Efficiency of Fuel Cells

Euel cells convert chemical energy directly into electricity, an inherently efficient process. Hence the thermodynamically attainable efficiencies are around 100%. The efficiency of a fuel cell is given by 

Here Tc is the temperature of the cooling reservoir, i.e. the surroundings, while Th is the temperature of the process, i.e. the temperature of combustion. The Carnot efficiency is applicable for conventional heat pump engines. Efficiencies of more than 100 % correspond to converting heat from the surroundings into electricity and is only of academic interest, as is the high efficiency listed in Tab. 8.10. 

In practice the situation is less favorable due to losses associated with overpotentials in the cell and the resistance of the membrane. Overpotential is an electrochemical term that, basically, can be seen as the usual potential energy barriers for the various steps of the reactions. Therefore, the practical efficiency of a fuel cell is around 40-60 %. For comparison, the Carnot efficiency of a modern turbine used to generate electricity is of order of 50 %. It is important to realize, though, that the efficiency of Carnot engines is in practice limited by thermodynamics, while that of fuel cells is largely set by material properties, which may be improved. 

---

If fuel cells could be used in transportation vehicles, it could have a major impact on worldwide consumption of petroleum. Major improvements that are needed for this to happen include increasing the efficiency of fuel cells, increasing their power density, reducing their manufacturing cost, and developing fuel cell designs capable of rapid start-up. 

The overall efficiency of fuel cells is higher than that of conventional heat engines. Running on pure hydrogen, a fuel cell has a theoretical efficiency up to 80%, and in some kinds of fuel cell practical efficiencies of over 70% have been reported. For most practical purposes modem fuel cells generally have efficiencies of over 40%. 

A fascinating point, especially to physical chemists, is the potential theoretical efficiency of fuel cells. Conventional combustion machines principally transfer energy from hot parts to cold parts of the machine and, thus, convert some of the energy to mechanical work. The theoretical efficiency is given by the so-called Carnot cycle and depends strongly on the temperature difference, see Fig. 13.3. In fuel cells, the maximum efficiency is given by the relation of the useable free reaction enthalpy G to the enthalpy H (AG = AH - T AS). For hydrogen-fuelled cells the reaction takes place as shown in Eq. (13.1a). With A//R = 241.8 kJ/mol and AGr = 228.5 under standard conditions (0 °C andp = 100 kPa) there is a theoretical efficiency of 95%. If the reaction results in condensed H20, the thermodynamic values are A//R = 285.8 kJ/ mol and AGR = 237.1 and the efficiency can then be calculated as 83%. 

Figure 13.3. Theoretical thermodynamic efficiency of fuel cells and Carnot machines as a function of temperature.

Countries that can supply hydrogen at a comparable cost to conventional fuels (maximally twice the price of gasoline without taxes, owing to the double efficiency of fuel cells compared with internal combustion engines). 

Several important factors motivate this research on fuel cell engines. One of these factors is the efficiency of fuel cells when compared to engines that burn gasoline, as discussed in the following section. 

As can be seen from Table 1.57, the efficiency of fuel cells is about double that of gas-burning internal combustion (IC) engines. Therefore, if fuel cells can be made at the same cost as IC engines, hydrogen fuel cell-based transportation is already cost competitive with gasoline-based transportation. Unfortunately, at this point in time, fuel cells are much more expensive, but that is likely to change as soon as mass production starts. 

The efficiency of fuel cells is largely limited by the kinetic barriers of the surface catalytic electrode reactions. In particular, the electroreduction of molecular oxygen at a PEMFC cathode severely limits high reaction rates and hence currents near the equilibrium cell voltage. 

Write down expressions in analogy to (3.12) for the efficiency of fuel cells in reverse operation, used to produce either hydrogen or both hydrogen and heat from electric power,... 

The outline shown in Fig. 5.79B indicates how this may be achieved. The figure assumes that reversible fuel cells are available in 2050, without the current problem of lower reversed operation efficiency than conventional elec-trolysers. The higher efficiency of fuel cells relative to current power plants implies that if waste heat should cover space and hot water heat requirements, these should be provided by more efficient means than the present ones. 

---