<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      width: 100%;
      height: 100%;
      justify-content: space-between;
    }

    /* Top interactive stage cards */
    .stages-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 8px;
      flex: 1;
      min-height: 160px;
    }

    .stage-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 8px 4px;
      position: relative;
      cursor: pointer;
      transition: border-color 0.25s ease, box-shadow 0.25s ease;
    }

    .stage-card.active {
      border-color: #2563eb;
      box-shadow: 0 0 0 2px rgba(37, 99, 235, 0.15);
    }

    .stage-title {
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .stage-svg {
      width: 100%;
      height: 90px;
    }

    .stage-val {
      font-size: 13px;
      font-weight: 600;
      color: #1e2945;
      background: #f1f5f9;
      padding: 2px 8px;
      border-radius: 4px;
      font-family: ui-monospace, SFMono-Regular, Menlo, monospace;
    }

    /* Live animation bar / controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
    }

    .btn {
      background: #1e2945;
      color: #ffffff;
      border: none;
      border-radius: 6px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: background 0.2s ease;
    }

    .btn:active {
      background: #2563eb;
    }

    /* Equation Summary Badge */
    .equation-badge {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 10px 12px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      flex-wrap: wrap;
      gap: 12px;
    }

    .eq-item {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 14px;
      font-weight: 700;
    }

    .eq-label {
      color: #64748b;
      font-size: 12px;
      text-transform: uppercase;
      font-weight: 600;
    }

    .math-formula {
      font-family: ui-monospace, SFMono-Regular, Menlo, monospace;
      color: #1e2945;
      font-size: 14px;
      letter-spacing: -0.2px;
    }

    .crimson {
      color: #e11d48;
    }

    .blue {
      color: #2563eb;
    }

    /* Wall visual styling in SVG */
    .wall-hatch {
      stroke: #94a3b8;
      stroke-width: 1.5;
    }
  </style>
</head>
<body>

  
  <div class="stages-grid">
    
    
    <div class="stage-card active" id="card-0" onclick="setStep(0)">
      <div class="stage-title">1. Approach</div>
      <svg class="stage-svg" viewBox="0 0 120 80">
        
        <rect x="105" y="5" width="10" height="70" fill="#cbd5e1" rx="1"/>
        <line x1="105" y1="15" x2="115" y2="5" class="wall-hatch"/>
        <line x1="105" y1="35" x2="115" y2="25" class="wall-hatch"/>
        <line x1="105" y1="55" x2="115" y2="45" class="wall-hatch"/>
        <line x1="105" y1="75" x2="115" y2="65" class="wall-hatch"/>
        <line x1="105" y1="5" x2="105" y2="75" stroke="#64748b" stroke-width="2"/>

        
        <line x1="10" y1="40" x2="35" y2="40" stroke="#93c5fd" stroke-dasharray="3,3" stroke-width="2"/>
        
        
        <circle cx="45" cy="40" r="11" fill="#2563eb"/>
        <circle cx="42" cy="37" r="3.5" fill="#93c5fd"/>

        
        <defs>
          <marker id="arr-blue" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
            <path d="M0,0 L6,3 L0,6 Z" fill="#2563eb"/>
          </marker>
          <marker id="arr-red" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
            <path d="M0,0 L6,3 L0,6 Z" fill="#e11d48"/>
          </marker>
        </defs>
        <line x1="45" y1="40" x2="80" y2="40" stroke="#2563eb" stroke-width="2.5" marker-end="url(#arr-blue)"/>
        <text x="62" y="30" font-size="11" font-weight="700" fill="#2563eb" text-anchor="middle">+v<tspan dy="2" font-size="8">x</tspan></text>
      </svg>
      <div class="stage-val">p<sub style="font-size:9px">i</sub> = +mv<sub style="font-size:9px">x</sub></div>
    </div>

    
    <div class="stage-card" id="card-1" onclick="setStep(1)">
      <div class="stage-title">2. Collision</div>
      <svg class="stage-svg" viewBox="0 0 120 80">
        
        <rect x="105" y="5" width="10" height="70" fill="#cbd5e1" rx="1"/>
        <line x1="105" y1="15" x2="115" y2="5" class="wall-hatch"/>
        <line x1="105" y1="35" x2="115" y2="25" class="wall-hatch"/>
        <line x1="105" y1="55" x2="115" y2="45" class="wall-hatch"/>
        <line x1="105" y1="75" x2="115" y2="65" class="wall-hatch"/>
        <line x1="105" y1="5" x2="105" y2="75" stroke="#64748b" stroke-width="2"/>

        
        <ellipse cx="96" cy="40" rx="9" ry="12" fill="#2563eb"/>
        <circle cx="93" cy="37" r="3" fill="#93c5fd"/>

        
        <line x1="96" y1="40" x2="48" y2="40" stroke="#e11d48" stroke-width="3" marker-end="url(#arr-red)"/>
        <text x="68" y="30" font-size="11" font-weight="800" fill="#e11d48" text-anchor="middle">F<tspan dy="3" font-size="8">wall</tspan></text>
        
        
        <text x="96" y="68" font-size="10" font-weight="700" fill="#e11d48" text-anchor="middle">Δt</text>
      </svg>
      <div class="stage-val crimson">J = F · Δt</div>
    </div>

    
    <div class="stage-card" id="card-2" onclick="setStep(2)">
      <div class="stage-title">3. Rebound</div>
      <svg class="stage-svg" viewBox="0 0 120 80">
        
        <rect x="105" y="5" width="10" height="70" fill="#cbd5e1" rx="1"/>
        <line x1="105" y1="15" x2="115" y2="5" class="wall-hatch"/>
        <line x1="105" y1="35" x2="115" y2="25" class="wall-hatch"/>
        <line x1="105" y1="55" x2="115" y2="45" class="wall-hatch"/>
        <line x1="105" y1="75" x2="115" y2="65" class="wall-hatch"/>
        <line x1="105" y1="5" x2="105" y2="75" stroke="#64748b" stroke-width="2"/>

        
        <line x1="100" y1="40" x2="65" y2="40" stroke="#93c5fd" stroke-dasharray="3,3" stroke-width="2"/>

        
        <circle cx="55" cy="40" r="11" fill="#2563eb"/>
        <circle cx="52" cy="37" r="3.5" fill="#93c5fd"/>

        
        <line x1="55" y1="40" x2="18" y2="40" stroke="#2563eb" stroke-width="2.5" marker-end="url(#arr-blue)"/>
        <text x="36" y="30" font-size="11" font-weight="700" fill="#2563eb" text-anchor="middle">-v<tspan dy="2" font-size="8">x</tspan></text>
      </svg>
      <div class="stage-val">p<sub style="font-size:9px">f</sub> = -mv<sub style="font-size:9px">x</sub></div>
    </div>

  </div>

  
  <div class="controls">
    <button class="btn" id="playBtn" onclick="togglePlay()">
      <span id="playIcon">⏸</span> Auto-Play
    </button>
  </div>

  
  <div class="equation-badge">
    <div class="eq-item">
      <span class="eq-label">Impulse:</span>
      <span class="math-formula">J = Δp = <span class="crimson">-2mv<sub>x</sub></span></span>
    </div>
    <div class="eq-item">
      <span class="eq-label">Wall Force:</span>
      <span class="math-formula"><span class="crimson">F<sub>wall</sub></span> = <span class="blue">2mv<sub>x</sub></span> / <span class="crimson">Δt</span></span>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    function setStep(index) {
      currentStep = index;
      for (let i = 0; i < 3; i++) {
        const card = document.getElementById(`card-${i}`);
        if (i === currentStep) {
          card.classList.add('active');
        } else {
          card.classList.remove('active');
        }
      }
    }

    function nextStep() {
      setStep((currentStep + 1) % 3);
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      document.getElementById('playIcon').textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        nextStep();
      }, 3000);
    }

    startTimer();
  </script>
</body>
</html>

Kinetic Molecular Theory and Pressure-Volume Gas Behavior

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .comparison-grid {
      display: flex;
      flex-direction: row;
      justify-content: center;
      align-items: flex-end;
      gap: 16px;
      width: 100%;
      max-width: 520px;
    }
    .cylinder-panel {
      flex: 1;
      display: flex;
      flex-direction: column;
      align-items: center;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px 8px 10px;
    }
    .metrics {
      display: flex;
      justify-content: space-between;
      width: 100%;
      padding: 0 4px;
      font-size: 14px;
      font-weight: 700;
      margin-bottom: 8px;
    }
    .val-vol {
      color: #0284c7;
    }
    .val-press {
      color: #ea580c;
    }
    .svg-container {
      width: 100%;
      max-width: 170px;
      height: 200px;
    }
    .counter-badge {
      margin-top: 8px;
      font-size: 12px;
      font-weight: 600;
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      padding: 4px 8px;
      border-radius: 6px;
      color: #475569;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .counter-badge strong {
      color: #ea580c;
    }
    .summary-bar {
      margin-top: 14px;
      background: #f1f5f9;
      border-radius: 8px;
      padding: 8px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      text-align: center;
      max-width: 520px;
      width: 100%;
    }
    .summary-bar span {
      color: #ea580c;
    }
  </style>
</head>
<body>

  <div class="comparison-grid">
    
    <div class="cylinder-panel">
      <div class="metrics">
        <span class="val-vol">V = 2.0 L</span>
        <span class="val-press">P = 1.0 atm</span>
      </div>
      <svg class="svg-container" viewBox="0 0 160 200">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#ea580c" />
          </marker>
        </defs>

        
        <rect x="14" y="16" width="132" height="174" rx="2" fill="#f8fafc" stroke="#94a3b8" stroke-width="4" stroke-dasharray="0 0" />
        <line x1="12" y1="16" x2="148" y2="16" stroke="#f8fafc" stroke-width="6" />

        
        <rect x="18" y="24" width="124" height="14" rx="3" fill="#64748b" />
        <rect x="74" y="4" width="12" height="20" fill="#64748b" rx="2" />
        <path d="M 80 2 L 80 18" stroke="#334155" stroke-width="2" stroke-linecap="round" />

        
        
        <line x1="42" y1="65" x2="28" y2="51" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="42" cy="65" r="5.5" fill="#0284c7" />

        
        <line x1="118" y1="75" x2="132" y2="61" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="118" cy="75" r="5.5" fill="#0284c7" />

        
        <line x1="68" y1="110" x2="88" y2="110" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="68" cy="110" r="5.5" fill="#0284c7" />

        
        <line x1="120" y1="140" x2="106" y2="154" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="120" cy="140" r="5.5" fill="#0284c7" />

        
        <line x1="45" y1="155" x2="45" y2="135" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="45" cy="155" r="5.5" fill="#0284c7" />

        
        <line x1="95" y1="172" x2="109" y2="158" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="95" cy="172" r="5.5" fill="#0284c7" />
      </svg>
      <div class="counter-badge">
        <span>⚡</span> <strong>10</strong> hits / ms
      </div>
    </div>

    
    <div class="cylinder-panel">
      <div class="metrics">
        <span class="val-vol">V = 1.0 L</span>
        <span class="val-press">P = 2.0 atm</span>
      </div>
      <svg class="svg-container" viewBox="0 0 160 200">
        
        <rect x="14" y="16" width="132" height="174" rx="2" fill="#f8fafc" stroke="#94a3b8" stroke-width="4" />
        <line x1="12" y1="16" x2="148" y2="16" stroke="#f8fafc" stroke-width="6" />

        
        <line x1="60" y1="62" x2="60" y2="92" stroke="#ea580c" stroke-width="2" marker-end="url(#arrow)" />
        <line x1="100" y1="62" x2="100" y2="92" stroke="#ea580c" stroke-width="2" marker-end="url(#arrow)" />

        
        <rect x="18" y="102" width="124" height="14" rx="3" fill="#64748b" />
        <rect x="74" y="10" width="12" height="92" fill="#64748b" rx="2" />

        
        
        <line x1="42" y1="130" x2="28" y2="116" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="42" cy="130" r="5.5" fill="#0284c7" />

        
        <line x1="118" y1="132" x2="132" y2="118" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="118" cy="132" r="5.5" fill="#0284c7" />

        
        <line x1="72" y1="145" x2="92" y2="145" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="72" cy="145" r="5.5" fill="#0284c7" />

        
        <line x1="120" y1="162" x2="106" y2="176" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="120" cy="162" r="5.5" fill="#0284c7" />

        
        <line x1="45" y1="172" x2="45" y2="152" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="45" cy="172" r="5.5" fill="#0284c7" />

        
        <line x1="88" y1="176" x2="102" y2="162" stroke="#ea580c" stroke-width="2.5" marker-end="url(#arrow)" />
        <circle cx="88" cy="176" r="5.5" fill="#0284c7" />
      </svg>
      <div class="counter-badge">
        <span>⚡</span> <strong>20</strong> hits / ms
      </div>
    </div>
  </div>

  <div class="summary-bar">
    Shorter travel path → <span>2× collision rate</span> → <span>2× Pressure</span>
  </div>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Kinetic Theory: Pressure Derivation</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 8px 12px;
      width: 100%;
      min-height: 100%;
    }

    .container {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    /* Diagram visual container - seamless without outer card borders */
    .visual-box {
      width: 100%;
      position: relative;
      overflow: visible;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Particle animation along x-axis in isometric projection */
    @keyframes bounceIsoX {
      0%, 100% {
        transform: translate(249px, 137.5px);
      }
      50% {
        transform: translate(171px, 92.5px);
      }
    }

    #particleGroup {
      animation: bounceIsoX 2.8s ease-in-out infinite;
    }

    /* Step display cards */
    .steps-container {
      position: relative;
      min-height: 105px;
    }

    .step-card {
      position: absolute;
      inset: 0;
      background: #f8fafc;
      border-left: 4px solid #cbd5e1;
      border-radius: 6px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      justify-content: center;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.25s ease, border-color 0.25s ease;
    }

    .step-card.active {
      opacity: 1;
      pointer-events: auto;
      border-left-color: #0284c7;
    }

    .step-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      margin-bottom: 6px;
    }

    .step-badge {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 2px 8px;
      border-radius: 4px;
      background: #e0f2fe;
      color: #0284c7;
    }

    .step-target {
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
    }

    .formula {
      font-family: "Cambria Math", "Times New Roman", Georgia, serif;
      font-size: 16px;
      font-weight: 600;
      color: #1e2945;
      text-align: center;
      letter-spacing: 0.3px;
      line-height: 1.4;
    }

    .highlight-cyan { color: #0284c7; font-weight: 700; }
    .highlight-amber { color: #d97706; font-weight: 700; }

    /* Interactive controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      margin-top: 2px;
    }

    .nav-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #1e2945;
      border-radius: 6px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: background 0.15s ease, border-color 0.15s ease;
    }

    .nav-btn:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }

    .dots-nav {
      display: flex;
      gap: 8px;
    }

    .dot {
      width: 9px;
      height: 9px;
      border-radius: 50%;
      background: #cbd5e1;
      border: none;
      cursor: pointer;
      padding: 0;
      transition: background 0.2s ease;
    }

    .dot.active {
      background: #0284c7;
    }

    .dot:hover {
      background: #94a3b8;
    }

    .dot.active:hover {
      background: #0284c7;
    }

    @media (max-width: 400px) {
      .formula {
        font-size: 14px;
      }
      .nav-btn {
        padding: 5px 10px;
        font-size: 12px;
      }
    }
  </style>
</head>
<body>
  <div class="container">
    
    <div class="visual-box">
      <svg viewBox="0 0 420 235">
        <defs>
          
          <linearGradient id="wallBack" x1="0%" y1="0%" x2="100%" y2="100%">
            <stop offset="0%" stop-color="#38bdf8" stop-opacity="0.30"/>
            <stop offset="100%" stop-color="#0284c7" stop-opacity="0.12"/>
          </linearGradient>
          <linearGradient id="wallFront" x1="0%" y1="0%" x2="100%" y2="100%">
            <stop offset="0%" stop-color="#f59e0b" stop-opacity="0.32"/>
            <stop offset="100%" stop-color="#d97706" stop-opacity="0.10"/>
          </linearGradient>
          
          <radialGradient id="pGrad" cx="35%" cy="35%" r="65%">
            <stop offset="0%" stop-color="#38bdf8"/>
            <stop offset="60%" stop-color="#0284c7"/>
            <stop offset="100%" stop-color="#0369a1"/>
          </radialGradient>
        </defs>

        
        <polygon points="210,25 132,70 132,160 210,115" fill="url(#wallBack)" stroke="#0284c7" stroke-width="1.6" stroke-dasharray="4,3"/>

        
        <line x1="210" y1="25" x2="288" y2="70" stroke="#cbd5e1" stroke-width="1.2" stroke-dasharray="3,3"/>
        <line x1="210" y1="115" x2="210" y2="205" stroke="#cbd5e1" stroke-width="1.2" stroke-dasharray="3,3"/>
        <line x1="210" y1="115" x2="288" y2="160" stroke="#cbd5e1" stroke-width="1.2" stroke-dasharray="3,3"/>

        
        <line x1="171" y1="92.5" x2="249" y2="137.5" stroke="#f59e0b" stroke-width="1.6" stroke-dasharray="3,3"/>

        
        <g id="particleGroup">
          <circle cx="0" cy="0" r="6" fill="url(#pGrad)"/>
          
          <line x1="0" y1="0" x2="16" y2="9.2" stroke="#0284c7" stroke-width="2"/>
          <polygon points="19,11 12,6 15,13" fill="#0284c7"/>
          <text x="-4" y="-8" font-size="11" font-weight="700" fill="#0284c7" font-style="italic">v<tspan font-size="8" dy="2">x</tspan></text>
        </g>

        
        <polygon points="288,70 210,115 210,205 288,160" fill="url(#wallFront)" stroke="#d97706" stroke-width="1.8"/>

        
        
        <line x1="132" y1="70" x2="210" y2="115" stroke="#1e2945" stroke-width="1.8"/>
        <line x1="210" y1="25" x2="132" y2="70" stroke="#1e2945" stroke-width="1.8"/>
        <line x1="210" y1="25" x2="288" y2="70" stroke="#1e2945" stroke-width="1.8"/>
        
        
        <line x1="132" y1="70" x2="132" y2="160" stroke="#1e2945" stroke-width="1.8"/>
        <line x1="288" y1="70" x2="288" y2="160" stroke="#1e2945" stroke-width="1.8"/>
        
        
        <line x1="132" y1="160" x2="210" y2="205" stroke="#1e2945" stroke-width="1.8"/>
        <line x1="210" y1="205" x2="288" y2="160" stroke="#1e2945" stroke-width="1.8"/>

        
        <line x1="126" y1="169" x2="204" y2="214" stroke="#64748b" stroke-width="1.2"/>
        <line x1="122" y1="166" x2="129" y2="173" stroke="#64748b" stroke-width="1.2"/>
        <line x1="201" y1="210" x2="208" y2="218" stroke="#64748b" stroke-width="1.2"/>
        <text x="157" y="200" font-size="12" font-weight="700" fill="#1e2945" font-style="italic">L</text>

        
        <line x1="298" y1="70" x2="298" y2="160" stroke="#64748b" stroke-width="1.2"/>
        <line x1="294" y1="70" x2="302" y2="70" stroke="#64748b" stroke-width="1.2"/>
        <line x1="294" y1="160" x2="302" y2="160" stroke="#64748b" stroke-width="1.2"/>
        <text x="306" y="119" font-size="12" font-weight="700" fill="#1e2945" font-style="italic">L</text>

        
        <text x="175" y="128" font-size="11" font-weight="700" fill="#d97706">2L round-trip</text>

        
        <text x="50" y="80" font-size="11" font-weight="700" fill="#0284c7">Wall A = L²</text>
        <path d="M 115,77 L 140,85" fill="none" stroke="#0284c7" stroke-width="1" stroke-dasharray="2,2"/>

        
        <text x="312" y="188" font-size="11" font-weight="700" fill="#d97706">Wall A = L²</text>
        <path d="M 310,185 L 275,175" fill="none" stroke="#d97706" stroke-width="1" stroke-dasharray="2,2"/>

        
        <text x="330" y="42" font-size="12" font-weight="700" fill="#1e2945">Volume<tspan x="330" y="56" font-size="11" font-weight="600" fill="#64748b">V = L³</tspan></text>
        <path d="M 324,45 L 265,55" fill="none" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2"/>
      </svg>
    </div>

    
    <div class="steps-container">
      
      <div class="step-card active" id="stepCard0">
        <div class="step-header">
          <span class="step-badge">Step 1 of 3</span>
          <span class="step-target">Collision Time Period</span>
        </div>
        <div class="formula">
          &Delta;t = <span class="highlight-amber">2L</span> / <span class="highlight-cyan">v<sub>x</sub></span>
        </div>
      </div>

      
      <div class="step-card" id="stepCard1">
        <div class="step-header">
          <span class="step-badge">Step 2 of 3</span>
          <span class="step-target">Single Particle Force</span>
        </div>
        <div class="formula">
          F<sub>single</sub> = &Delta;p / &Delta;t = 2mv<sub>x</sub> / (2L / v<sub>x</sub>) = <span class="highlight-cyan">m v<sub>x</sub>²</span> / <span class="highlight-amber">L</span>
        </div>
      </div>

      
      <div class="step-card" id="stepCard2">
        <div class="step-header">
          <span class="step-badge">Step 3 of 3</span>
          <span class="step-target">Total Gas Pressure</span>
        </div>
        <div class="formula">
          P = F<sub>total</sub> / L² = (N m &lang;v<sub>x</sub>²&rang;) / <span class="highlight-amber">L³</span> = <span class="highlight-cyan">(N m &lang;v<sub>x</sub>²&rang;) / V</span>
        </div>
      </div>
    </div>

    
    <div class="controls">
      <button class="nav-btn" id="playBtn" aria-label="Play or Pause">
        <span id="playIcon">⏸</span> Auto
      </button>
      <div class="dots-nav">
        <button class="dot active" data-idx="0" aria-label="Step 1"></button>
        <button class="dot" data-idx="1" aria-label="Step 2"></button>
        <button class="dot" data-idx="2" aria-label="Step 3"></button>
      </div>
      <button class="nav-btn" id="nextBtn">
        Next →
      </button>
    </div>
  </div>

  <script>
    const totalSteps = 3;
    let currentStep = 0;
    let isPlaying = true;
    let autoInterval = null;

    const cards = [
      document.getElementById('stepCard0'),
      document.getElementById('stepCard1'),
      document.getElementById('stepCard2')
    ];
    const dots = document.querySelectorAll('.dot');
    const playBtn = document.getElementById('playBtn');
    const playIcon = document.getElementById('playIcon');
    const nextBtn = document.getElementById('nextBtn');

    function setStep(idx) {
      currentStep = (idx + totalSteps) % totalSteps;
      cards.forEach((c, i) => c.classList.toggle('active', i === currentStep));
      dots.forEach((d, i) => d.classList.toggle('active', i === currentStep));
    }

    function nextStep() {
      setStep(currentStep + 1);
    }

    function startAuto() {
      isPlaying = true;
      playIcon.textContent = '⏸';
      clearInterval(autoInterval);
      autoInterval = setInterval(nextStep, 3500);
    }

    function pauseAuto() {
      isPlaying = false;
      playIcon.textContent = '▶';
      clearInterval(autoInterval);
    }

    function toggleAuto() {
      if (isPlaying) pauseAuto();
      else startAuto();
    }

    playBtn.addEventListener('click', toggleAuto);
    nextBtn.addEventListener('click', () => {
      pauseAuto();
      nextStep();
    });

    dots.forEach((dot, idx) => {
      dot.addEventListener('click', () => {
        pauseAuto();
        setStep(idx);
      });
    });

    startAuto();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      background: #f8f9fa;
      color: #1e2945;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .main-grid {
      display: grid;
      grid-template-columns: 1.1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 660px;
      align-items: center;
    }

    @media (max-width: 520px) {
      .main-grid {
        grid-template-columns: 1fr;
      }
    }

    /* Simulation Container */
    .sim-panel {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
    }

    .canvas-wrapper {
      position: relative;
      width: 100%;
      aspect-ratio: 1 / 1;
      max-width: 270px;
      background: #ffffff;
      border: 2px solid #0284c7;
      border-radius: 12px;
      overflow: hidden;
      box-shadow: inset 0 2px 6px rgba(2, 132, 199, 0.08);
    }

    canvas {
      display: block;
      width: 100%;
      height: 100%;
    }

    .temp-control {
      display: flex;
      align-items: center;
      gap: 8px;
      background: #ffffff;
      padding: 4px 12px;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
      font-size: 13px;
      font-weight: 600;
      color: #1e2945;
    }

    .temp-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 50%;
      width: 24px;
      height: 24px;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      font-size: 14px;
      font-weight: bold;
      color: #0284c7;
      user-select: none;
    }
    .temp-btn:active { background: #e2e8f0; }

    /* Postulate Cards */
    .cards-list {
      display: flex;
      flex-direction: column;
      gap: 6px;
      width: 100%;
    }

    .postulate-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-left: 4px solid #0284c7;
      border-radius: 8px;
      padding: 7px 10px;
      display: flex;
      align-items: center;
      gap: 10px;
      cursor: pointer;
      transition: background 0.2s ease, border-color 0.2s ease;
      user-select: none;
    }

    .postulate-card.active {
      background: #f0f9ff;
      border-color: #0284c7;
      border-left: 4px solid #0284c7;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.15);
    }

    .badge-num {
      width: 22px;
      height: 22px;
      min-width: 22px;
      border-radius: 50%;
      background: #e0f2fe;
      color: #0284c7;
      font-size: 12px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .postulate-card.active .badge-num {
      background: #0284c7;
      color: #ffffff;
    }

    .card-text {
      display: flex;
      flex-direction: column;
    }

    .card-title {
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
      line-height: 1.2;
    }

    .card-desc {
      font-size: 11px;
      color: #64748b;
      line-height: 1.2;
      margin-top: 1px;
    }

    .hint-bar {
      font-size: 11px;
      color: #64748b;
      margin-top: 4px;
      text-align: center;
    }
  </style>
</head>
<body>

<div class="main-grid">
  
  <div class="sim-panel">
    <div class="canvas-wrapper">
      <canvas id="gasCanvas" width="300" height="300"></canvas>
    </div>
    <div class="temp-control">
      <span>Temp (K):</span>
      <button class="temp-btn" id="coolBtn">−</button>
      <span id="tempVal" style="min-width: 38px; text-align: center; color: #0284c7;">300 K</span>
      <button class="temp-btn" id="heatBtn">+</button>
    </div>
  </div>

  
  <div class="cards-list" id="cardList">
    <div class="postulate-card active" data-id="0">
      <div class="badge-num">1</div>
      <div class="card-text">
        <div class="card-title">Point Masses</div>
        <div class="card-desc">Particle size is negligible vs container</div>
      </div>
    </div>

    <div class="postulate-card" data-id="1">
      <div class="badge-num">2</div>
      <div class="card-text">
        <div class="card-title">Random Motion</div>
        <div class="card-desc">Straight lines until collisions</div>
      </div>
    </div>

    <div class="postulate-card" data-id="2">
      <div class="badge-num">3</div>
      <div class="card-text">
        <div class="card-title">No Forces</div>
        <div class="card-desc">Zero attraction or repulsion</div>
      </div>
    </div>

    <div class="postulate-card" data-id="3">
      <div class="badge-num">4</div>
      <div class="card-text">
        <div class="card-title">Elastic Collisions</div>
        <div class="card-desc">Total kinetic energy is conserved</div>
      </div>
    </div>

    <div class="postulate-card" data-id="4">
      <div class="badge-num">5</div>
      <div class="card-text">
        <div class="card-title">Temp ∝ Avg KE</div>
        <div class="card-desc">Higher Kelvin = faster speed</div>
      </div>
    </div>
  </div>
</div>
<div class="hint-bar">Tap any postulate to highlight visual focus</div>

<script>
  const canvas = document.getElementById('gasCanvas');
  const ctx = canvas.getContext('2d');
  const width = 300;
  const height = 300;

  let activePostulate = 0;
  let temp = 300; // Kelvin
  let speedMultiplier = 1.0;

  // 9 Gas particles
  const numParticles = 9;
  const radius = 6;
  const particles = [];

  // Initialize particles spread out
  const cols = 3, rows = 3;
  for (let i = 0; i < numParticles; i++) {
    const c = i % cols;
    const r = Math.floor(i / cols);
    const angle = Math.random() * Math.PI * 2;
    const baseSpeed = 2.2 + Math.random() * 0.8;
    particles.push({
      x: 50 + c * 90 + (Math.random() * 20 - 10),
      y: 50 + r * 90 + (Math.random() * 20 - 10),
      vx: Math.cos(angle) * baseSpeed,
      vy: Math.sin(angle) * baseSpeed,
      trail: [],
      collisionFlash: 0
    });
  }

  // Cards interaction
  const cards = document.querySelectorAll('.postulate-card');
  cards.forEach((card) => {
    card.addEventListener('click', () => {
      cards.forEach(c => c.classList.remove('active'));
      card.classList.add('active');
      activePostulate = parseInt(card.getAttribute('data-id'), 10);
    });
  });

  // Temperature controls
  const tempVal = document.getElementById('tempVal');
  document.getElementById('coolBtn').addEventListener('click', () => {
    temp = Math.max(100, temp - 50);
    tempVal.textContent = temp + ' K';
    speedMultiplier = Math.sqrt(temp / 300);
    setActiveCard(4);
  });
  document.getElementById('heatBtn').addEventListener('click', () => {
    temp = Math.min(600, temp + 50);
    tempVal.textContent = temp + ' K';
    speedMultiplier = Math.sqrt(temp / 300);
    setActiveCard(4);
  });

  function setActiveCard(index) {
    cards.forEach((c, idx) => {
      c.classList.toggle('active', idx === index);
    });
    activePostulate = index;
  }

  // Physics update & render loop
  function animate() {
    ctx.clearRect(0, 0, width, height);

    // Update positions
    for (let i = 0; i < particles.length; i++) {
      const p = particles[i];

      p.x += p.vx * speedMultiplier;
      p.y += p.vy * speedMultiplier;

      // Wall collisions (elastic)
      if (p.x - radius < 0) {
        p.x = radius;
        p.vx = -p.vx;
        p.collisionFlash = 8;
      } else if (p.x + radius > width) {
        p.x = width - radius;
        p.vx = -p.vx;
        p.collisionFlash = 8;
      }
      if (p.y - radius < 0) {
        p.y = radius;
        p.vy = -p.vy;
        p.collisionFlash = 8;
      } else if (p.y + radius > height) {
        p.y = height - radius;
        p.vy = -p.vy;
        p.collisionFlash = 8;
      }

      // Record trail for Postulate 2 (Random Motion in straight lines)
      p.trail.push({ x: p.x, y: p.y });
      if (p.trail.length > 18) p.trail.shift();
    }

    // Particle-to-particle collisions (elastic)
    for (let i = 0; i < particles.length; i++) {
      for (let j = i + 1; j < particles.length; j++) {
        const p1 = particles[i];
        const p2 = particles[j];
        const dx = p2.x - p1.x;
        const dy = p2.y - p1.y;
        const dist = Math.hypot(dx, dy);

        if (dist < radius * 2) {
          // Normal & Tangent vectors
          const nx = dx / dist;
          const ny = dy / dist;

          // Relative velocity
          const kx = p1.vx - p2.vx;
          const ky = p1.vy - p2.vy;
          const p = 2 * (nx * kx + ny * ky) / 2;

          p1.vx -= p * nx;
          p1.vy -= p * ny;
          p2.vx += p * nx;
          p2.vy += p * ny;

          // Separate overlapping spheres
          const overlap = (radius * 2 - dist) / 2;
          p1.x -= nx * overlap;
          p1.y -= ny * overlap;
          p2.x += nx * overlap;
          p2.y += ny * overlap;

          p1.collisionFlash = 10;
          p2.collisionFlash = 10;
        }
      }
    }

    // Draw paths if activePostulate == 1 (Random straight-line motion)
    if (activePostulate === 1) {
      for (const p of particles) {
        if (p.trail.length > 1) {
          ctx.beginPath();
          ctx.moveTo(p.trail[0].x, p.trail[0].y);
          for (let k = 1; k < p.trail.length; k++) {
            ctx.lineTo(p.trail[k].x, p.trail[k].y);
          }
          ctx.strokeStyle = 'rgba(2, 132, 199, 0.35)';
          ctx.lineWidth = 2;
          ctx.stroke();
        }
      }
    }

    // Draw particles
    for (const p of particles) {
      // Elastic collision visual impulse
      if (activePostulate === 3 && p.collisionFlash > 0) {
        ctx.beginPath();
        ctx.arc(p.x, p.y, radius + 5, 0, Math.PI * 2);
        ctx.strokeStyle = `rgba(2, 132, 199, ${p.collisionFlash / 10})`;
        ctx.lineWidth = 2;
        ctx.stroke();
      }

      ctx.beginPath();
      // If postulate 0 (point masses), draw extra small with high empty space contrast
      const r = activePostulate === 0 ? 3.5 : radius;
      ctx.arc(p.x, p.y, r, 0, Math.PI * 2);

      if (activePostulate === 4) {
        // Color based on temperature (cool blue to warm orange/red)
        const heatRatio = (temp - 100) / 500;
        const red = Math.round(2 + heatRatio * 220);
        const blue = Math.round(199 * (1 - heatRatio * 0.7));
        ctx.fillStyle = `rgb(${red}, 130, ${blue})`;
      } else {
        ctx.fillStyle = '#0284c7';
      }
      ctx.fill();

      // Velocity vectors for Random Motion (Postulate 2)
      if (activePostulate === 1) {
        ctx.beginPath();
        ctx.moveTo(p.x, p.y);
        ctx.lineTo(p.x + p.vx * 6, p.y + p.vy * 6);
        ctx.strokeStyle = '#0369a1';
        ctx.lineWidth = 2;
        ctx.stroke();
      }

      if (p.collisionFlash > 0) p.collisionFlash--;
    }

    // Overlay visual indicator tag inside canvas
    ctx.fillStyle = '#1e2945';
    ctx.font = '600 12px system-ui, sans-serif';
    ctx.textAlign = 'right';
    if (activePostulate === 0) {
      ctx.fillText('99.9% Empty Space', width - 10, 22);
    } else if (activePostulate === 1) {
      ctx.fillText('Straight Lines →', width - 10, 22);
    } else if (activePostulate === 2) {
      ctx.fillText('No Attractions (F = 0)', width - 10, 22);
    } else if (activePostulate === 3) {
      ctx.fillText('ΔKE = 0 (Conserved)', width - 10, 22);
    } else if (activePostulate === 4) {
      ctx.fillText('KE_avg = 3/2 kT', width - 10, 22);
    }

    requestAnimationFrame(animate);
  }

  animate();
</script>

</body>
</html>

OGS.11.PS.BD.4

Aligned learning resources

Related diagrams