feat: page interactive, démos Play/Step et simulateur Carnot
Ajoute le pipeline PageSpec (validation, rendu, publication /p/{slug}),
les démos TipTap /demo, et le simulateur Carnot (modes frigo/PAC/moteur,
énergie kJ vs puissance W, unités K/°C/°F) avec correctifs d’équations KaTeX.
Co-authored-by: Cursor <cursoragent@cursor.com>
This commit is contained in:
Antigravity
254
memento-note/lib/simulators/carnot-cycle.ts
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254
memento-note/lib/simulators/carnot-cycle.ts
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import type { SimulatorPlugin } from './types'
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/**
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* Ideal Carnot machine between two reservoirs (2nd law).
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*
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* Physics (absolute temperatures only):
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* - Refrigerator: COP_R = Tc/(Th−Tc), W_min = Qc/COP_R, Qh = Qc+W
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* - Heat pump: COP_HP = Th/(Th−Tc) = COP_R+1, W_min = Qh/COP_HP
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* - Engine: η = 1−Tc/Th, W_out = η·Qh, Qc = Qh−W
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*
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* `q_cold` is the primary load magnitude (kJ or W — same number; unit is UI-only).
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* For fridge it is Qc; the view remaps for PAC / engine. Temperatures always Kelvin.
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*
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* Refs: COP_R Carnot = Tc/(Th−Tc); 1st law Qh=Qc+W; energy↔power interchangeable
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* if all rates use the same time basis (see standard thermo textbooks / Carnot fridge calculators).
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*/
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export const carnotCycleSimulator: SimulatorPlugin = {
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family: 'sim',
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id: 'carnot-cycle',
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title: {
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fr: 'Machine de Carnot (frigo / PAC / moteur)',
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en: 'Carnot machine (fridge / heat pump / engine)',
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},
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summary: {
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fr: 'Limites de Carnot entre deux sources : COP frigo Tc/(Th−Tc), COP pompe à chaleur Th/(Th−Tc), rendement moteur η=1−Tc/Th, travail ou puissance minimal(e). 1er et 2e principes.',
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en: 'Carnot limits between two reservoirs: fridge COP Tc/(Th−Tc), heat-pump COP Th/(Th−Tc), engine η=1−Tc/Th, minimum work or power. 1st and 2nd laws.',
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},
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keywords: [
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'carnot',
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'thermodynamique',
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'thermodynamics',
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'cop',
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'réfrigérateur',
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'frigo',
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'refrigerator',
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'pompe à chaleur',
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'heat pump',
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'moteur',
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'engine',
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'rendement',
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'efficiency',
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'watt',
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'puissance',
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'power',
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'deuxième principe',
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'second law',
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],
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params: [
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{
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id: 't_cold',
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symbol: 'T_c',
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label: { fr: 'Source froide', en: 'Cold reservoir' },
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min: 200,
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max: 320,
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step: 1,
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defaultValue: 260,
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unit: 'K',
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intent: 'cache',
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},
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{
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id: 't_hot',
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symbol: 'T_h',
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label: { fr: 'Source chaude', en: 'Hot reservoir' },
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min: 273,
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max: 400,
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step: 1,
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defaultValue: 300,
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unit: 'K',
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intent: 'warning',
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},
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{
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id: 'q_cold',
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symbol: 'Q_c',
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label: { fr: 'Charge (Qc frigo)', en: 'Load (fridge Qc)' },
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min: 10,
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max: 500,
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step: 5,
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defaultValue: 100,
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unit: 'kJ',
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intent: 'flow',
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},
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],
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outputs: [
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{
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id: 'cop_fridge',
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symbol: '\\mathrm{COP}_{R}',
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label: { fr: 'COP réfrigérateur', en: 'Fridge COP' },
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intent: 'output',
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digits: 2,
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},
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{
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id: 'cop_hp',
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symbol: '\\mathrm{COP}_{HP}',
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label: { fr: 'COP pompe à chaleur', en: 'Heat-pump COP' },
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intent: 'output',
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digits: 2,
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},
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{
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id: 'eta',
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symbol: '\\eta',
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label: { fr: 'Rendement moteur', en: 'Engine efficiency' },
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unit: '%',
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intent: 'highlight',
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digits: 1,
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},
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{
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id: 'w_min',
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symbol: 'W',
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label: { fr: 'Travail (énergie)', en: 'Work (energy)' },
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unit: 'kJ',
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intent: 'compute',
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digits: 1,
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},
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{
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id: 'q_hot',
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symbol: 'Q_h',
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label: { fr: 'Chaleur côté chaud', en: 'Hot-side heat' },
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unit: 'kJ',
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intent: 'flow',
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digits: 1,
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},
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],
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compute(env) {
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const tc = env.t_cold
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const th = env.t_hot
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const qc = env.q_cold
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if (!(th > tc) || !(qc > 0)) {
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return {
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cop_fridge: NaN,
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cop_hp: NaN,
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eta: NaN,
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w_min: NaN,
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q_hot: NaN,
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}
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}
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const copFridge = tc / (th - tc)
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const copHp = th / (th - tc)
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const eta = 1 - tc / th
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const wMin = qc / copFridge
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return {
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cop_fridge: copFridge,
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cop_hp: copHp,
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eta: eta * 100,
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w_min: wMin,
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q_hot: qc + wMin,
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}
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},
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}
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/** Operating mode for the interactive view (UI-only; physics shared). */
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export type CarnotMode = 'fridge' | 'heat_pump' | 'engine'
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/** Energy (kJ) vs power (W) — same ratios; only unit labels change. */
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export type CarnotQuantity = 'energy' | 'power'
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export type CarnotPhysics = {
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ok: boolean
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tc: number
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th: number
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copR: number
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copHP: number
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eta: number
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/** Heat exchanged with cold reservoir (magnitude > 0). */
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qc: number
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/** Heat exchanged with hot reservoir (magnitude > 0). */
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qh: number
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/** Work magnitude > 0 (input for fridge/PAC, output for engine). */
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w: number
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/** Reversible check: Qc/Tc ≈ Qh/Th */
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entropyOk: boolean
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}
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/**
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* Resolve magnitudes for the selected mode.
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* `load` is the primary useful quantity:
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* - fridge: Qc extracted from cold
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* - heat_pump: Qh delivered to hot
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* - engine: Qh absorbed from hot
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*/
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export function resolveCarnotPhysics(
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tc: number,
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th: number,
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load: number,
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mode: CarnotMode
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): CarnotPhysics {
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if (!(th > tc) || !(load > 0) || !Number.isFinite(tc) || !Number.isFinite(th)) {
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return {
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ok: false,
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tc,
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th,
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copR: NaN,
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copHP: NaN,
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eta: NaN,
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qc: NaN,
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qh: NaN,
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w: NaN,
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entropyOk: false,
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}
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}
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const copR = tc / (th - tc)
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const copHP = th / (th - tc)
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const eta = 1 - tc / th
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let qc: number
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let qh: number
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let w: number
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if (mode === 'fridge') {
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qc = load
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w = qc / copR
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qh = qc + w
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} else if (mode === 'heat_pump') {
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qh = load
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w = qh / copHP
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qc = qh - w
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} else {
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qh = load
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w = eta * qh
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qc = qh - w
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}
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const ratioC = qc / tc
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const ratioH = qh / th
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const entropyOk =
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Number.isFinite(ratioC) &&
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Number.isFinite(ratioH) &&
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Math.abs(ratioC - ratioH) / Math.max(ratioC, ratioH, 1e-9) < 1e-6
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return { ok: true, tc, th, copR, copHP, eta, qc, qh, w, entropyOk }
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}
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/** Convert fridge-stored Qc load ↔ display load for other modes (fixture-compatible). */
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export function fridgeLoadFromModeLoad(
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tc: number,
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th: number,
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modeLoad: number,
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mode: CarnotMode
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): number {
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if (!(th > tc) || !(modeLoad > 0)) return modeLoad
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if (mode === 'fridge') return modeLoad
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if (mode === 'heat_pump') return modeLoad * (tc / th) // Qc = Qh · Tc/Th
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return modeLoad * (tc / th) // engine: Qc = Qh · (1−η) = Qh · Tc/Th
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}
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export function modeLoadFromFridgeLoad(
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tc: number,
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th: number,
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fridgeQc: number,
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mode: CarnotMode
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): number {
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if (!(th > tc) || !(fridgeQc > 0)) return fridgeQc
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if (mode === 'fridge') return fridgeQc
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if (mode === 'heat_pump') return fridgeQc * (th / tc) // Qh = Qc · Th/Tc
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return fridgeQc * (th / tc) // engine Qh = Qc / (1−η) = Qc · Th/Tc
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}
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