{ "node": { "id": "term:entropy-coefficient", "type": "Term", "label": "Entropy coefficient", "properties": { "id": "entropy-coefficient", "name": "Entropy coefficient", "section": "topic-electrochemistry", "definition": "The change of open-circuit voltage with temperature, dE/dT, usually a fraction of a millivolt per kelvin and varying with state of charge. It sets the reversible heat a cell absorbs or releases, which can be a large share of total heat at low current.", "formula": "q_rev = I·T·(dE/dT)", "unit": "mV/K", "related": [ "heat-generation", "gibbs-free-energy", "open-circuit-voltage" ], "example": { "title": "Track reversible heat with the sign convention", "text": "With positive charging current of 5 A, temperature 300 K and dE/dT = 0.1 mV/K, q_rev = IT(dE/dT) gives +0.15 W. Reversing the current reverses this contribution." }, "notes": [ "The glossary plot takes positive heat as heat released. Other sources may use positive-discharge current and a different written sign." ], "url": "https://lemonergy.com/learn/glossary/entropy-coefficient/", "mentions": [ "state-of-charge" ] } }, "edges": [ { "id": "edge:1999", "source": "term:entropy-coefficient", "target": "topic:topic-electrochemistry", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:2000", "source": "term:entropy-coefficient", "target": "term:heat-generation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2001", "source": "term:entropy-coefficient", "target": "term:gibbs-free-energy", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2002", "source": "term:entropy-coefficient", "target": "term:open-circuit-voltage", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/entropy-coefficient/state-of-charge", "source": "term:entropy-coefficient", "target": "term:state-of-charge", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:2004", "source": "term:entropy-coefficient", "target": "visual:reversible-heat", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:2005", "source": "term:entropy-coefficient", "target": "reference:bernardi-energy", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "topic:topic-electrochemistry", "type": "Topic", "label": "Electrochemistry fundamentals", "properties": { "id": "topic-electrochemistry", "name": "Electrochemistry fundamentals", "lede": "The reactions and potentials that make a cell a battery.", "context": "Connect reaction sites and transport paths.", "example": "A circuit can predict terminal voltage while leaving electrode potentials and reaction kinetics unresolved.", "lesson_url": "https://lemonergy.com/learn/fundamentals/cell-anatomy/", "lesson_label": "Open cell anatomy" } }, { "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:gibbs-free-energy", "type": "Term", "label": "Gibbs free energy", "properties": { "id": "gibbs-free-energy", "name": "Gibbs free energy", "abbr": "ΔG", "section": "topic-electrochemistry", "definition": "The maximum useful work a reaction can deliver at constant temperature and pressure. For a cell it equals the charge transferred times the cell voltage, with a negative sign, which ties the thermodynamics of the materials to the voltage on the terminals.", "formula": "ΔG = −nFE", "unit": "kJ/mol", "related": [ "cell-voltage", "nernst-equation", "faradays-constant", "entropy-coefficient" ], "example": { "title": "Convert voltage to molar free energy", "text": "For a one-electron reaction with equilibrium voltage 3.0 V, ΔG = −nFE is approximately −289 kJ/mol. The sign refers to the reaction direction and the equilibrium electrical work." }, "url": "https://lemonergy.com/learn/glossary/gibbs-free-energy/", "mentions": [] } }, { "id": "term:open-circuit-voltage", "type": "Term", "label": "Open-circuit voltage", "properties": { "id": "open-circuit-voltage", "name": "Open-circuit voltage", "abbr": "OCV", "section": "topic-state", "definition": "The voltage across a cell’s terminals when no current flows and the cell has rested long enough for the voltage to settle. It depends on state of charge and temperature, and a cell whose open-circuit voltage falls unusually fast in storage may have an internal short.", "unit": "V", "related": [ "ocv-soc-curve", "relaxation", "voltage-hysteresis", "k-value", "internal-short-circuit" ], "lesson": "fundamentals/cell-production/#finishing", "url": "https://lemonergy.com/learn/glossary/open-circuit-voltage/", "mentions": [ "state-of-charge" ] } }, { "id": "term:state-of-charge", "type": "Term", "label": "State of charge", "properties": { "id": "state-of-charge", "name": "State of charge", "abbr": "SOC", "section": "topic-state", "definition": "How full a cell is, as a fraction of its available capacity. State of charge, like temperature, affects how fast a stored cell ages.", "unit": "%", "related": [ "depth-of-discharge", "ocv-soc-curve", "coulomb-counting", "state-of-health", "bms" ], "lesson": "fundamentals/battery-aging/#storage-soc", "example": { "title": "Interpret a charge inventory", "text": "If available capacity is 5 Ah and 3 Ah remains by the chosen estimator, SOC is 60%. A different estimate of available capacity changes this percentage, so compare SOC values only with the capacity convention recorded." }, "url": "https://lemonergy.com/learn/glossary/state-of-charge/", "mentions": [ "usable-capacity" ] } }, { "id": "visual:reversible-heat", "type": "Visual", "label": "Reversible heat can change sign", "properties": { "title": "Reversible heat can change sign", "summary": "The OCV temperature slope sets the reversible heat term for the stated current convention.", "readout": "At +10 A the stated term is 0.2981 W. Reversing current reverses the term.", "formula": "q_reversible = I × T × (dE/dT)", "note": "Positive current charges the cell; positive q means heat released. Check the solver convention before combining it with other heat terms. The coefficient is held constant across SOC.", "software": { "status": "reference", "label": "Reference concept", "body": "This reference term is separate from I²R heating. The core Arrhenius function does not calculate reversible heat or OCV entropy coefficients.", "href": "../chapter-1/" }, "html": "
Signed reversible heat term
Signed reversible heat termCurrent (A, + = charge) versus q_reversible (W). Reversible term. Interpretation follows the graphs.-4-20-2-1000210420Current (A, + = charge)q_reversible (W)
Reversible term
" } }, { "id": "reference:bernardi-energy", "type": "Reference", "label": "A General Energy Balance for Battery Systems", "properties": { "title": "A General Energy Balance for Battery Systems", "publisher": "Journal of The Electrochemical Society", "url": "https://doi.org/10.1149/1.2113792", "type": "Research article", "scope": "Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.", "year": 1985, "authors": [ "Dawn Bernardi", "Ellen Pawlikowski", "John Newman" ], "accessed": "2026-10-27" } } ] }