Environmental Engineering Reference
In-Depth Information
100%
Voltage
50%
Power
0
Current
0
1
Power
Max. power
(a)
(b)
Figure 3.10
(a) Fuel cell voltage and power as a function of current and (b) efficiency as a function
of power.
the maximum work
f
,
w
η
fc
≡
(3.52)
f
The high efficiencies of fuel cells, compared to heat engines utilizing the direct combustion of
fuel with air, stems from the electrode processes where the electrostatic energy binding molecules
can be converted directly to electrostatic energy of the ions and electrons that move in the cell
circuit. In contrast, in an adiabatic combustion process the fuel energy is converted to random
kinetic and potential energy of product molecules, which cannot be fully recovered in subsequent
flow processes.
Figure 3.10(a) illustrates how the fuel cell voltage and power vary with the current when the
electrolyte provides the only resistance to current flow within the cell. As the current increases, the
cell voltage drops linearly from its maximum value given in equation (3.51). The power output,
which is the product of the current times the voltage, reaches a maximum when the voltage has
fallen to 50% of its maximum value. The fuel cell efficiency, given in equation (3.52), declines with
increasing power, as shown in Figure 3.10(b), to 50% at maximum cell power. When operating at
part load, fuel cells can have significantly higher efficiencies than do combustion engines.
To maintain the fuel cell temperature at a fixed value, heat must be removed. The magnitude of
the heat removed per unit mass of fuel,
|
q
fc
|
, is determined from the first law of thermodynamics
applied to this steady flow process to be
|
q
fc
|=
FHV
−
w
≥
FHV
−
f
(3.53)
where
FHV
is the fuel heating value and the inequality follows from the second law constraint. In
fuel cells used to generate electric utility power, the heat removed from the fuel cell may be used to
generate additional electricity in a Rankine cycle plant, provided that the fuel cell operating tem-
perature is sufficiently high. This combined cycle plant can achieve very high thermal efficiencies.
