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EECS – Prof. A. Casalegno – 5th February 2021 1 Basic Part (4.5 points per questions, minimum score 12) 1. Write the Nernst-Plank equation for mass transport in a solid electrolyte 2. Define the efficiency for a battery following a complex operation profile 3. Write Faraday’s law applied to reactants in a PEM electrolyser 4. Exercise A PEM electrolyser stack consumes at full load 500 A at 450 V with an efficiency equal to 67.5% (LHV=120 MJ/kg). Assuming that 2% of H2 is wasted and its performance follows the reported polarization curve, estimate the number of cell, cell area and efficiency at 20% current load. Intermediate Part (3 points per theory questions and 3.5 for the exercise) 1. Is the overpotential positive when H2 oxidation occurs? Demonstrate analyzing 𝐺" 2. Show how voltage limits could reduce the available capacity at high C-rate in batteries 3. Exercise A PEM fuel cell operates at 75°C with pure H2 and air at 2 atm pressure and supplies at 0.6 V a current density equal to 2 A/cm2 and related impedance is reported in the figure. Assuming that: 1. anode behaves as an ideal H2 electrode (𝐸!+𝜂!=0) 2. ion and mass transport effects in catalyst layers are negligible 3. the average O2 chemical activity in the cathode channel is equal to 0.25 4. diffusion layer diffusivity is equal to 0.03 cm2/s (at 2 atm) and its thickness is 200 μm 5. cost of the fuel cell stack is 80 €/kW if operated at 2 A/cm2. Design a 100 kW stack with a maximum current density of 1.6 A/cm2, assuming a cell area of 200 cm2 and a fuel utilization of 97%, providing: minimum efficiency, number of cells and cost per kW. 𝑅𝑒(𝑍) −𝐼𝑚(𝑍) 0.1 𝛺 𝑐𝑚2 −0.015 𝛺 𝑐𝑚2 0.135 𝛺 𝑐𝑚2 ∆𝑉 0 𝑗 1.5 V 1.8 V 0.4 A cm-2 2 A cm-2 EECS – Prof. A. Casalegno – 5th February 2021 2 Difficult Part (1.5 points) Exercise A…