This paper compares the theoretical maximum efficiency of a fuel cell to the efficiency of a Carnot cycle driven by the same net reaction. The comparison dispels the misconception that an ideal fuel cell is potentially more efficient than an ideal heat engine. The paper presents expressions for the thermal efficiencies of an ideal fuel cell and a Carnot heat engine. To show that the maximum efficiency is the same, the analysis of the Carnot cycle is modified to consider an engine driven by a combustion reaction. The derivation invokes the approximations that the enthalpy and entropy changes for the reaction are independent of temperature, these approximations are justified by the hydrogen-oxidation reaction. The analysis extends that presented by Appleby and Foulkes (Fuel Cell Handbook, Van Nostrand Reinhold, New York 1989) by showing that with proper accounting for heat addition, the maximum efficiency of a fuel cell is 100%-not larger-for reactions with a positive entropy change. In addition, this paper explains the difference between the combustion temperature, at which an idealized Carnot cycle would operate, and the adiabatic flame temperature. (C) 2002 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.