TDS represents the fraction of inlet chemical energy
converted into thermal energy instead of electricity.
If the same reaction (
3.13
) is realized in an internal combustion engine, i.e., as
combustion reaction, the entropy change remains unaltered (because it depends
only on the same overall chemical reaction involved in both processes), but not
100% of DG can be converted in useful work, but only a fraction of it, according to
Carnot theorem [
3
].
The substitution of (
3.14
) into (
3.10
) gives the dependence of the theoretical
potential on temperature (potential value decreases when cell temperature
increases); however, the values of thermodynamic quantities involved in Eq.
3.14
do not change in significant way up to 100C (as shown in Table
3.1
), which is the
temperature range typical of polymeric electrolyte fuel cells, suitable for auto-
motive applications (as discussed later). Then the effect of temperature on the
theoretical potential can be neglected for these types of cells, while its effect on
practical potentials of operating fuel cells is positive and not completely negli-
gible, and it is examined in
Sect. 3.3.2
.
For a fuel cell based on reaction (
3.13
) a basic thermodynamic analysis can also
evidence the positive effect of reactant pressures on cell potential, which is
expressed by the Nernst equation written for gaseous reactants and products [
5
]:
nF
ln
p
H
2
p
0
:
5
E
¼
E
þ
RT
O
2
p
H
2
O
ð
3
:
15
Þ
where p
H
2
O
¼
1 if liquid water is produced by the fuel cell.
Equation
3.15
shows that the cell potential E increases at higher reactant
pressures, and of course it is lower when a diluted oxidant is used, i.e., air instead
of pure oxygen. The practical effects of reactant pressures in real fuel cells will be
discussed in
Sect. 3.2
.
The above recalls of basic thermodynamics are also useful to define the concept
of theoretical fuel cell efficiency. If DG represents the useful electrical work
obtainable at the outlet of a fuel cell, and DH the inlet chemical energy, the
theoretical efficiency g
th
can be calculated by the following equation:
g
th
¼
DG
DH
ð
3
:
16
Þ
which becomes for the cell based on reaction (
3.13
), considering the higher heating
value for hydrogen and DG at 25C:
