Describing a fuel cell’s performance and efficiency

1 Describing a fuel cell s performance and efficiencyBasic energy conversion of a fuel cell was described as:Chemical energy of fuel = Electrical energy + Heat energyHydrogenFuel CellHydrogenEnergy = ?Electricity Energy = V I tHeat (byproduct)OxygenEnergy = ?Water (byproduct)The input energy is that produced during reactions at the this section we will describe the above energy balance in more detail usinggygthe first and second laws of thermodynamics . performance (cont.)The performance of a fuel cell is governed by its Polarization performanceThis type of performance curve showsthe DC voltage delivered at the cellterminals as a function of the currentpdensity (current per unit area of membrane)being drawn by the external curve and the losses associatedThis curve and the losses associated with its shape will be discussed later.(ref. 1)One measure of the energy conversion efficiencyof a fuel cell is the ratioof the actual voltage at a given current density to the maximum voltageobtained under no load (open circuit) Analysis: 1stLawControl VolumeEElectrolyteFuelOxidant-E+E1stLaw for a control volume: E = Q W where E = KE + PE + U + (PV) = HFor a fuel cell, the work is obtained from the transport of electrons acrossttildifftbhilh t i f=> H = Q - Wa potential difference, not by mechanical means, such as turning ofturbine the work termElectrical work is, in general, described by the relation: W = EI twhere E is the cell voltage and I is the currentwhere E is the cell voltage and I is the currentIn a fuel cell reaction, electrons are transferred from the anode to the cathode,generating a current.

2 The amount of electricity (I t) transferred when thereaction occurs is given by NF, where N = number of electrons transferredF = Faraday s constant = 96,493 coloumbsSo the electrical work can be calculated as: W = NFEThe First Law then becomes: H = Q - NFET hermodynamic Analysis: 2ndLawWill consider the fuel cell to be ideal for now, meaning that it is reversible andthus behaves as a perfect electrochemical apparatus (Gibbs): If no changes take place in the cell except during the passage ofcurrent, and all changes which accompany the current can be reversed byreversing the current, the cell may be called a perfect electrochemicalreversing the current, the cell may be called a perfect electrochemicalapparatus. Recall that the heat transferred during a reversible process was expressed as:Q = T SCombining the First and Second Law analysis, we get: H = T S - NFEGibb s Free Energy (chemical potential)From our previous result for a cell operating reversibly:dH = TdS FEdNUnder these conditions:- the losses are minimalthe useful work obtained is maximized-the useful work obtained is maximizedThis maximum work is represented by the Gibbs free energy: dG = -FEdNSo the thermodynamic expression for the maximum useful work obtained from a fuel cell becomes:dGdHTdSdG = dH -TdSPhysical Interpretation of dG = dH - TdSdH represents the total energy of the represents the total energy of the represents the unavailable energy (that which cannot beconverted to useful work).

3 ThfGt th f thTherefore G represents the free energy or the energy available to do useful on Gibbs Free EnergyThe electrons released to generate the electrical work are, of course,inherently related to the chemical reaction taking place. So G can alsoygpbe associated with the chemical energy released during the reactionoccurring in the fuel a free energy of formation Gor Gois computed for theseTypically, a free energy of formation, Gfor Gois computed for thesereactions, where the free energy is referenced with respect to standardtemperature and pressure (STP) a given reaction, Go= Goproducts GoreactantsSee example problem for calculation of GoElectrochemistry: fuel Cell ReactionsHydrogen fuel cell:Oidti hlfti2H 4H++4 Oxidation half reaction2H2 4H++ 4e-Reduction half reactionO2+ 4H++ 4e- 2H2 OEnergy formation (kJ/mol)- Ho- Go_____Cell reaction2H2+ O2 2H2O286 237 Methanol fuel cell:Cell reaction:CH4+ 2O2 CO2+ 2H2O890818 Maximum Voltage Produced by a Single CellThe reversible open circuit voltage ( the maximum voltage that couldbe generated) can be calculated based on Goas.

4 Be generated) can be calculated based on Gas:GEo =NFEFor example, in the previous reaction where Gowas 237 kJ/mol, theopen circuit voltage would be:E = 237,000(2 mol H2)/(4 electrons)(96,493) = voltsFuel Cell Vs. Carnot Cycle EfficiencyThe efficiency limit of a Carnot heat engine is defined as:HLcarnotTT =1 So the higher the hot temperature source, the higher the , for example, one wanted to calculate the maximum efficiency of asteam turbine operating at 400 C with the water exhausted through acondenser at 50 C it would be:condenser at 50C, it would =car Under these conditions the t rbine co ld be no more than 52% efficientUnder these conditions, the turbine could be no more than 52% cells Vs. Carnot Engines (cont.) fuel cells , on the other hand: Operate isothermally no temperature cycling. Operate with less energy lost in maintaining the temperature of the h hot source.

5 Are inherently less cells are not limited by the Carnot efficiency Cell EfficiencySince fuel cells use materials that are typically burnt to release theirenergy, the fuel cell efficiency is described as the ratio of the electricalgy,yenergy produced to the heat that is produced by burning the fuel (itsenthalpy of formation or hf).From the basic definition of efficiency : =W/QFrom the basic definition of efficiency : = W / Qinwhere W is given by G (or NFE)Qinis the enthalpy of formation of the reaction takingplace. Since two values can often be computed depending on the state of the reactant, the larger ofthe two values ( higher heating value ) is used (HHV)the two values ( higher heating value ) is used (HHV).NFEG= = HHVHHV Maximum fuel Cell EfficiencyThe maximum efficiency occurs under open circuit conditions (reversible)when the highest cell voltage is obtainedwhen the highest cell voltage is = HHVHHV==max For the hydrogen fuel cell reactions shown previously where Gowas 237 kJ/mol and Howas 286 kJ/mol, the maximum efficiencyof the fuel cell would be 83%.

6 How does a Carnot engine match up?A Carnot engine would have to have a high temperature of 1753 K, with a corresponding low temperature ofof 1753 K, with a corresponding low temperature of 298 K, to achieve an efficiency of 83%!However, the work done by a Carnot engine increaseswith increasing reverse is true for the G based fuel cell work (andhence efficiency ) because G decreases with Cell Vs. Carnot EfficienciesAs can be seen, there exists a temperature above which the fuel cellefficiency is lowerthan the Carnot efficiency . This temperature isapproximately 950 K for a Associated With fuel Cell OperationIliflllhihiIn reality fuel cells achieve theirhighest output voltage at opencircuit (no load) conditions andthe voltage drops off with increasingthe voltage drops off with increasingcurrent draw. This is known aspolarization.(ref. 2)()The polarization curve shows the electrochemical efficiency of the fuel cellat any operating of Losses in an Actual fuel Cell3 Activation Losses: These losses are caused by the slowness of the reactiontaking place on the surface of the electrodes.

7 A proportionof the voltage generated is lost in driving the chemicalreaction that transfers the Losses:The voltage drop due to the resistance to the flow of electronsOhmic Losses:The voltage drop due to the resistance to the flow of electronsthrough the material of the electrodes. This loss varieslinearly with current Losses:Losses that result from the change in concentration ofthe reactants at the surface of the electrodes as thefuel is Crossover Losses:Losses that result from the waste of fuel passingthrough the electrolyte and electron conduction through the electrolyte. This loss is typically small,but can be more important in low temperature cellsbut can be more important in low temperature , S. & Zalbowitz,M. fuel cells - Green Power , Los Alamos National Laboratory, Cell , J. & Dicks, A. 2000 fuel Cell Systems Explained, John Wiley & Sons.