Fundamental thermodynamics of fuel cell, engine, and combined heat and power system efficiencies

Abstract

At the 2001 Grove Symposium on Fuel Cells attended by representatives of the world-wide fuel cell industry, fuel cells and fuel cells integrated with gas turbines were discussed. Combined heat and power (CHP) aspects were also discussed. Without exception, ef ciency gures were irrationally based on the measured, Carnot-limited, lower calori c value (CV) of the fuel in energy units J. The rational basis, on the other hand, is the fuel chemical exergy (work units, Ws) calculated via an equilibrium diagram. In Joules experiment 1 Ws ¾ 1 J, where the irreversible ¾ must not become anˆsign. A misnomer like potential energy (exergy) ts on the left of the diagram, CV on the right. Moreover credence was also given, at the symposium, to the popular misconception that a CHP system has an ef ciency of the order of 80 per cent.An essential precursor to reading the paper is to grasp the theory of chemical equilibrium and equilibrium constants [3] as an aid to exploring the equilibrium diagram mentioned above. NOTATIONH enthalpy (kJ) h speci c enthalpy (kJ/mol) B thermomechanical exergy (kWs/mol) b speci c thermomechanical exergy (kWs/mol) C p speci c heat at constant pressure, …qu/qt †p C v speci c heat at constant volume, …qu/qt †v G Gibb's potential (kWs/mol) g speci c Gibb's potential (kWs/mol) m mass ow (kg/s) P pressure …bar; 1 Pascalˆ10 barŝ 10 £ atmospheric pressure † P 0 standard atmospheric pressure (1 bar) PP 0 partial pressure of component of standard atmosphere (bar) P i initial or inlet pressure (bar) P f nal or outlet pressure (bar) S speci c entropy (kJ/mol ¢ K) T temperature (¯C or K) T 0 25¯C or 298:15 K, temperature of standard atmosphere u speci c internal energy (kJ/mol) speci c volume …m 3 /mol † V n Nernst potential difference, at equilibrium as de ned in this paper (V) z fractional amount of fuel in a gas mixture z CO fraction of carbon monoxide g speci c heat ratio, C p /C v g CO fraction of carbon monoxide in an equilibrium mixture of gases DC r circulator isothermal power …kW;ˆRT log n …P i /P f † † DC t Carnot cycle work, pro rata to DS DG fuel cell power (kW;ˆRT log n …P i /P f †: suf x t, means at temperature; suf x tp means at temperature and pressure; suf x 0 means at standard pressure and temperature) DS reversible entropy change associated with isothermal equilibrium chemical reaction, or physico-chemical process (kJ/mol ¢ K) Dx ch change of chemical exergyˆfuel chemical exergyˆwork of standard conditionsˆisothermal oxidation in an equilibrium fuel cellˆelectrical work DG 0 ‡ circulator work, DC r (kWs/mol) Dx tm change of thermo-mechanical exergyˆwork of a reversible expansion or compression process, or of a reversible heat cycle (kWs/mol) Z c Carnot ef ciency …T ¡ T 0 †=T n electrons transferred per molecule of fuel x speci c energy (kWs/mol) Abbreviations AFC alkaline fuel cell DMFC direct methanol fuel cellThe MS was

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