The Fuel-Cell Efficiency Ceiling, Recounted from Thermodynamics: ΔG/ΔH as a Function of Temperature for Hydrogen, Methanol, and Carbon Monoxide

The maximum electrical efficiency of a fuel cell is the ratio of the Gibbs energy to the enthalpy of its reaction, not a Carnot factor. Recomputed from NIST formation data and Shomate heat capacities integrated through Kirchhoff's laws: the hydrogen ceiling is 82.97% (liquid-water basis) and 94.52% (steam basis) at 298.15 K and falls with temperature, to 80.79% at 600 C and 73.51% at 900 C on the steam basis. Methanol's liquid-water ceiling is 96.68% and its steam-basis figure exceeds 100% because its reaction entropy is positive; carbon monoxide's ceiling is 90.89% at 298.15 K. Against a Carnot engine between the cell temperature and 298.15 K, the hydrogen advantage is 77.71 percentage points at 80 C, 14.93 points at 600 C, and -1.08 points at 900 C, with a crossover at 1150 K. Every computed number is produced by the accompanying Python script.