Heat engines, heat pumps and Carnot efficiency
PhysicsThermal Physics & GasesAges 17–18
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An ideal gas runs a Carnot, Otto or Diesel cycle between a hot reservoir at T_h and a cold reservoir at T_c on a p–V diagram. A Sankey diagram shows the heat taken in Q_h, the work W and the heat rejected Q_c; the efficiency η = W/Q_h always stays below the Carnot limit 1 − T_c/T_h, and the entropy change ΔS = Q/T of each reservoir is shown. A reversed mode turns the cycle into a refrigerator or heat pump with its coefficient of performance.
Lesson: Heat engines and the second law of thermodynamics
What it shows
A heat engine takes heat Q_h from a hot reservoir, turns part of it into work W and rejects the rest, Q_c, to a cold reservoir. Its efficiency η = W/Q_h can never reach 100 %: the Kelvin–Planck statement of the second law. The best possible engine between temperatures T_h and T_c (in kelvin) is the reversible Carnot engine, with η = 1 − T_c/T_h. Run backwards, the cycle becomes a refrigerator or heat pump. The model uses 0.040 mol of ideal gas and slow, reversible processes; Otto and Diesel are air-standard cycles.
How to use
Choose the Cycle and the Gas, set the Hot reservoir temperature T_h and the Cold reservoir temperature T_c, and watch the gas go round the p–V loop. Press Record cycle to add the current cycle to the table and graph; repeat with other temperatures. Add Losses to see a real engine. Open the Refrigerator / heat pump tab to see the coefficient of performance, then open Tasks to check yourself.
Parameters you can change
- Mode Heat engine, Refrigerator / heat pump
- Cycle Carnot, Otto (petrol engine), Diesel
- Hot reservoir temperature T_h 250–2500 K
- Cold reservoir temperature T_c 200–600 K
- Isothermal expansion ratio (Carnot) 1.5–5
- Compression ratio (Otto, Diesel) 2–25
- Gas Air, Monatomic gas
- Losses (friction, heat leaks) 0–40 %
Questions to explore
- Why can no engine working between 600 K and 300 K have an efficiency above 50 %?
- How does the efficiency of an Otto engine change when the compression ratio r increases?
- Why does a heat pump work best when the outside air is only a little colder than the room?
