Fuel_cell - Wikiparency

# Fuel cell  ## Microsims — three.js ### Fuel cell (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Fuel_cell.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Fuel cell — three.js microsim"></iframe> </div> **Open it full-screen:** [Fuel_cell.html](https://wikitube-3d-microsims.netlify.app/Fuel_cell.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Hydronium]] - [[Haber_process]] - [[Electrolysis_of_water]] - [[Interstellar_medium]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Overview William Robert Grove, a Welsh barrister turned physicist, had been splitting water with a battery when he noticed that the apparatus, disconnected, gave a small current of its own. In 1839 he described the "gas voltaic battery" in the *Philosophical Magazine*: platinum strips in dilute sulfuric acid, one in hydrogen and one in oxygen, making current by recombining them. By 1842 fifty in series were electrolysing water -- the whole round trip, in 1842. A fuel cell is an [[Electrolysis_of_water]] cell run backwards, and that is worth saying flatly: the same reaction, membrane, platinum, four-electron oxygen chemistry and 1.229 V, read the other way. The electrolyser is pushed uphill and every loss adds on top of 1.229 V; the fuel cell falls downhill and every loss subtracts. The sign of each term flips and nothing else does -- including, here, the sign of the terminals: the anode is now the *negative* one. ## The physics Carnot does not apply, and the reason is structural. A heat engine must turn dH into heat and then heat into work, and that second step is capped at 1 - T_cold/T_hot. A fuel cell never makes the heat: it takes the electrons off the fuel at one electrode and puts them back on the oxidant at the other, so the work available is dG, not dH, and the ceiling is eta_max = dG/dH = 237.1/285.8 = 83.0 per cent at 25 C against 15.6 per cent for a heat engine between 80 and 25 C. That gap is why the technology exists. But "not Carnot-limited" is not "unlimited": dG becomes less negative as temperature rises while Carnot rises, so the ceiling *falls* and the two converge -- at 800 C, 76 per cent against Carnot's 72, both printed live. Hot cells win on kinetics, not the ceiling. Then reality subtracts: V_cell = E_nernst - eta_act - eta_ohm - eta_conc. **Activation** is almost entirely the oxygen reduction reaction at the cathode, which moves *four* electrons and breaks O=O through adsorbed OOH*, O* and OH* whose binding energies are not independent -- the relation that floors oxygen *evolution* in the electrolyser floors *reduction* here. Hydrogen oxidation on platinum is five orders of magnitude faster and nearly free. It is also why open-circuit voltage is 0.95 to 1.0 V, not 1.229: crossover hydrogen keeps a small current running at zero load and the ORR charges activation on it. **Ohmic** loss is linear in current and mostly the membrane's resistance to protons, so it is ferociously sensitive to how wet that membrane is. **Concentration** loss is the cliff at the right-hand end: oxygen cannot reach the catalyst as fast as the current consumes it, and the loss diverges logarithmically as the current nears the limit -- in a PEM cell usually low because product water has *flooded* the cathode. Region boundaries are computed, not asserted: each point is coloured by whichever loss grows fastest there. **Peak power is not the operating point.** Power density is V*i, so it rises, peaks and falls; efficiency goes as V alone and falls monotonically from open circuit. The consequence, which most explanations omit, is that everything *right* of peak power is strictly dominated -- less power **and** less efficiency than some lower current gives. Real designs sit left of it, near 0.65 V a cell. **Hydration cuts both ways.** A perfluorosulfonic acid membrane conducts protons only when its sulfonate groups are solvated; on the Springer correlation lambda = 14 gives about 0.12 S/cm at 80 C and lambda = 2 is an order of magnitude worse, at which point the ohmic term swallows the cell. So wetter is better -- except that the cathode is where the product water appears, and liquid there blocks oxygen from the platinum. Too dry and protons cannot cross; too wet and oxygen cannot arrive. The sim locates the optimum in an inset, and holding a stack there across a changing duty cycle is most of what water management does. **Efficiency, both bases, always.** Two voltages correspond to recovering all the fuel's enthalpy, because the product water counts as liquid or as vapour: HHV 141.8 MJ/kg -> 1.481 V and LHV 120.0 MJ/kg -> 1.253 V, an 18 per cent gap. A cell at 0.65 V is **43.9 per cent HHV and 51.9 per cent LHV**, and both get quoted as "the" efficiency. It is voltage efficiency only: multiply by fuel utilisation, then subtract compressor and pumps. **The round trip, honestly.** For storage the number that matters is electricity -> hydrogen -> electricity. Measured ranges are **27.4 to 48.0 per cent** through a fuel cell, 27.4-32.9 through a hydrogen engine and 24.0-26.8 through a gas turbine (OIES, ET48, 2025) -- roughly 25 to 48 per cent, basis named. Lithium-ion returns **85 to 95 per cent**, pumped hydro **70 to 80**. Batteries win decisively. Hydrogen's case is duration -- a terawatt-hour held for a season in a salt cavern -- and sector coupling: steel, ammonia, shipping and aviation need a molecule, not an electron. ## Controls -> what each maps to | Control | Maps to | Range / values | Physical meaning | |---|---|---|---| | Load | external resistance per area | 0 open circuit to 100 short circuit | The master control: slides the operating point along the curve | | Cell | fuel cell type | PEM 80 C / SOFC 800 C | Polymer and platinum, or ceramic and nickel; H+ becomes O2- | | Hydration | lambda, waters per sulfonate | 2 to 22, default 12 | Conductivity one way, flooding the other; inert for SOFC, and says so | | T | cell temperature | 30-95 C PEM, 600-1000 SOFC | Lowers E_rev, speeds kinetics, caps the hydration the membrane can hold | | Oxidant | oxygen partial pressure | air 1 bar / air 2.5 bar / pure O2 | 12 mV of Nernst at the left of the curve, 5x the limit at the right | | Catalyst | exchange current density multiplier | 10 x log10 of the factor; 0.40 mg/cm2 Pt | Moves the activation region | | Cells | cells in series | 1 to 400, default 100 | Stack volts and kilowatts; the operating point stays | | Explode | layer separation | 0 to 62 | Pulls the seven layers apart so each loss shows where it lives | | curve | -- | on / off | Polarisation, power and efficiency curves; hydration inset | | water | -- | on / off | Product water and the flooding droplets on the cathode | | running | -- | on / off | Pauses the particles; the solve continues | The HUD's headline quantity is the voltage budget -- 1.229 V plus the Nernst term, minus each loss, equalling V_cell -- with efficiency on both bases. ## Learning objective After playing, a learner can say why a fuel cell is not Carnot-limited and what limits it instead, attribute each region of the polarisation curve to the right physics, explain why peak power is the wrong place to run, and quote a round trip against a battery honestly. ## Limits and connections Every constant here is identical, to the digit, to the one in [[Electrolysis_of_water]]: the two files describe one reaction in opposite directions and must not disagree about a number. The thermodynamics is shared verbatim; the concentration term is derived, not fitted, from oxygen depletion feeding both the Nernst term and the ORR exchange current density. The kinetics is calibrated, as in the companion sim: exchange current densities are *apparent* values referred to the geometric area, not intrinsic values for flat platinum, and the transfer coefficients reproduce measured Tafel slopes. One real effect is absent and it matters: the sim scales activity with catalyst loading, but real cells at very low platinum loading do worse, because a thin layer concentrates the local oxygen flux through the ionomer film around each particle. That resistance is unmodelled, and it is why the low-loading problem is harder than activity arguments suggest. Two honesties about the water. Springer fitted lambda only to 14; above that the sim extrapolates on a reduced slope and flags it. And the flooding model -- stick probability, drainage constant, sixteen puddle sites, a 0.72 coverage cap because the ribs shed water -- is a plausible parameterisation, not a measured one. Its steady-state coverage uses the live droplets' constants, so the two agree by construction: consistency, not validation. The drawing is not to scale and says so on its own ruler: a 50 um membrane between 2 mm plates would be a black line; real thicknesses are printed above each layer and used in the physics. The hydration slider is inert for the solid oxide cell and reads "n/a: no membrane" rather than hiding -- the more honest failure. The round-trip figure is a *specific* chain -- this cell times an electrolyser at the companion default of 1.90 V, 78.0 per cent HHV -- not a general number. The hydrogen here is made by [[Electrolysis_of_water]] and consumed industrially by the [[Haber_process]]; the proton crossing the membrane moves by the relay in [[Hydronium]], which is why a dry membrane is an insulator.  **Part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]]** — main article for section 11, *Fuel cells: the same reaction without a flame*. Related sections: [[Combustion]] · [[Electrolysis_of_water]] · [[Hydrogen_economy]].   **Microsim — three.js (Wikitube framework):** *Fuel cell* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Fuel_cell.html" data-title="Fuel cell"></div> *Built from `MICROSIM_GUIDE/specs/sims/Fuel_cell.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Fuel_cell) : [Wikitube](https://en.wikitube.io/wiki/Fuel_cell) ## Previous hub tags Tree parent: [[Hydrogen]]. Legacy hubs: `HYDROGEN`. --- *Created 2026-08-05 - append-only - authored to WIKI_REPOPULATION_PROTOCOL v1.0 section 5 - portal-microsim-pass (PORTAL_Hydrogen batch 2) - 0 deletions*