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Voltage Efficiency of Fuel Cells and Stacks The electrical system efficiency calculations discussed above are applied globally to complete fuel cell systems that include many individual components, such as fuel processors, humidifiers, fuel cell stacks, power conditioners, and controls. Many experimenters and developers, however, also wish to assess the efficiency of the fuel cell stack separate from the efficiency of the system. For this reason it is convenient to use the concept of voltage efficiency, which is defined as the actual cell (or cell stack) operating voltage divided by the thermodynamic cell voltage. Voltage efficiency = Operating voltage (V ) Thermodynamic voltage (E) The thermodynamic cell voltage can be calculated using the Gibbs free energy and the Nernst equation. E = E°− RT ln [H2O] nF [H2 ][O2 ]1/ 2 Where: • E = the thermodynamic voltage under prevailing conditions • E° = the thermodynamic voltage under standard conditions • R = the gas constant (8.314 J deg K-1 mole-1) • T = temperature in degrees Kelvin (25°C = 298 K) • n = the number of electrons transferred (2 in this case) • F = Faraday constant (96,485 Coulomb mole-1) • [ ] = the thermodynamic activity of the reactants and products, which, for gases, can be approximated by their partial pressure in atmospheres. Gibbs free energy can be converted into a thermodynamic voltage using the formula in which free energy is in joules per mole, as shown below. Gibbs free energy (standard conditions) = nFE° Under standard conditions, the Gibbs free energy for the hydrogen-oxygen reaction is 237.2 kJ/mole for the production of liquid water at 25°C. Therefore, the thermodynamic voltage for a hydrogen-oxygen fuel cell operating at standard temperature and pressure is 1.229 volts. E°=237,200J =1.229V 2(96,485) The Nernst equation is useful for calculating the thermodynamic voltage at varying pressures and reactant concentrations, but it should be noted that the Gibbs free energy of the hydrogen/oxygen reaction changes with temperature. Therefore, to calculate the thermodynamic voltage of a cell at a temperature other than standard temperature requires looking up the Gibbs free energy for the reaction at that temperature in a thermodynamic table. For example, the thermodynamic voltage for a high-temperature fuel cell operating on hydrogen/oxygen at atmospheric pressure at 1,000 K is 0.998 volts. Experimenters and developers of higher-temperature fuel cells typically use the 4PDF Image | Hydrogen Production: Fundamentals
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