A machine that converts heat energy into work is called a heat engine. Thermal efficiency indicates how efficiently the conversion can be performed.
Basic Knowledge
A heat engine (heat engine) absorbs heat Q₁ from a high-temperature reservoir, converts part of it into work W, and releases the remaining heat Q₂ to a low-temperature reservoir (waste heat).W = Q₁ - Q₂
Thermal efficiency e:e = W / Q₁ = (Q₁ - Q₂) / Q₁
Thermal efficiency is always 0 < e < 1 (= 0–100%).
Second law of thermodynamics: Heat naturally flows only from high temperature → low temperature. A heat engine with 100% thermal efficiency (a perpetual-motion machine of the second kind) cannot be realized. Even an ideal heat engine has a maximum value called Carnot efficiency:e_max = 1 - T₂/T₁(T₁ and T₂ are the absolute temperatures of the high- and low-temperature reservoirs)
Real heat engines (automobile engines about 25–35%, thermal power generation about 40–50%) have lower efficiencies than the Carnot efficiency.
Heat engine (heat engine)（A machine that converts heat into work, such as a steam engine or internal-combustion engine）
Thermal efficiency e（Work/absorbed heat = W/Q₁. Always less than 1）
Carnot efficiency（Maximum efficiency of an ideal heat engine. e = 1 - T₂/T₁）
Second law of thermodynamics（Heat naturally moves from high temperature → low temperature. 100% thermal efficiency is impossible）
Perpetual-motion machine of the second kind（An engine that absorbs heat from a low-temperature reservoir and converts all of it into work. Impossible）
Waste heat（Heat Q₂ that a heat engine cannot convert into work and releases to the low-temperature reservoir）
Further Study (Background and Significance)
The second law of thermodynamics is also a law that indicates the “arrow of time.” Coffee cooling is the natural direction (increasing entropy), but cooled coffee does not naturally become hot. The amount of energy does not change (the first law), but the “quality” of energy (how easily it can be used) continually decreases.
The Carnot efficiency was derived in 1824 by the French physicist Carnot. The greater the temperature difference between the high- and low-temperature reservoirs, the higher the efficiency. In supercritical-pressure power generation, raising the steam temperature increases the Carnot efficiency and improves generation efficiency.
A heat pump (an air conditioner or refrigerator) operates in the reverse manner of a heat engine, using external work to move heat from low temperature → high temperature. This is why an air conditioner can move three to six times as much heat energy indoors as the electrical energy it consumes (coefficient of performance COP).
- W = Q₁ - Q₂ (absorbed heat - waste heat)
- Thermal efficiency e = W/Q₁ (0 < e < 1)
- Carnot efficiency: e_max = 1 - T₂/T₁
- 100% thermal efficiency is impossible (second law)
- The greater the high–low temperature difference, the higher the efficiency ↑
- Automobile engines: ~30%, thermal power generation: ~40%
- A heat pump operates in the reverse manner of a heat engine
Important Notes (Common Confusions)
① Thermal efficiency is W/Q₁, not W/Q₂ (the denominator is the “absorbed heat quantity”). ② T in the Carnot efficiency formula is absolute temperature (K). Using ℃ gives an incorrect result. ③ “Thermal efficiency = 1” (100%) is impossible according to the second law of thermodynamics. It does not violate the law of conservation of energy, but it is thermodynamically impossible. ④ The “efficiency (COP)” of a heat pump is different from the thermal efficiency of a heat engine and can exceed 1.
Practice
- A heat engine absorbs 1000 J of heat from a high-temperature reservoir and releases 400 J as waste heat. Find its thermal efficiency.
- Find the maximum thermal efficiency of a Carnot engine with a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K.
- Explain, using the second law of thermodynamics, why “a heat engine with 100% thermal efficiency cannot be realized.”