Physics — Otto Cycle (Air-Standard, Worked)

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    {
      "id": "ot-isentropic",
      "type": "note",
      "label": "Isentropic relations do the work: T₂/T₁ = r^(γ−1) = 10^0.4 = 2.512 and P₂/P₁ = r^γ = 10^1.4 = 25.12.",
      "x": 60,
      "y": 60,
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      "fill": "#fef9c3",
      "stroke": "#ca8a04"
    },
    {
      "id": "ot-s2",
      "type": "rounded",
      "label": "② end of compression  ·  754 K  ·  2.51 MPa  ·  V₁/10",
      "x": 340,
      "y": 60,
      "width": 240,
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      "fill": "#fef3c7",
      "stroke": "#b45309"
    },
    {
      "id": "ot-qin",
      "type": "gas-flame",
      "label": "q_in = 800 kJ kg⁻¹ — combustion, modelled at constant volume",
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      "y": 60,
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      "fill": "#dcfce7",
      "stroke": "#15803d"
    },
    {
      "id": "ot-s3",
      "type": "rounded",
      "label": "③ end of combustion  ·  1868 K  ·  6.23 MPa  ·  V₃ = V₂",
      "x": 900,
      "y": 60,
      "width": 240,
      "height": 117,
      "fill": "#fee2e2",
      "stroke": "#b91c1c"
    },
    {
      "id": "ot-state3",
      "type": "note",
      "label": "T₃ = T₂ + q_in/c_v = 754 + 800/0.718 = 1868 K. At constant volume P₃ = P₂ × T₃/T₂ = 6.23 MPa.",
      "x": 1180,
      "y": 60,
      "width": 240,
      "height": 117,
      "fill": "#fef9c3",
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    },
    {
      "id": "ot-wnet",
      "type": "rect",
      "label": "w_net = q_in − q_out = 800 − 318 = 482 kJ kg⁻¹",
      "x": 60,
      "y": 235,
      "width": 240,
      "height": 117,
      "fill": "#fce7f3",
      "stroke": "#be185d"
    },
    {
      "id": "ot-params",
      "type": "note",
      "label": "Compression ratio r = V₁/V₂ = 10  ·  γ = 1.40  ·  c_v = 0.718 kJ kg⁻¹ K⁻¹  ·  working fluid treated as air throughout.",
      "x": 620,
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    },
    {
      "id": "ot-eta",
      "type": "target",
      "label": "η = 1 − r^(1−γ) = 1 − 10^(−0.4) = 60.2 %",
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      "y": 235,
      "width": 240,
      "height": 117,
      "fill": "#fce7f3",
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    },
    {
      "id": "ot-s1",
      "type": "rounded",
      "label": "① intake valve closed  ·  300 K  ·  100 kPa  ·  V₁",
      "x": 340,
      "y": 410,
      "width": 240,
      "height": 117,
      "fill": "#e0f2fe",
      "stroke": "#0369a1"
    },
    {
      "id": "ot-qout",
      "type": "rect",
      "label": "q_out = c_v(T₄ − T₁) = 318 kJ kg⁻¹ rejected to the exhaust",
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      "y": 410,
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      "fill": "#fee2e2",
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    },
    {
      "id": "ot-s4",
      "type": "rounded",
      "label": "④ end of expansion  ·  744 K  ·  248 kPa  ·  V₄ = V₁",
      "x": 900,
      "y": 410,
      "width": 240,
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      "fill": "#fef3c7",
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    },
    {
      "id": "ot-assume",
      "type": "note",
      "label": "Air-standard cold-air assumptions: air as an ideal gas with constant specific heats, combustion replaced by external heat addition, no friction and no heat loss through the walls.",
      "x": 60,
      "y": 585,
      "width": 520,
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      "fill": "#fef9c3",
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    },
    {
      "id": "ot-strokes",
      "type": "note",
      "label": "Four processes, not four strokes: the intake and exhaust strokes are constant-pressure legs that cancel in the idealisation, leaving compression, ignition, power and blow-down.",
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      "y": 585,
      "width": 520,
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      "fill": "#fef9c3",
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    },
    {
      "id": "ot-real",
      "type": "note",
      "label": "Real petrol engines manage 25–35 % brake thermal efficiency. Knock caps r at about 10–12, combustion is neither instantaneous nor at constant volume, and the walls leak heat.",
      "x": 1180,
      "y": 585,
      "width": 240,
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      "fill": "#fef9c3",
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    }
  ],
  "edges": [
    {
      "id": "ot-e1",
      "source": "ot-s1",
      "target": "ot-s2",
      "label": "1→2 isentropic compression, work in"
    },
    {
      "id": "ot-e2",
      "source": "ot-s2",
      "target": "ot-qin"
    },
    {
      "id": "ot-e3",
      "source": "ot-qin",
      "target": "ot-s3",
      "label": "2→3 constant-volume heat addition"
    },
    {
      "id": "ot-e4",
      "source": "ot-s3",
      "target": "ot-s4",
      "label": "3→4 isentropic expansion, the power stroke"
    },
    {
      "id": "ot-e5",
      "source": "ot-s4",
      "target": "ot-qout"
    },
    {
      "id": "ot-e6",
      "source": "ot-qout",
      "target": "ot-s1",
      "label": "4→1 constant-volume heat rejection"
    },
    {
      "id": "ot-e7",
      "source": "ot-qin",
      "target": "ot-wnet",
      "style": "dotted",
      "arrowEnd": false
    },
    {
      "id": "ot-e8",
      "source": "ot-qout",
      "target": "ot-wnet",
      "label": "q_in − q_out",
      "style": "dotted",
      "arrowEnd": false
    },
    {
      "id": "ot-e9",
      "source": "ot-wnet",
      "target": "ot-eta",
      "label": "η = w_net / q_in",
      "style": "dotted",
      "arrowEnd": false
    }
  ]
}