FIGURE C-2 Ragone plot comparing the specific energy vs. specific power of various batteries and of an internal combustion engine.

SOURCE: Cairns, 2004.

produced relative to the change in the amount of stored chemical energy.

Fuel Cells

For a fuel cell, these parameters are described by the Gibbs free energy, G, and the enthalpy, H, of the system and fuel. The maximum thermal efficiency for such an electrochemical system is the ratio of the Gibbs free energy for the reaction to the enthalpy change for the reaction:

ηth(max) = ∆G/∆H

The standard free energy change of a hydrogen-fueled system is typically calculated from the reaction of gaseous hydrogen to form liquid water:

H2 (g) + 12O2 → H2O (l)

At room temperature, this chemical energy of the system, ∆H, is 285.8 kJ/mole and the free energy for useful work, ∆G, is 237.1 kJ/mol, so the thermal efficiency of an ideal fuel cell operating reversibly on pure hydrogen and oxygen at standard conditions would be

ηth = ∆G/∆H = 237.1/285.8 = 0.83

The values needed to calculate enthalpy and free energy of fuel cells reactions can be easily obtained from sources such as the JANAF Thermochemical Tables (Chase, 1986).

The efficiency of a real operating fuel cell is calculated from the actual vs. ideal voltage of the cell. The ideal (reversible) voltage of an H2/O2 fuel cell under no load at room temperature and pressure is 1.229 V when the product is liquid water (with a higher heating value [HHV]) and 1.18 V when the product is gaseous water (with a lower heating value [LHV]). Thus, the thermal efficiency of a fuel cell operating at voltage Va at room temperature and utilizing all of the fuel, according to the last reaction above, is calculated from the equation

ηth = 0.83 × Va/1.229

Therefore, a fuel cell that produces liquid water operating at 0.8 V has an ideal thermal efficiency of 54 percent, while a fuel cell operating at 0.6 V has one of 40 percent. Of course, practical fuel cells do not usually consume all of the fuel supplied, and some leaves the system unreacted. This unreacted fuel needs to be taken into account in the effi-

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