Thermodynamic Efficiency
Thermodynamic efficiency is the ratio of useful output to input for an energy-converting process. The first-law (energy) efficiency ηI compares useful energy out with energy in; the second-law (exergetic) efficiency ηII compares actual performance with the best performance permitted by the second law, using exergy, the maximum useful work obtainable as a system comes to equilibrium with its environment at temperature T0.
Curious
A car engine turns perhaps a quarter to a third of its fuel energy into motion; the rest becomes heat (see Heat Engines). An electric kettle converts nearly all its electricity into heat in the water. Measured this way, the kettle seems far better. But electricity is a high-quality form of energy that could have been used to drive a heat pump delivering three times as much heat (see Refrigerators and Heat Pumps).
The second law says not all energy is equally useful: a joule of electricity or of high-temperature heat can do more work than a joule of lukewarm heat. Second-law efficiency, based on a quantity called exergy, measures this quality as well as quantity.
Exploring
| Device or process | Typical efficiency (first law, approximate) |
|---|---|
| Large electric motor | ~90–97% |
| Combined-cycle gas power plant | ~55–62% |
| Coal-fired power plant | ~33–45% |
| Car petrol engine (peak) | ~25–35% |
| Commercial silicon solar module | ~20–23% |
| Photosynthesis (field crops, light to biomass) | ~1–2% |
Deep Dive
Exergy. The exergy of a system relative to an environment at T0, p0 is X = (U − U0) + p0(V − V0) − T0(S − S0). The Gouy–Stodola theorem states that the exergy destroyed in any process equals T0 times the entropy generated, so second-law analysis locates where irreversibility wastes work (see Entropy). The term “exergy” was coined by Zoran Rant in 1956; the concept is older (Gibbs's available energy, Gouy's énergie utilisable).
Fundamental limits. Heat engines are bounded by the Carnot efficiency (see Carnot Cycle), and finite-power engines are better described by bounds such as the Curzon–Ahlborn efficiency. Single-junction solar cells are bounded by the Shockley–Queisser limit (about 33% for a 1.34 eV band gap under standard sunlight; see P-N Junction), while fuel cells are bounded by ΔG/ΔH of their reaction rather than by Carnot (see Gibbs Free Energy).
Information. Landauer's principle sets a minimum dissipation of kBT ln 2 per erased bit (see Second Law); present-day computers dissipate many orders of magnitude more per operation, so the bound is far from limiting practical computing today.
Concept Relationship Map
Requires: first law, second law
Enables: exergy analysis, energy policy comparisons
Commonly confused with: coefficient of performance
Sources
- Gouy, G. (1889). Journal de Physique, 8, 501–518.
- Shockley, W., Queisser, H.J. (1961). “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells.” Journal of Applied Physics, 32, 510–519.
- Çengel, Y.A., Boles, M.A. (2015). Thermodynamics: An Engineering Approach (8th ed.). McGraw-Hill.