{ "node": { "id": "term:joule-heating", "type": "Term", "label": "Joule heating", "properties": { "id": "joule-heating", "name": "Joule heating", "aka": [ "ohmic heating", "resistive heating", "I²R loss" ], "section": "topic-thermal", "definition": "Heat produced by current flowing through a resistance, equal to the current squared times the resistance. Doubling the current quadruples it: a 1 mΩ cell gives 10 W at 100 A but 40 W at 200 A. It dominates heat generation at high C-rates and also warms busbars, welds and connectors.", "formula": "P = I²·R", "unit": "W", "related": [ "heat-generation", "internal-resistance", "busbar", "hot-spot", "ohms-law" ], "example": { "title": "See the squared-current penalty", "text": "A 10 mΩ resistance dissipates 1 W at 10 A and 4 W at 20 A. Doubling current quadruples resistive heat when resistance stays constant." }, "url": "https://lemonergy.com/learn/glossary/joule-heating/", "mentions": [] } }, "edges": [ { "id": "edge:54", "source": "term:joule-heating", "target": "workflow:loss-accounting", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:4613", "source": "term:joule-heating", "target": "topic:topic-thermal", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:4614", "source": "term:joule-heating", "target": "term:heat-generation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4615", "source": "term:joule-heating", "target": "term:internal-resistance", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4616", "source": "term:joule-heating", "target": "term:busbar", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4617", "source": "term:joule-heating", "target": "term:hot-spot", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4618", "source": "term:joule-heating", "target": "term:ohms-law", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:4619", "source": "term:joule-heating", "target": "visual:heat", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } } ], "neighbors": [ { "id": "workflow:loss-accounting", "type": "Workflow", "label": "Compare grid and battery energy", "properties": { "id": "loss-accounting", "title": "Compare grid and battery energy", "kind": "studio", "summary": "Separate energy and loss signals make efficiency visible.", "steps": [ "Keep battery settings fixed.", "Change converter efficiency." ], "example": "7 kW battery-side power at 95% efficiency requires about 7.37 kW grid power and produces about 0.37 kW converter loss.", "observe": "Battery I²R loss differs from converter loss.", "limits": "A loss signal is not a predicted temperature. This network takes external temperature.", "url": "https://design.lemonergy.com/cosim.html?example=charging-home", "label": "Open the Studio example", "evidence": [ "js/charging-control.js", "js/charging-scenarios.js", "docs/CHARGING_BLOCKS_SPEC.md" ] } }, { "id": "topic:topic-thermal", "type": "Topic", "label": "Thermal management and heat transfer", "properties": { "id": "topic-thermal", "name": "Thermal management and heat transfer", "lede": "How heat is made, moved and removed in cells and packs, and the hardware that keeps a battery at the right temperature.", "context": "Select spatial detail for the question.", "example": "Equal total heat in different layouts can produce different gradients. Average temperature can miss a hot spot.", "lesson_url": "https://lemonergy.com/learn/fundamentals/battery-aging/", "lesson_label": "Open temperature and aging" } }, { "id": "term:heat-generation", "type": "Term", "label": "Heat generation", "properties": { "id": "heat-generation", "name": "Heat generation", "aka": [ "Bernardi equation" ], "section": "topic-thermal", "definition": "The heat a cell produces in operation: an irreversible part equal to current times overpotential, and a reversible part from the entropy change, I·T·dE/dT. The Bernardi equation sums them and feeds every thermal model.", "formula": "q = I(V − E_OCV) + I·T·(dE/dT)", "unit": "W", "related": [ "entropy-coefficient", "internal-resistance", "thermal-model", "thermal-management", "exothermic" ], "example": { "title": "Keep reversible and irreversible heat separate", "text": "With charging current +5 A and terminal voltage 0.10 V above OCV, the irreversible term is 0.50 W. At 300 K with dE/dT = +0.1 mV/K, the reversible contribution is +0.15 W, giving 0.65 W under this sign convention." }, "url": "https://lemonergy.com/learn/glossary/heat-generation/", "mentions": [ "overpotential" ] } }, { "id": "term:internal-resistance", "type": "Term", "label": "Internal resistance", "properties": { "id": "internal-resistance", "name": "Internal resistance", "abbr": "IR", "aka": [ "DC resistance", "DCIR" ], "section": "topic-units", "definition": "The resistance a cell presents to current, from its foils, electrolyte, interfaces and the reactions themselves. It converts part of the delivered energy into heat, sets the voltage drop under load, and rises as the cell ages; a large automotive cell has about a milliohm, a small cylindrical cell tens.", "unit": "mΩ", "related": [ "ohms-law", "ir-drop", "impedance-rise", "dcir", "area-specific-resistance", "resistance-capacity-product" ], "lesson": "fundamentals/battery-basics/#datasheet", "url": "https://lemonergy.com/learn/glossary/internal-resistance/", "mentions": [ "electrolyte", "cylindrical-cell" ] } }, { "id": "term:busbar", "type": "Term", "label": "Busbar", "properties": { "id": "busbar", "name": "Busbar", "section": "topic-pack", "definition": "A rigid copper or aluminium conductor that joins cell terminals into series and parallel groups, and modules into the pack. Its cross-section is sized for current and heating, and its joints — welded or bolted — are a classic source of resistance and failure.", "related": [ "series-parallel", "terminal", "laser-welding", "internal-resistance", "wire-bonding" ], "url": "https://lemonergy.com/learn/glossary/busbar/", "mentions": [] } }, { "id": "term:hot-spot", "type": "Term", "label": "Hot spot", "properties": { "id": "hot-spot", "name": "Hot spot", "aka": [ "hotspot" ], "section": "topic-thermal", "definition": "A small region that runs markedly hotter than its surroundings — near a tab, at a high-resistance weld or busbar joint, in the centre of a large cell or around an internal short. Because aging speeds up roughly twofold for every 10 °C, that spot ages fastest, and a temperature sensor a few centimetres away may not see it.", "related": [ "thermal-gradient", "joule-heating", "temperature-sensor", "thermography", "arrhenius", "thermal-runaway" ], "url": "https://lemonergy.com/learn/glossary/hot-spot/", "mentions": [ "busbar" ] } }, { "id": "term:ohms-law", "type": "Term", "label": "Ohm’s law", "properties": { "id": "ohms-law", "name": "Ohm’s law", "section": "topic-units", "definition": "Voltage across a resistance equals current times that resistance. Applied to a cell it predicts the voltage drop under load from the internal resistance, which is the first-order reason terminal voltage sags.", "formula": "V = I × R", "related": [ "internal-resistance", "ir-drop", "ohm", "kirchhoffs-laws" ], "example": { "title": "Convert a resistance into a voltage drop", "text": "A 10 A current through a 20 mΩ resistance produces 0.2 V of voltage drop. Use 0.020 Ω in V = IR; inserting the number 20 without converting milliohms would be wrong." }, "url": "https://lemonergy.com/learn/glossary/ohms-law/", "mentions": [ "voltage" ] } }, { "id": "visual:heat", "type": "Visual", "label": "Current and resistive heating", "properties": { "title": "Current and resistive heating", "summary": "Double the current and ohmic heating increases fourfold.", "readout": "At 5 A: 0.5 W. At 10 A: 2 W.", "formula": "P_heat = I²R", "note": "Resistance is constant; reversible entropic heat and other losses are excluded.", "software": { "status": "reference", "label": "Reference concept", "body": "P = I²R is the ohmic contribution. The product Charge session can also use a lumped thermal model; the native Studio battery does not calculate temperature evolution.", "href": "https://design.lemonergy.com/" }, "html": "
Ohmic heating
Ohmic heatingCurrent magnitude (A) versus Heat rate (W). I²R. Interpretation follows the graphs.0025410615820Current magnitude (A)Heat rate (W)
I²R
" } } ] }