Physical Transformation AtlasPTA
Constraint · constraint:carnot-limit

Carnot limit

No engine taking heat from a hot reservoir and rejecting it to a cold one can beat the Carnot efficiency. Evaluated only against an efficiency datum that records the absolute hot- and cold-side temperatures it was measured between.

Atlas record: 16 claims reference this constraint — 15 established and 1 demonstrated.

Explorerelations · sources · cite

η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c

16claims0enumerated routes0routes with complete-composition evidence0candidate routes not searched15cited sources

Relations

bounded by · 16
Alkali-metal thermal-to-electric conversion—bounded by→Carnot limitdemonstrated
Magnetohydrodynamic generation—bounded by→Carnot limitestablished
  • when the flow is produced by a thermal expansion
Ionic thermoelectric effect—bounded by→Carnot limitestablished
Thermal shape-memory effect—bounded by→Carnot limitestablished
  • applies when the shape-memory effect is operated cyclically as a heat engine between hot and cold reservoirs; it does not bound a one-shot thermally triggered shape-recovery event
Thermochemical redox cycle—bounded by→Carnot limitestablished
  • for an ideal solar thermochemical process the heat-to-work (exergy) factor is bounded by 1 − T_L/T_H, with T_H the receiver/process temperature and T_L the heat-rejection reservoir, usually the environment; T_L is not in general the re-oxidation temperature; the receiver absorption efficiency multiplies this factor
Spin Seebeck effect—bounded by→Carnot limitestablished
Seebeck effect—bounded by→Carnot limitestablished
Thermionic emission—bounded by→Carnot limitestablished
Thermoacoustic effect—bounded by→Carnot limitestablished
Pyroelectric effect—bounded by→Carnot limitestablished
Thermogalvanic effect—bounded by→Carnot limitestablished
Thermally regenerative electrochemical cycle—bounded by→Carnot limitestablished
Thermomagnetic (Curie-point) transition—bounded by→Carnot limitestablished
Working-fluid expansion (heat-engine cycle)—bounded by→Carnot limitestablished
Ocean thermal energy conversion—bounded by→Carnot limitestablished
  • Carnot efficiency ≈ 7% for 300 K against 280 K
Temperature gradient—bounded by→Carnot limitestablished
  • conversion of a heat flow between reservoirs at T_h and T_c into work or a non-thermal free energy; the bound is evaluated against a datum that records both temperatures

Cited sources · 15

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    Science 221, 915–920 · doi:10.1126/science.221.4614.915 · crossref ✓ 2026-09-19 · record
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    R. J. Rosa. Physical principles of magnetohydrodynamic power generation (1961)
    Physics of Fluids 4, 182–194 · doi:10.1063/1.1724426 · crossref ✓ 2026-09-19 · record
  3. [3]
    A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)
    Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
  4. [4]
    D. Zhao, A. Würger, X. Crispin. Ionic thermoelectric materials and devices (2021)
    Journal of Energy Chemistry 61, 88-103 · doi:10.1016/j.jechem.2021.02.022 · crossref ✓ 2026-09-20 · record
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    P. Kumar et al.. Shape memory alloy engine for high efficiency low-temperature gradient thermal to electrical conversion (2019)
    Applied Energy 251, 113277 · doi:10.1016/j.apenergy.2019.05.080 · crossref ✓ 2026-09-20 · record
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    A. Steinfeld. Solar thermochemical production of hydrogen––a review (2005)
    Solar Energy 78, 603-615 · doi:10.1016/j.solener.2003.12.012 · crossref ✓ 2026-09-20 · record
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    G. E. W. Bauer, E. Saitoh, B. J. van Wees. Spin caloritronics (2012)
    Nature Materials 11, 391–399 · doi:10.1038/nmat3301 · crossref ✓ 2026-09-19 · record
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    H. J. Goldsmid. Introduction to Thermoelectricity (2nd ed.) (2016)
    Springer Series in Materials Science 121 · doi:10.1007/978-3-662-49256-7 · crossref ✓ 2026-09-19 · record
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    G. N. Hatsopoulos, E. P. Gyftopoulos. Thermionic Energy Conversion, Vol. 1: Processes and Devices (1973)
    MIT Press · book, no DOI · record
  10. [10]
    G. W. Swift. Thermoacoustic engines (1988)
    Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
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    C. R. Bowen et al.. Pyroelectric materials and devices for energy harvesting applications (2014)
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    T. I. Quickenden, Y. Mua. A review of power generation in aqueous thermogalvanic cells (1995)
    Journal of the Electrochemical Society 142, 3985 · doi:10.1149/1.2048446 · crossref ✓ 2026-09-19 · record
  13. [13]
    S. W. Lee et al.. An electrochemical system for efficiently harvesting low-grade heat energy (2014)
    Nature Communications 5, 3942 · doi:10.1038/ncomms4942 · crossref ✓ 2026-09-19 · record
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    R. A. Kishore, S. Priya. A review on design and performance of thermomagnetic devices (2018)
    Renewable and Sustainable Energy Reviews 81, 33–44 · doi:10.1016/j.rser.2017.07.035 · crossref ✓ 2026-09-19 · record
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    H. B. Callen. The application of Onsager's reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects (1948)
    Physical Review 73, 1349 · doi:10.1103/PhysRev.73.1349 · crossref ✓ 2026-09-19 · record

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