Copper electrowinning plates dissolved Cu²⁺ ions onto a stainless-steel cathode while a lead anode evolves oxygen. Two real laws drive every number on this panel:
Faraday: dm/dt = I · η · M / (z·F)
Ohm: V = E0 + J · d / σ(T)
Energy: kWh/kg = z·F·V / (3600·M·η)
I is the cell current (current density J × cathode area), η the current efficiency, M = 63.55 g/mol for copper, z = 2 electrons per Cu²⁺, F = 96 485 C/mol. The ohmic term uses electrolyte conductivity σ, which rises roughly 2%/°C with temperature — hotter electrolyte and a narrower electrode gap both cut cell voltage and therefore energy cost per kilogram, at the price of more anode fog and cathode nodulation in a real cell house.
- Ion drift — Cu²⁺ (blue) migrates anode→cathode at a speed proportional to current density.
- O₂ bubbles — rise from the anode face; their rate scales with current too.
- Deposit layer — the copper thickness on the cathode integrates the Faraday deposition rate over simulated time (1 real second ≈ 6 simulated minutes).