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For other electrochemical reactions, different ideal efficiencies apply. Curiously, for direct electrochemical oxidation of carbon ∆G is larger than ∆H, and consequently the ideal efficiency is slightly greater than 100% when using this definition of ideal efficiency. For convenience, the efficiency of an actual fuel cell is often expressed in terms of the ratio of the operating cell voltage to the ideal cell voltage. As will be described in greater detail in the sections following, the actual cell voltage is less than the ideal cell voltage because of losses associated with cell polarization and ohmic losses. The thermal efficiency of a hydrogen/oxygen fuel cell can then be written in terms of the actual cell voltage: η = Useful Energy = Useful Power = Voltsactual x Current = (0.83)(Vactual ) ∆H (∆G/0.83) Voltsideal xCurrent/0.83 Eideal (2-18) As mentioned previously, the ideal voltage of a cell operating reversibly on pure hydrogen and oxygen at 1 atm pressure and 25oC is 1.229 V. Thus, the thermal efficiency of an actual fuel cell operating at a voltage of Vcell, based on the higher heating value of hydrogen, is given by η = 0.83 x Vcell / Eideal = 0.83 x Vcell /1.229 = 0.675 x Vcell (2-19) The foregoing has assumed that the fuel is completely converted in the fuel cell, as is common in most types of heat engines. This efficiency is also referred to as the voltage efficiency. However, in fuel cells, the fuel is typically not completely converted. To arrive at the net cell efficiency, the voltage efficiency must be multiplied by the fuel utilization. An excellent review of the impact of this phenomenon is provided by Winkler (4). Because the reactant activities in gas-fueled fuel cells drop as the utilization rises, and because the cell voltage cannot be higher than the lowest local potential in the cell, utilization considerations further limit the efficiency. Figure 2-2 shows the impact of fuel utilization on the Nernst voltage, voltage efficiency, and maximum overall cell efficiency for operating conditions typical for an SOFC (800 °C, 50% initial hydrogen concentration). Figure 2-2 shows that to achieve 90% fuel utilization, the Nernst voltage drops by over 200 mV. As a consequence, the maximum cell efficiency (on a higher heating value basis) is not 62%, as predicted based on the ideal potential, but 54%. Of course, practical cell operating effects and cell non-idealities further reduce this efficiency in real life. These effects are somewhat less profound at lower operating temperatures, such as those found in lower temperature SOFC, MCFC, or in low-temperature fuel cells. 2-9PDF Image | Fuel Cell Handbook (Seventh Edition)
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