# Electric battery An **electric battery** is a device made of one or more [[Electrochemical_cell|electrochemical cells]] that converts stored chemical energy into [[Electrical_energy|electrical energy]] by letting a [[Redox|redox]] reaction run through an external circuit instead of by direct contact. The reaction's [[Gibbs_free_energy|Gibbs free energy]] fixes the voltage the cell would deliver if nothing were flowing, through `dG = -n F V_eq`, where F ≈ 96,485 C per mole of electrons; everything the user actually experiences — sag under load, warmth, a run time shorter than the label — is the difference between that ideal and a cell carrying current.[^hav-thermo] In the microsim below the reader sets the load current on a logarithmic slider and the number of cells in series, and watches the terminal voltage fall by three stacked losses, `V = E0 - b asinh(I/(2 I*)) - I R`, so that power `P = I V` peaks at a current well above the one that delivers the most energy.[^hav-stack][^murphy-elec] On the Energy flagship's spine this page is the main article for Part IV — Scientific use, section *Batteries*, and it is the root of the storage branch. [[Lithium-ion_battery|The lithium-ion cell]] is its densest modern instance, [[Daniell_cell|the Daniell cell]] its clearest historical one, [[Capacitor|the capacitor]] the store whose voltage falls linearly instead of sitting on a plateau, and [[Grid_energy_storage|grid storage]] the place where all of them are compared against pumped hydro and [[Flywheel_energy_storage|flywheels]]. A battery is not a store of electricity. It is a store of chemical reagents held apart, plus a path that forces their reaction to pay out as charge moved through a potential difference. That distinction explains most of the surprises in the sections below: why capacity depends on how fast you draw it, why a cold battery is a weak one, and why a battery that has "gone flat" still weighs the same. ## History ### Invention The battery begins with the observation that two dissimilar metals in a conducting liquid produce a steady current, and with the pile of alternating discs that turned the observation into an instrument at the very end of the eighteenth century. Within a generation the pile had been replaced by cells with separated electrolytes, of which [[Daniell_cell|the Daniell cell]] is the canonical example: zinc in zinc sulfate, copper in copper sulfate, and a porous barrier between them. The design mattered because it held a steady voltage for hours rather than minutes, which made it the working power supply of early telegraphy. The theory arrived afterwards and is still the framework in use. A cell is two half-reactions, each with a [[Standard_electrode_potential|standard electrode potential]] measured against a reference, and the cell voltage is their difference. The Portal Book's table of reference values gives 0 V for 2H⁺/H₂ by definition, 1.229 V for O₂/H₂O, 0.4 V for O₂/OH⁻ and −0.83 V for 2H₂O/H₂,OH⁻.[^hav-pot] A caution comes with the table: potentials are not additive quantities — Gibbs energies are — so half-cell potentials may only be subtracted in pairs, and the fact that 0.4 − (−0.83) = 1.23 V reproduces the water-splitting voltage is described by the book as working "fortuitously".[^hav-fortuit] ### Ongoing developments Modern work is mostly a hunt for more [[Energy_density|energy density]] and longer life at acceptable cost and safety, which means better electrode materials, thinner separators, and electrolytes that do not decompose at the voltages the electrodes want to reach. The analytical modelling literature adds a structural theme: a battery electrode is a porous solid, and its useful thickness is set by how far reactant and current can penetrate before the front of the electrode does all the work. Past a Thiele modulus of about 3, only the leading 1/M fraction of an electrode reacts, so building it thicker buys capacity that cannot be reached at rate.[^hav-porous] Chapter-length treatments of the battery case, including redox flow designs in which the reagents are stored outside the cell entirely, occupy the later chapters of the same book.[^hav-batt][^hav-flow] ## Chemistry and principles Every cell is the same three-part object: two electrodes at which charge crosses between an electronic and an ionic conductor, and an [[Electrolyte|electrolyte]] between them that carries [[Ion|ions]] but not electrons. Oxidation happens at one electrode and reduction at the other; the electrolyte closes the circuit internally while the load closes it externally, and the electron count on the two sides must match exactly. The thermodynamic anchor is `dG = -n F V_eq` with the Faraday constant F ≈ 96,485 C/mol.[^hav-thermo] Read backwards, this says a reaction releasing 237 kJ per mole with two electrons transferred gives about 1.23 V, which is where the familiar water-splitting number comes from.[^hav-thermo] Because ΔG = ΔH − TΔS, part of the reaction's enthalpy appears as heat rather than work even in the ideal case, and the split between the two moves with temperature — the reason the same chemistry is quoted at slightly different voltages in warm and cold conditions.[^hav-thermo] Concentration enters through [[Nernst_equation|the Nernst equation]], `E_eq = E0' + (R T/(n F)) ln(c_O/c_R)`, so a cell's open-circuit voltage drifts as the reaction consumes one species and makes another.[^hav-nernst] This is the origin of the sloping discharge curve in some chemistries and, in chemistries where a two-phase reaction pins the concentrations, of the flat plateau in others. The rate at which charge crosses each interface follows [[Butler–Volmer_equation|the Butler–Volmer equation]]. In its concentration-independent form, `j = jstar*[exp(eta/b_a) - exp(-eta/b_c)]`, and for a symmetric transfer coefficient it collapses to `j = 2 jstar sinh(eta/b)` with `b = 2 R T/F`, which inverts cleanly to `eta = b asinh(j/(2 jstar))`.[^hav-bv] Two limits are worth carrying: below about RT/F ≈ 25.7 mV of [[Overpotential|overpotential]] the interface behaves like a resistor, `eta = (R T/(F jstar)) j`, and far above it behaves exponentially, which is [[Tafel_equation|the Tafel regime]] where one decade of current costs `b_a ln 10` — about 118 mV at 298.15 K, the "roughly 120 mV per decade" of the practical literature.[^hav-bv] Finally, [[Faraday's_laws_of_electrolysis|Faraday's law]] converts current to chemistry: `j = n F N`, so a two-electron reaction consumes 5.18 × 10⁻⁶ mol per second per ampere.[^hav-faraday] ## Types Batteries are classified first by whether the reaction can be reversed, then by chemistry, then by the package. The classification is not cosmetic: it decides the energy density, the safe current, the shelf life and the disposal route all at once. ### Primary and secondary batteries A primary cell is discharged once and discarded; a secondary cell is recharged by driving current backwards through it, which runs the redox reaction uphill in exactly the way an [[Electrolysis|electrolysis]] cell does. The sign convention in the modelling literature makes the symmetry explicit: a galvanic cell delivering power has the reaction running downhill and V_cell between zero and V_eq, while an electrolytic cell has V_cell beyond V_eq on the other side, so that the same stack of loss terms is *subtracted* from the equilibrium voltage on discharge and *added* to it on charge.[^hav-sign] A cell's round-trip efficiency is therefore bounded by the ratio of those two voltages, and the losses are paid twice. ### Sizes Cell voltage is fixed by chemistry, so voltage is obtained by putting cells in series and current capacity by putting them in parallel. A nominal 9 V block is six 1.5 V cells in series; a vehicle pack is hundreds of cells in both directions. The reader's second control in the microsim is exactly this: cell count in series multiplies the terminal voltage and the loss terms together, so a string's sag scales with its length while its capacity in ampere-hours does not change at all. ### Comparison The honest way to compare stores is on two axes at once, energy per unit mass and power per unit mass, because no chemistry maximises both. A reference point from the Portal Books keeps the scale in view: a small 9 V alkaline block rated at 0.5 Ah holds 4.5 Wh, or 16.2 kJ, which will run a 1 W load for 4.5 hours.[^murphy-elec] That is about the energy in a gram of sugar, delivered over an afternoon. Chemical fuels beat every battery on energy per kilogram by an order of magnitude or more; batteries win on efficiency of conversion, since they pay out as work directly rather than through a [[Heat_engine|heat engine]]. ## Performance, capacity and discharge This is the section the article's microsim belongs to. The quantity on the label is capacity in ampere-hours, and the quantity the user wants is energy in watt-hours, related by `Ah × V = Wh` — but V is not a constant, and that is the whole difficulty.[^murphy-elec] Under load the terminal voltage is the equilibrium voltage minus a stack of losses. The Portal Book assembles them for a cell as an equilibrium term plus a kinetic overpotential at each electrode plus an ohmic drop through electrolyte and hardware, and its footnote 19 replaces the logarithm of the Tafel form with an inverse hyperbolic sine so that no overpotential goes negative below the exchange current density.[^hav-stack] Written for a battery on discharge and for one symmetric electrode pair, that is the sim's governing equation: `V = E0 - b asinh(I/(2 I*)) - I R` with `b = 2 R T/F` ≈ 51.4 mV at 298.15 K for a symmetric transfer coefficient.[^hav-bv] The shape is the point. At small current the asinh term is nearly linear and the cell looks like a resistor; over the middle decades it is nearly logarithmic, so ten times the current costs only about 118 mV; at large current the `I R` term takes over and the curve turns down hard.[^hav-bv][^hav-stack] The reader's log slider walks across all three regimes, and the stacked bars underneath show which loss is dominant at each point — the same display the electrolyser polarization curve uses in the reverse direction, where at 10 mA/cm² the slow oxygen electrode costs 0.23 V against 0.03 V for everything else combined, and at 1 A/cm² the electrolyte gap alone costs 0.50 V.[^hav-stack] Two readouts follow from V(I). Power `P = I V` rises, peaks and falls, because V is falling while I rises; the peak sits where the marginal loss exactly cancels the marginal current, which for a purely ohmic cell is at half the open-circuit voltage.[^murphy-elec] Delivered energy moves the other way: the faster the discharge, the lower the average voltage and the fewer watt-hours the same ampere-hours are worth. The sim shows the two curves crossing, which is the practical lesson — the current that gets the most power out of a battery is not the current that gets the most energy out of it. Usable capacity itself shrinks at rate, an effect usually fitted by an empirical run-time expression of the form `t = H (C/(I H))^k`, where C is the capacity measured over the rating time H and k is an exponent above 1.[citation needed] The sim treats this curve as **ILLUSTRATIVE**: it is a display fit chosen to show the trend, not a measured law derived from the Portal Book's electrochemistry, and k is exposed as a parameter rather than presented as a constant of nature. Its mechanistic origin is transport — at high current the reaction front cannot penetrate the porous electrode, so part of the active material is never reached, which is the effectiveness-factor argument of the porous-electrode chapter applied to a discharge.[^hav-porous] ## Lifespan and endurance Two clocks run on every cell. Calendar life is the slow chemistry that proceeds whether or not the cell is used: self-discharge through side reactions, [[Corrosion|corrosion]] of current collectors, and decomposition of the electrolyte at the electrode surfaces. Cycle life is the damage done by charging and discharging — volume changes in the active material, loss of electrical contact within the porous electrode, and the slow consumption of mobile ions into films that do not give them back. The modelling view adds a geometric reason why these two clocks interact. Electrode performance depends on maintaining a connected, wetted porous network with a short enough transport path; anything that thickens a surface film or blocks pores raises the effective transport resistance, which raises the `I R` term in the discharge equation, which raises the heat generated at a given current, which accelerates the chemistry that caused the film.[^hav-porous][^hav-batt] Ageing in a battery is a feedback loop, not a countdown, which is why the last 10 % of a cell's life usually disappears much faster than the first 10 %. ## Hazards The hazards of a battery follow from what it is: a large amount of chemical energy held in a small volume behind a thin barrier, together with an electrolyte that is often corrosive and sometimes flammable. A short circuit converts the stored energy to heat at the maximum rate the internal resistance allows, and because that resistance falls as the cell warms, the process can run away. ### Leakage Alkaline and acid electrolytes attack the metal around them once a seal fails, and a cell left flat in a device is the usual case, because a fully discharged cell has no reaction left to consume the gas that its side reactions make. The leaked electrolyte then does its own damage through [[Galvanic_corrosion|galvanic corrosion]] wherever it bridges two dissimilar metals. ### Disposal Disposal is a materials question as much as a safety one. A discarded cell still contains its metals — [[Lithium|lithium]], [[Cobalt|cobalt]], [[Nickel|nickel]], [[Manganese|manganese]], zinc, lead — in concentrations far above any ore, so collection is the cheapest mining available, and the case for separate collection rests on that arithmetic as much as on keeping the electrolyte out of landfill. ## Legislation and regulation Battery law addresses three distinct risks, and it is worth separating them because they pull in different directions. The first is transport: a charged cell is an energy source that can ignite in an enclosed space, so shipping rules restrict state of charge and packaging rather than the chemistry itself. The second is collection and recycling, aimed at the metals described above. The third is consumer safety, dominated by small cells that can be swallowed, where the harm is caused by electrolysis in tissue rather than by the cell's stored energy. ### United States Jurisdiction-specific rules for the United States — the federal transport classification of lithium cells, state-level collection mandates, and product-safety standards for button cells — are documented on the Wikipedia pair, which carries the statutory citations; this page does not restate them, because the Portal Books used here are engineering texts and carry no legal sources. ### European Union The same holds for the European Union's battery regime, whose collection targets, producer-responsibility obligations and material-recovery requirements are cited on the pair. What the engineering literature does contribute is the reason such targets are achievable at all: the metals in a cell are neither consumed nor transformed by cycling, so a recovered cell is a concentrated feedstock rather than a waste stream.[^hav-batt] ## See also - [[Daniell_cell]] - [[Capacitor]] - [[Electrochemical_cell]] - [[Lithium-ion_battery]] - [[Fuel_cell]] - [[Energy_storage]] - [[Supercapacitor]] ## References [^hav-thermo]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, pp. 25–26 (`ΔG = −nFV_eq` with F ≈ 96,485 C/mol e⁻; ΔG ≈ 237 kJ/mol over two electrons gives V_eq ≈ 1.23 V; ΔH = ΔG + TΔS and the thermoneutral voltage V_tn ≈ 1.48 V). https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling [^hav-pot]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, p. 28 (standard potentials: 2H⁺/H₂ 0 V; O₂/H₂O 1.229 V; O₂/OH⁻ 0.4 V; 2H₂O/H₂,OH⁻ −0.83 V). [^hav-fortuit]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, p. 27 (potentials do not add, ΔG does; 0.4 − (−0.83) = 1.23 V works only "fortuitously"; the standard hydrogen electrode is an idealization). [^hav-nernst]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, p. 32 (the single-electron Nernst form `E_eq = E0' + (RT/nF) ln(c_O/c_R)`). [^hav-bv]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, pp. 30, 33–35 (Butler–Volmer `j = j*[exp(η/b_a) − exp(−η/b_c)]` with b_a = RT/(α_O F); the α = ½ form `j = 2j* sinh(η/b)` with b = 2RT/F and its inverse `η = b asinh(j/(2j*))`; the linear regime valid for η ≲ RT/F ≈ 25 mV; Tafel slope b_a ≈ 50 mV so one decade costs b_a ln 10 ≈ 120 mV, exactly 118 mV at 298.15 K with b_a = 51.4 mV and RT/F = 25.7 mV, values derived in the Wikitube extract from the book's forms). [^hav-faraday]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, p. 28 (Faraday's law `j = nFN`; the figure 1/(2F) = 5.18 × 10⁻⁶ mol s⁻¹ A⁻¹ is derived in the Wikitube extract). [^hav-sign]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, p. 25 (sign convention: an electrolytic cell has V_cell < V_eq < 0, so the loss stack is added on charge and subtracted on discharge; voltage efficiency φ_e = V_eq/V_cell; the measured open-circuit voltage can differ from V_eq when side reactions occur). [^hav-stack]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 1 Electrochemistry, pp. 36–38 (the stacked loss equation `V_cell = V_eq + η_c − η_a − Δφ − ΔV`, its Eq. 1.36 form, and footnote 19's replacement of ln(x) by asinh(x/2) so no overpotential goes negative below j*; Fig. 1.8 parameters b_a ≈ b_c ≈ 50 mV, j*_c = 10⁻² A/cm², j*_a = 10⁻⁴ A/cm², electrolyte 0.5 Ω·cm², electronic 0.01 Ω·cm²; activation losses dominate at low current and the ohmic term at high current. The 0.23 V, 0.03 V and 0.50 V loss splits quoted here are derived from those parameters in the Wikitube extract). [^hav-porous]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 5 Porous electrodes, pp. 96, 99–100 (the effectiveness factor `E = tanh(M)/M`, falling to 1/M for M ≫ 1, so past M ≈ 3 only the front 1/M of the electrode reacts; the combined-limitation form and the optimum thickness with E_opt ≈ 1/3). [^hav-batt]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 7 Batteries, pp. 110–129 (page to pin) (the battery chapter: electrode, electrolyte and diffusion limits, energy density and the discharge model). [^hav-flow]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053, Chapter 13 Redox Flow Batteries, pp. 178–195 (page to pin) (cells in which the reagents are stored in external tanks, decoupling energy from power). [^murphy-elec]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097, Chapter 5 Energy and Fossil Fuels, pp. 97–98 (`E = qV` Eq. 5.1, 1 A = 1 C/s, `P = IV` Eq. 5.2, and Ah × V = Wh; a 9 V, 0.5 Ah battery holds 4.5 Wh = 16.2 kJ and runs a 1 W load for 4.5 h; 1 eV = 1.6 × 10⁻¹⁹ J). https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^kerlin-batt]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Portal Book 048, Chapter 9, pp. 354–466 (page to pin) (batteries and electrical storage in the energy-system context). https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^mitofsky-batt]: Mitofsky, Andrea (2018). *Direct Energy*. Portal Book 055, Batteries and Fuel Cells, pp. 211–246 (page to pin) (direct chemical-to-electrical conversion devices treated alongside the other direct converters). https://open.umn.edu/opentextbooks/textbooks/direct-energy ## Bibliography - Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Portal Book 053 — Chapter 1 Electrochemistry (pp. 20–41), Chapter 3 Transport (pp. 46–65), Chapter 5 Porous electrodes (pp. 78–101), Chapter 7 Batteries (pp. 110–129), Chapter 13 Redox Flow Batteries (pp. 178–195), Chapter 16 Formula sheet (pp. 212–224). - Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Portal Book 097 — Chapter 5 Energy and Fossil Fuels (pp. 87–182), for the unit ladder and the battery energy example. - Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Portal Book 048 — Chapter 9 (pp. 354–466).[^kerlin-batt] - Mitofsky, Andrea (2018). *Direct Energy*. Portal Book 055 — Batteries and Fuel Cells (pp. 211–246).[^mitofsky-batt] ## External links - *Electrolysers, Fuel Cells and Batteries: Analytical Modelling* (2024), Portal Book 053 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling - *Direct Energy* (2018), Portal Book 055 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/direct-energy - The Wikipedia pair's External links section lists the pair's own links, including the statutory sources behind the Legislation and regulation section. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Electric_battery.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Electric battery* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Electric_battery.html" data-title="Electric battery"></div> *Built from `MICROSIM_GUIDE/specs/sims/Electric_battery.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Electric_battery) : [Wikitube](https://en.wikitube.io/wiki/Electric_battery) · pinned revision [1373978617](https://en.wikipedia.org/w/index.php?oldid=1373978617) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E19 · sim pending (matter/Electric_battery).*