4. You are responsible for approximating the current-voltage characteristics for an individual SOFC fuel cell stack. As a first approximation, you assume that the cathode side of the fuel cell dominates both the kinetic losses and the transport losses. Also assume that the open-circult potential of the cell is 1'V. The fuel cell operates at 700C (973 Kelvin) and the cathode input is air at 1 atm pressure. a. Write the cathode half reaction for this fuel cell (as a 4-electron process). b. Your first step is to determine the kinetics at the cathode. You find that the catalyst exchange current density is 0.01 mAjcm? and that the symmetry factor or transfer coefficient is 0.5. Use the Butler-Volmer equation to plot the kinetic data over the overpotential range of 0 to -0.4 V. c. Your next step is to determine the transport at the cathode. The diffusion coefficient of Oz in Nz is 0.22 cm?/s at room temperature, and increases with absolute temperature (Kelvin) to the 1.5 power: To af2 Do, in vy. T = Dozinn,, 7 * (=) 1 What is the diffusion coefficient of O2 in Nz at 700 C? If the porosity of the gas diffusion layer is 35%, the tortuosity is 16, the thickness of the gas diffusion layer is 400 micrometers, and ambient heated air is used as the feed, what is the maximum limiting current density? d. As an approximation, assume that the limiting current density is the same at all voltages. Use the KouteckyLevich equation (lecture 2D) to make a current density- voltage plot for the fuel cell. You can define both kinetic and transport currents as positive values. Plot the cell operating voltage on y axis and operating current density on the x axis. e. Plot the power density (mW/cm*) of the fuel cell as a function of voltage. What is the maximum power density and the operating voltage at this maximum power? Briefly explain how accounting for ohmic losses would affect the max power. How would the voltage at the new maximum power be affected (increase, decrease, or stay the same)? f. List 3 ways that the limiting current density of the fuel cell stack can be increased. g. Describe 2 ways that you can refine your method and assumptions to make it more realistic