Heat Engines
A heat engine is a device that takes in heat Qh from a high-temperature source, converts part of it into work W, and rejects the remainder Qc to a lower-temperature sink, by taking a working substance through a repeated cycle. Its thermal efficiency is η = W/Qh = 1 − Qc/Qh, which the second law limits to the Carnot value 1 − Tc/Th.
Curious
The steam engines of the Industrial Revolution were the first widespread heat engines, and the effort to improve them gave birth to thermodynamics (see Carnot Cycle). Today, petrol and diesel engines, gas turbines in jet engines and power stations, and steam turbines in coal, nuclear and solar-thermal plants are all heat engines.
None of them can turn all their heat into work (see Second Law). A typical car engine converts roughly a quarter to a third of its fuel energy into motion at best, and the rest leaves as hot exhaust and radiator heat. Running an engine backwards gives a refrigerator or heat pump, which uses work to move heat from cold to hot.
Exploring
| Cycle | Used in | Ideal efficiency depends on |
|---|---|---|
| Otto | Petrol (spark-ignition) engines | Compression ratio r, γ |
| Diesel | Diesel (compression-ignition) engines | r and cut-off ratio |
| Rankine | Steam turbines (coal, nuclear, solar-thermal) | Boiler and condenser conditions |
| Brayton | Gas turbines, jet engines | Pressure ratio |
| Stirling | Niche engines, cryocoolers | Can approach Carnot with ideal regenerator |
Deep Dive
Efficiency analysis. For a cycle, ΔU = 0, so W = Qh − Qc (see First Law). Entropy generation by irreversibilities (friction, finite temperature differences, unrestrained expansion) reduces work below the Carnot value; the lost work equals Tc times the entropy generated (the Gouy–Stodola theorem). Combined-cycle gas power plants, which use a gas turbine’s hot exhaust to raise steam for a second turbine, reach about 60% thermal efficiency, among the highest of any large heat engines.
Refrigerators and heat pumps. Reversed engines use work W to move heat Qc from a cold reservoir. Their performance is measured by the coefficient of performance, COPref = Qc/W and COPhp = Qh/W, which can exceed 1 without violating energy conservation because the work moves heat rather than creating it. Carnot limits are Tc/(Th − Tc) and Th/(Th − Tc).
Beyond macroscopic engines. Stochastic thermodynamics extends heat-engine concepts to microscopic systems; single-atom and single-colloid heat engines have been built in laboratories (for example, a single-ion engine reported in 2016) and obey the Carnot bound on average while fluctuating strongly cycle by cycle.
Concept Relationship Map
Requires: Carnot cycle, first law, second law
Enables: refrigerators and heat pumps, power-plant analysis
Commonly confused with: electric motors and fuel cells
Sources
- Rankine, W.J.M. (1859). A Manual of the Steam Engine and Other Prime Movers. London: Griffin.
- Çengel, Y.A., Boles, M.A. (2015). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill.
- Roßnagel, J., et al. (2016). “A single-atom heat engine.” Science, 352, 325–329.