69c99e4f4f
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>
673 lines
20 KiB
TypeScript
673 lines
20 KiB
TypeScript
'use client'
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import { useMemo, useState } from 'react'
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import {
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carnotCycleSimulator as sim,
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fridgeLoadFromModeLoad,
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modeLoadFromFridgeLoad,
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resolveCarnotPhysics,
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type CarnotMode,
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type CarnotQuantity,
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} from '@/lib/simulators/carnot-cycle'
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import { intentColor } from '@/lib/interactive-demo/intent-colors'
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import { useDarkMode } from '@/components/interactive-demo/demo-speak'
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import { SimHeading, SimOutputCard, SimSlider } from './sim-controls'
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import { cn } from '@/lib/utils'
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const SVG_W = 360
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const SVG_H = 270
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type TempUnit = 'K' | 'C' | 'F'
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const TEMP_UNITS: { id: TempUnit; label: string }[] = [
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{ id: 'K', label: 'K' },
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{ id: 'C', label: '°C' },
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{ id: 'F', label: '°F' },
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]
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const MODES: { id: CarnotMode; fr: string; en: string }[] = [
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{ id: 'fridge', fr: 'Frigo', en: 'Fridge' },
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{ id: 'heat_pump', fr: 'PAC', en: 'Heat pump' },
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{ id: 'engine', fr: 'Moteur', en: 'Engine' },
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]
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const QTY: { id: CarnotQuantity; fr: string; en: string }[] = [
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{ id: 'energy', fr: 'Énergie (kJ)', en: 'Energy (kJ)' },
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{ id: 'power', fr: 'Puissance (W)', en: 'Power (W)' },
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]
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function kelvinToDisplay(k: number, unit: TempUnit): number {
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if (unit === 'C') return k - 273.15
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if (unit === 'F') return (k * 9) / 5 - 459.67
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return k
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}
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function displayToKelvin(v: number, unit: TempUnit): number {
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if (unit === 'C') return v + 273.15
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if (unit === 'F') return ((v + 459.67) * 5) / 9
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return v
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}
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function formatTemp(k: number, unit: TempUnit): string {
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const v = kelvinToDisplay(k, unit)
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if (unit === 'K') return `${Math.round(v)} K`
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if (unit === 'C') {
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const r = Math.round(v * 10) / 10
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return `${Number.isInteger(r) ? r : r.toFixed(1)} °C`
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}
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return `${Math.round(v)} °F`
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}
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function tempSliderMeta(
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param: { min: number; max: number; step: number },
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unit: TempUnit
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): { min: number; max: number; step: number; unitLabel: string } {
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if (unit === 'K') {
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return { min: param.min, max: param.max, step: param.step, unitLabel: 'K' }
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}
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if (unit === 'C') {
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return {
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min: Math.round((param.min - 273.15) * 10) / 10,
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max: Math.round((param.max - 273.15) * 10) / 10,
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step: 0.5,
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unitLabel: '°C',
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}
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}
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return {
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min: Math.round(((param.min * 9) / 5 - 459.67) * 10) / 10,
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max: Math.round(((param.max * 9) / 5 - 459.67) * 10) / 10,
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step: 1,
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unitLabel: '°F',
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}
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}
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function formatQty(v: number): string {
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if (!Number.isFinite(v)) return '—'
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if (Math.abs(v - Math.round(v)) < 0.05) return String(Math.round(v))
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return v.toFixed(1)
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}
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function Segmented<T extends string>({
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value,
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onChange,
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options,
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ariaLabel,
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}: {
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value: T
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onChange: (v: T) => void
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options: { id: T; label: string }[]
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ariaLabel: string
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}) {
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return (
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<div
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className="inline-flex max-w-full flex-wrap rounded-lg border border-border/60 bg-background/80 p-0.5"
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role="group"
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aria-label={ariaLabel}
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>
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{options.map((o) => (
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<button
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key={o.id}
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type="button"
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onClick={() => onChange(o.id)}
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className={cn(
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'rounded-md px-2 py-1 text-[11px] font-semibold transition-colors',
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value === o.id
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? 'bg-foreground text-background'
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: 'text-muted-foreground hover:text-foreground'
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)}
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aria-pressed={value === o.id}
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>
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{o.label}
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</button>
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))}
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</div>
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)
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}
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/** Arrowhead + shaft, thickness ∝ |value|/maxRef. */
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function FlowArrow({
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x1,
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y1,
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x2,
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y2,
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value,
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maxRef,
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color,
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label,
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unit,
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labelSide = 'right',
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}: {
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x1: number
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y1: number
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x2: number
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y2: number
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value: number
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maxRef: number
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color: string
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label: string
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unit?: string
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labelSide?: 'left' | 'right' | 'above' | 'below'
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}) {
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const mag = Math.max(0, value)
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const t = 2.2 + (mag / Math.max(1, maxRef)) * 10
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const dx = x2 - x1
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const dy = y2 - y1
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const len = Math.hypot(dx, dy) || 1
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const ux = dx / len
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const uy = dy / len
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const headLen = Math.min(14, Math.max(9, 7 + t * 0.45))
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const headHalf = Math.min(7, 3.2 + t * 0.35)
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const bx = x2 - ux * headLen
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const by = y2 - uy * headLen
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const px = -uy
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const py = ux
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const mx = (x1 + bx) / 2
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const my = (y1 + by) / 2
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const labelGap = 11 + t * 0.45
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let lx = mx
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let ly = my
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let textAnchor: 'start' | 'middle' | 'end' = 'middle'
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if (labelSide === 'above') ly = my - labelGap
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else if (labelSide === 'below') ly = my + labelGap
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else if (labelSide === 'right') {
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lx = mx + labelGap
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textAnchor = 'start'
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} else {
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lx = mx - labelGap
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textAnchor = 'end'
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}
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return (
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<g>
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<line
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x1={x1}
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y1={y1}
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x2={bx}
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y2={by}
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stroke={color}
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strokeWidth={t}
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strokeLinecap="round"
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opacity={0.9}
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/>
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<polygon
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points={`${x2},${y2} ${bx + px * headHalf},${by + py * headHalf} ${bx - px * headHalf},${by - py * headHalf}`}
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fill={color}
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opacity={0.95}
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/>
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<text
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x={lx}
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y={ly}
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fontSize={11}
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fill={color}
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fontWeight={600}
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dominantBaseline="middle"
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textAnchor={textAnchor}
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>
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{label} {formatQty(value)}
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{unit ? ` ${unit}` : ''}
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</text>
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</g>
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)
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}
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export function CarnotCycleView({
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preset,
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disclaimer,
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lang,
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}: {
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preset?: Record<string, number>
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title?: string
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disclaimer?: string
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lang: string
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}) {
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const fr = lang.startsWith('fr')
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const dark = useDarkMode()
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const [tempUnit, setTempUnit] = useState<TempUnit>('K')
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const [mode, setMode] = useState<CarnotMode>('fridge')
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const [qty, setQty] = useState<CarnotQuantity>('energy')
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const [values, setValues] = useState<Record<string, number>>(() => {
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const env: Record<string, number> = {}
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for (const p of sim.params) env[p.id] = preset?.[p.id] ?? p.defaultValue
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return env
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})
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const phys = useMemo(
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() =>
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resolveCarnotPhysics(
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values.t_cold,
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values.t_hot,
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modeLoadFromFridgeLoad(values.t_cold, values.t_hot, values.q_cold, mode),
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mode
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),
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[values.t_cold, values.t_hot, values.q_cold, mode]
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)
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const unitE = qty === 'energy' ? 'kJ' : 'W'
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const workName =
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qty === 'energy'
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? fr
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? 'Travail'
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: 'Work'
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: fr
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? 'Puissance'
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: 'Power'
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const maxRef = Math.max(phys.qh || 0, phys.qc || 0, phys.w || 0, 1)
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const cHot = intentColor('warning', dark)
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const cCold = intentColor('cache', dark)
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const cWork = intentColor('compute', dark)
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const text = dark ? '#e4e4e7' : '#27272a'
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const cx = SVG_W / 2 - 20
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const hotY = 28
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const coldY = SVG_H - 42
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const midY = SVG_H / 2 - 4
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const r = 32
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const qOffset = 42
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const isEngine = mode === 'engine'
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const loadMeta = useMemo(() => {
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if (mode === 'fridge') {
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return {
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symbol: qty === 'energy' ? 'Q_c' : '\\dot{Q}_c',
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label: fr ? 'Chaleur extraite (froid)' : 'Heat extracted (cold)',
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hint: fr
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? 'Charge utile du réfrigérateur'
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: 'Useful fridge cooling load',
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}
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}
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if (mode === 'heat_pump') {
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return {
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symbol: qty === 'energy' ? 'Q_h' : '\\dot{Q}_h',
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label: fr ? 'Chaleur fournie (chaud)' : 'Heat delivered (hot)',
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hint: fr ? 'Charge utile de la PAC' : 'Useful heat-pump output',
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}
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}
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return {
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symbol: qty === 'energy' ? 'Q_h' : '\\dot{Q}_h',
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label: fr ? 'Chaleur absorbée (chaud)' : 'Heat absorbed (hot)',
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hint: fr ? 'Entrée thermique du moteur' : 'Engine heat input',
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}
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}, [mode, qty, fr])
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const modeLoad = modeLoadFromFridgeLoad(
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values.t_cold,
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values.t_hot,
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values.q_cold,
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mode
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)
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const workSym = qty === 'energy' ? 'W' : 'P'
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const qLabel = (base: 'c' | 'h') => (qty === 'energy' ? `Q_${base}` : `Q̇_${base}`)
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const lawLine = !phys.ok
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? fr
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? 'Il faut T_h > T_c (températures absolues).'
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: 'Need T_h > T_c (absolute temperatures).'
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: fr
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? `1ᵉʳ principe : ${qLabel('h')} = ${qLabel('c')} + ${workSym} → ${formatQty(phys.qh)} = ${formatQty(phys.qc)} + ${formatQty(phys.w)} ${unitE}`
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: `1st law: ${qLabel('h')} = ${qLabel('c')} + ${workSym} → ${formatQty(phys.qh)} = ${formatQty(phys.qc)} + ${formatQty(phys.w)} ${unitE}`
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return (
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<div>
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<div className="mb-3 flex flex-wrap items-center gap-2">
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<Segmented
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value={mode}
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onChange={setMode}
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ariaLabel={fr ? 'Mode machine' : 'Machine mode'}
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options={MODES.map((m) => ({ id: m.id, label: fr ? m.fr : m.en }))}
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/>
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<Segmented
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value={qty}
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onChange={setQty}
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ariaLabel={fr ? 'Énergie ou puissance' : 'Energy or power'}
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options={QTY.map((q) => ({ id: q.id, label: fr ? q.fr : q.en }))}
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/>
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<Segmented
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value={tempUnit}
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onChange={setTempUnit}
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ariaLabel={fr ? 'Unité de température' : 'Temperature unit'}
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options={TEMP_UNITS.map((u) => ({ id: u.id, label: u.label }))}
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/>
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</div>
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<div className="grid gap-5 md:grid-cols-[minmax(0,1.1fr)_minmax(0,1fr)]">
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<div>
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<svg
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viewBox={`0 0 ${SVG_W} ${SVG_H}`}
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className="mx-auto w-full max-w-md"
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role="img"
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aria-label={fr ? sim.title.fr : sim.title.en}
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>
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<rect
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x={cx - 105}
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y={hotY - 18}
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width={210}
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height={34}
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rx={10}
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fill={`${cHot}14`}
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stroke={cHot}
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strokeWidth={1.5}
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/>
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<text
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x={cx}
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y={hotY}
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textAnchor="middle"
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fontSize={11.5}
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fontWeight={600}
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fill={cHot}
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dominantBaseline="middle"
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>
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{fr ? 'Source chaude' : 'Hot'} · T_h = {formatTemp(values.t_hot, tempUnit)}
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</text>
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<rect
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x={cx - 105}
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y={coldY - 18}
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width={210}
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height={34}
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rx={10}
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fill={`${cCold}14`}
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stroke={cCold}
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strokeWidth={1.5}
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/>
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<text
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x={cx}
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y={coldY}
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textAnchor="middle"
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fontSize={11.5}
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fontWeight={600}
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fill={cCold}
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dominantBaseline="middle"
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>
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{fr ? 'Source froide' : 'Cold'} · T_c ={' '}
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{formatTemp(values.t_cold, tempUnit)}
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</text>
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<circle
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cx={cx}
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cy={midY}
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r={r}
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fill={dark ? '#141820' : '#ffffff'}
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stroke={text}
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strokeWidth={1.5}
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/>
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<text
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x={cx}
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y={midY}
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textAnchor="middle"
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fontSize={11}
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fontWeight={600}
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fill={text}
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dominantBaseline="middle"
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>
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{fr ? 'Machine' : 'Engine'}
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</text>
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{phys.ok && !isEngine ? (
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<>
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{/* Fridge / PAC: Qc↑ into machine, W→ into machine, Qh↑ to hot */}
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<FlowArrow
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x1={cx - qOffset}
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y1={coldY - 22}
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x2={cx - qOffset}
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y2={midY + r + 2}
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value={phys.qc}
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maxRef={maxRef}
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color={cCold}
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label={qLabel('c')}
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unit={unitE}
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labelSide="left"
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/>
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<FlowArrow
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x1={cx + qOffset}
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y1={midY - r - 2}
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x2={cx + qOffset}
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y2={hotY + 22}
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value={phys.qh}
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maxRef={maxRef}
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color={cHot}
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label={qLabel('h')}
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unit={unitE}
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/>
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<FlowArrow
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x1={cx + r + 78}
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y1={midY}
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x2={cx + r + 4}
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y2={midY}
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value={phys.w}
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maxRef={maxRef}
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color={cWork}
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label={workSym}
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unit={unitE}
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labelSide="above"
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/>
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</>
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) : null}
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{phys.ok && isEngine ? (
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<>
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{/* Engine: Qh↓ from hot into machine, W→ out, Qc↓ to cold */}
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<FlowArrow
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x1={cx + qOffset}
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y1={hotY + 22}
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x2={cx + qOffset}
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y2={midY - r - 2}
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value={phys.qh}
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maxRef={maxRef}
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color={cHot}
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label={qLabel('h')}
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unit={unitE}
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/>
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<FlowArrow
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x1={cx - qOffset}
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y1={midY + r + 2}
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x2={cx - qOffset}
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y2={coldY - 22}
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value={phys.qc}
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maxRef={maxRef}
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color={cCold}
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label={qLabel('c')}
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unit={unitE}
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labelSide="left"
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/>
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<FlowArrow
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x1={cx + r + 4}
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y1={midY}
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x2={cx + r + 78}
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y2={midY}
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value={phys.w}
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maxRef={maxRef}
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color={cWork}
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label={workSym}
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unit={unitE}
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labelSide="above"
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/>
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</>
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) : null}
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<text x={10} y={SVG_H - 10} fontSize={10} fill={dark ? '#8b8b93' : '#6b7280'}>
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{fr
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? qty === 'energy'
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? 'Épaisseur ∝ énergie (kJ) — W = travail (pas le watt)'
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: 'Épaisseur ∝ puissance — P et W (watt) = même unité ici'
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: qty === 'energy'
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? 'Thickness ∝ energy (kJ) — W = work (not the watt)'
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: 'Thickness ∝ power — P uses watts'}
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</text>
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</svg>
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<p className="mt-2 text-center text-[11px] text-muted-foreground">{lawLine}</p>
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{phys.ok && phys.entropyOk ? (
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<p className="mt-1 text-center text-[10px] text-muted-foreground/80">
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{fr
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? '2ᵉ principe (réversible) : Q_c/T_c = Q_h/T_h'
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: '2nd law (reversible): Q_c/T_c = Q_h/T_h'}
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</p>
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) : null}
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</div>
|
|
|
|
<div className="space-y-3">
|
|
<div>
|
|
<SimHeading>{fr ? 'Paramètres' : 'Parameters'}</SimHeading>
|
|
<div className="space-y-2">
|
|
{sim.params
|
|
.filter((p) => p.id === 't_cold' || p.id === 't_hot')
|
|
.map((p) => {
|
|
const meta = tempSliderMeta(p, tempUnit)
|
|
const displayVal = kelvinToDisplay(values[p.id], tempUnit)
|
|
return (
|
|
<SimSlider
|
|
key={`${p.id}-${tempUnit}`}
|
|
symbol={p.symbol}
|
|
label={fr ? p.label.fr : p.label.en}
|
|
unit={meta.unitLabel}
|
|
min={meta.min}
|
|
max={meta.max}
|
|
step={meta.step}
|
|
value={
|
|
tempUnit === 'K'
|
|
? Math.round(displayVal)
|
|
: Math.round(displayVal * 10) / 10
|
|
}
|
|
intent={p.intent}
|
|
onChange={(v) => {
|
|
const k = displayToKelvin(v, tempUnit)
|
|
const clamped = Math.min(p.max, Math.max(p.min, k))
|
|
setValues((s) => ({ ...s, [p.id]: clamped }))
|
|
}}
|
|
/>
|
|
)
|
|
})}
|
|
|
|
<SimSlider
|
|
key={`load-${mode}-${qty}`}
|
|
symbol={loadMeta.symbol}
|
|
label={loadMeta.label}
|
|
unit={unitE}
|
|
min={10}
|
|
max={500}
|
|
step={5}
|
|
value={Math.round(modeLoad * 10) / 10}
|
|
intent="flow"
|
|
onChange={(v) => {
|
|
const fridgeQc = fridgeLoadFromModeLoad(
|
|
values.t_cold,
|
|
values.t_hot,
|
|
v,
|
|
mode
|
|
)
|
|
setValues((s) => ({
|
|
...s,
|
|
q_cold: Math.min(500, Math.max(10, fridgeQc)),
|
|
}))
|
|
}}
|
|
/>
|
|
<p className="px-1 text-[10px] text-muted-foreground">{loadMeta.hint}</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div>
|
|
<SimHeading>
|
|
{fr ? 'Résultats (limites de Carnot)' : 'Results (Carnot limits)'}
|
|
</SimHeading>
|
|
<div className="grid grid-cols-2 gap-2">
|
|
{mode === 'fridge' || mode === 'heat_pump' ? (
|
|
<>
|
|
<SimOutputCard
|
|
symbol={String.raw`\mathrm{COP}_{R}`}
|
|
label={fr ? 'COP frigo' : 'Fridge COP'}
|
|
value={phys.copR}
|
|
intent="output"
|
|
digits={2}
|
|
/>
|
|
<SimOutputCard
|
|
symbol={String.raw`\mathrm{COP}_{HP}`}
|
|
label={fr ? 'COP PAC' : 'Heat-pump COP'}
|
|
value={phys.copHP}
|
|
intent="output"
|
|
digits={2}
|
|
/>
|
|
</>
|
|
) : (
|
|
<SimOutputCard
|
|
symbol={String.raw`\eta`}
|
|
label={fr ? 'Rendement moteur' : 'Engine efficiency'}
|
|
value={phys.eta * 100}
|
|
unit="%"
|
|
intent="highlight"
|
|
digits={1}
|
|
/>
|
|
)}
|
|
<SimOutputCard
|
|
symbol={workSym}
|
|
label={
|
|
isEngine
|
|
? fr
|
|
? `${workName} fourni`
|
|
: `${workName} out`
|
|
: fr
|
|
? `${workName} minimale`
|
|
: `Minimum ${workName.toLowerCase()}`
|
|
}
|
|
value={phys.w}
|
|
unit={unitE}
|
|
intent="compute"
|
|
digits={1}
|
|
/>
|
|
<SimOutputCard
|
|
symbol={
|
|
qty === 'energy' ? String.raw`Q_h` : String.raw`\dot{Q}_h`
|
|
}
|
|
label={
|
|
isEngine
|
|
? fr
|
|
? 'Chaleur absorbée'
|
|
: 'Heat absorbed'
|
|
: fr
|
|
? 'Chaleur côté chaud'
|
|
: 'Hot-side heat'
|
|
}
|
|
value={phys.qh}
|
|
unit={unitE}
|
|
intent="flow"
|
|
digits={1}
|
|
/>
|
|
<SimOutputCard
|
|
symbol={
|
|
qty === 'energy' ? String.raw`Q_c` : String.raw`\dot{Q}_c`
|
|
}
|
|
label={
|
|
isEngine
|
|
? fr
|
|
? 'Chaleur rejetée (froid)'
|
|
: 'Heat rejected (cold)'
|
|
: fr
|
|
? 'Chaleur côté froid'
|
|
: 'Cold-side heat'
|
|
}
|
|
value={phys.qc}
|
|
unit={unitE}
|
|
intent="cache"
|
|
digits={1}
|
|
/>
|
|
</div>
|
|
<p className="mt-2 text-[10px] leading-relaxed text-muted-foreground">
|
|
{qty === 'energy'
|
|
? fr
|
|
? 'W = travail (énergie en kJ), pas le watt. Passe en « Puissance (W) » pour raisonner en watts.'
|
|
: 'W = work (energy in kJ), not the watt. Switch to “Power (W)” to use watts.'
|
|
: fr
|
|
? 'Mode puissance : P, Q̇_c et Q̇_h sont en watts (W). Les COP / η restent sans unité.'
|
|
: 'Power mode: P, Q̇_c and Q̇_h are in watts (W). COP / η stay dimensionless.'}
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
{disclaimer ? (
|
|
<p className="mt-3 text-xs italic text-muted-foreground">{disclaimer}</p>
|
|
) : null}
|
|
</div>
|
|
)
|
|
}
|