1. NTU ME H.K. Ma Department of Mechanical Engineering National Taiwan University, Taipei, Taiwan November, 2009 台灣大學機械工程系能源環境實驗室

2.  Maximum electric work (W el ) at constant temp. and pressure is given by Gibbs free energy: n is no. of electrons F is Farady’s constant E is ideal potential of the cell

3.  Besides, Gibbs’ free energy can be written as: ∆H is enthaply change ∆S is entropy change T∆S represents the unavailable energy resulting from the entropy change

4. At constant pressure, the specific entropy at temperature T is given by It than follows that,

5.  The Gibbs’ free energy can be expressed by the equation For the generation reaction, Substituting the equation into then, This is general form of the Nernest Equation

6. NTU ME

10.  The ideal efficiency of a fuel cell, operating reversibly, is then, At standard condition (298K, 1atm), thermal energy (∆H ) in the hydrogen/oxygen reaction is 285.8KJ/mole, and the free energy for useful work is 237KJ/mole, therefore,

11.  The thermal efficiency of a hydrogen/oxygen can be written in term of the actual cell voltage

13.  Activation losses are caused by sluggish electrode kinetics. It is possible to approximate the voltage drop by a semi-empirical equation, called the Tafel equation. α is the electron transfer coefficient of the reaction at the electron being addressed i 0 is the exchange current density

15.  Ohmic losses occur because of resistance to the flow in the electrolyte and resistance to the flow electrons through the electrode.  Because the electrolyte and fuel cell electrodes obey Ohm’s law, the ohmic losses can be expressed by the equation,

16.  The total resistance, R, which includes electronic, ionic, and contact resistance

17.  The combined effect of the losses for a given cell and given operating conditions can be expressed as polarizations. The total polarization at the electrode is the sum of anode and cathode.

18.  The cell voltage includes the contribution of the anode and cathode potentials and ohmic polarization When and are substituted in then,

19. 19 AFCPEMFCDMFCPAFCMCFCSOFC IonOH - H+H+ H+H+ H+H+ CO -2 3 O -2 Temperature 50~200 ℃ 30~120 ℃ 20~90 ℃ ~220 ℃ ~650 ℃ 500~1000 ℃ FuelH2H2 H2H2 CH 3 OHH2H2 NG, H 2 … OxidesO2O2 O2O2 O2O2 O2O2 O2O2 O2O2 Output (W)1KW~10K1~100K1~10010K~1M1M~10M1K~10M 2015/12/25

20. 20 Water productT (K)E (V) Liquid2981.23 Liquid3531.18 Gas3731.17 Gas4731.14 Gas6731.09 Gas8731.04 Gas12730.92 2015/12/25

21. 21 Volume flow rate H2H2 6.964 cc/min. O2O2 3.483 cc/min. Air16.586 cc/min. 2015/12/25

22. 22 Water productT (K)Efficiency limit (%) Liquid29883 Liquid35380 Gas37379 Gas127362 Efficiency of fuel cell = electric energy produced per mole of fuel / enthalpy of formation Limit of fuel cell efficiency = Carnot Limit= Thermodynamic efficiency 2015/12/25

23. Reactant Product Reactant Product Energy Barrier Reaction Rate 2015/12/2523

24. Activation losses: Ohmic losses: Concentration losses: 2015/12/2524