Electric vehicle

Fuel Cells
99
Efficiency limit / Operating temperature / Celsius
Carnot limit, C exhaust 40 50 60 70 Fuel cell, liquid product
Fuel cell, steam product 400 600 800 1000 0
90
Figure 5.9
Maximum hydrogen fuel cell efficiency at standard pressure, with reference to the higher heating value. The Carnot limit is shown for comparison, with a C exhaust temperature from Figure 5.3. We also know that the electrical energy is given by the fundamental energy equation
Energy
= charge × voltage
The Faraday constant F gives the charge on 1 mol of electrons. So, when 1 mol of hydrogen fuel is used in a fuel cell, if it were 100% efficient, as defined by Equation (then we would be able to say that
Energy
= 2F × V
100%
= H
and thus
V
100%
=
H
2
F
Using standard values for the Faraday constant (96 485 C, and the two values for
H
given above, we can easily calculate that the ‘100% efficient’ voltage fora single cell is V if using the HHV or 1.25 V if using the LHV.
Now of course a fuel cell never is, and we have shown in the last section never can be, 100% efficient. The actual fuel cell voltage will be a lower value, which we can call
V
c
. Since voltage and electrical energy are directly proportional, it is clear that
Fuel cell efficiency
=
V
c
V
100%
=
V
c
1
.48
(5.6)
Clearly it is very easy to measure the voltage of a fuel cell. In the case of a stack of many cells, remember that the voltage of concern is the average voltage of one cell, so the system voltage should be divided by the number of cells. The efficiency can thus be found remarkably easily.

100
Electric Vehicle Technology Explained, Second Edition
It is worth noting in passing that the maximum voltage of a fuel cell occurs when of the Gibbs free energy is converted into electrical energy. Thus we have a ‘sister’
equation to Equation (5.4) giving the maximum possible fuel cell voltage:
V
max
=
G
2
F
(5.7)
This is also a very important fuel cell equation, and was used to find the figures shown in the fourth column of Table 5.3.
5.3.3 Practical Fuel Cell Voltages
Equation (5.7) above gives the maximum possible voltage obtainable from a single fuel cell. In practice the actual cell voltage is less than this. Now of course this applies to ordinary batteries too as current is drawn out of any electric cell the voltage falls, due to internal resistances. However, with a fuel cell this effect is more marked than with almost all types of conventional cell. Figure 5.10 shows atypical voltage/current density curve fora good PEMFC. It can be seen that the voltage is always less, and often much less, than the 1.18 V that would be obtained if all of the Gibbs energy were converted into electrical energy.
There are three main reasons for this loss of voltage. The energy required to drive the reactions at the electrodes, usually called the activation energy, causes a voltage drop. This is especially a problem at the air cathode, and shows itself as a fairly constant voltage drop. This explains the initial fall in voltage even at quite low currents.
Cell voltage/
Volts
Current density/mA cm
−2
Voltage begins to fall faster at higher currents 0.2 0.4 0.6 0.8 1.0 Even the open circuit voltage is less than the theoretical no loss value
Voltage falls more slowly,
and graph is fairly linear 400 600 800 1000 Rapid initial fall in voltage "No loss" voltage of 1.2 Volts

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