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EECS – Prof. A. Casalegno – 12th June 2020 1 Basic Part (4.5 points per question, minimum score 12) 1. Write the Nernstian equilibrium potentials for both electrodes of a PEM electrolyser as a function of chemical activities 2. Define the energy efficiency for a battery following a complex operation profile, indicating ΔSoC variation 3. Write Faraday’s law applied to reactants in a Vanadium Flow Battery Exercise A Li-ion battery with nominal capacity of 50 Ah operates at ambient pressure and temperature , supplying 3.8 V during discharge at SoC=80% and C-rate=2. Assuming that: 1. Tafel kinetics is valid for both electrodes 2. ion and mass transport effects in electrodes are negligible 3. activities of reactants in discharge are close to the value of SoC 4. electrolyte resistance is equal to 1.8 mΩ 5. transfer coefficients of both electrodes during discharge are equal to 0.5 During discharge at C-rate=3, the voltage reaches the value of 3.6 V, estimate the achieved SoC. Intermediate Part (3 points for each theory question and 3.5 for the exercise) 1. Is the overpotential negative when H2 evolution reaction occurs? Demonstrate analyzing 𝐺̃ 2. Show how voltage limit affects the charging time at high C-rate in batteries Exercise 1 A PEM fuel cell operates at 90°C with pure H2 and air at 0.25 MPa pressure and supplies at 0.65 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 H 2 electrode [𝐸− + 𝜂−=0] 2. ion and mass transport effects in catalyst layers are negligible 3. the average O 2 molar fraction in the cathode channel is equal to 0.1 4. diffusion layer diffusivity Dref is equal to 0.05 cm2/s (at Pref=1 atm) and its thickness is 200 μm [assume D=Dref Pref/P ]. Assuming a fuel utilization of…