Draft:Lorenz cycle

• Comment: Note that the creator of this draft has used LLMs in a wide variety of areas and has been blocked as a sockpuppet. Ed ^{[talk] [OMT]} 02:28, 17 August 2026 (UTC)

• Comment: Source 1 fails to verify (dead link), and source 2 is not on the Lorenz cycle. It appears that random refs were thrown in based upon the prior declinations. The page also contains vast amounts of irrelevant material (e.g. Lorenz's position), and large numbers of weasel words. If it is submitted yet again in such bad shape I recommend rejection. Ldm1954 (talk) 04:42, 12 July 2026 (UTC)

• Comment: Hey can you please add some more sources to this. As a physicist myself, I understand its hard to cite everything, but please try to conform to encyclopedic guidelines. right now it reads like textbook excerpt Flyingphoenixchips (talk) 23:39, 5 May 2026 (UTC)

• Comment: "Thermodynamics description" is entirely unsourced Warm Regards, Miminity (Talk?) (me contribs) 13:07, 31 January 2026 (UTC)

• Comment: Please link all online sources. User:CabinetCavers ^{(thou shalt speaketh)} 16:13, 15 January 2026 (UTC)

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Not to be confused with Lorenz energy cycle.

The Lorenz cycle is an idealized thermodynamic cycle that defines the maximum coefficient of performance (COP) of a heat pump or refrigeration system exchanging heat with external streams whose temperatures change during heat transfer. It generalizes the Carnot cycle, which assumes heat exchange with constant-temperature reservoirs, to heat sources and heat sinks of finite heat capacity, such as a stream of water or air that is heated or cooled over a temperature range. The finite temperature change of a stream during heat transfer is called a temperature glide.

The cycle is named after the German engineer Hans Lorenz, who derived the corresponding performance limit in 1895. In heat-pump engineering, the Lorenz COP serves as the theoretical upper bound for machines coupled to non-isothermal streams, and the ratio of an actual machine's COP to the Lorenz COP, the Lorenz efficiency, is used as a second-law performance metric in energy planning and process integration studies.

History

Hans Lorenz derived the coefficient of performance of an ideal heat pump process exchanging heat with streams of varying temperature in an 1895 paper, "Die Ermittelung der Grenzwerte der thermodynamischen Energieumwandlung" ("The determination of the limiting values of thermodynamic energy conversion"), published in the Zeitschrift für die gesammte Kälte-Industrie, a refrigeration journal that Lorenz founded and edited. The work formed the basis of his doctoral dissertation at the Ludwig-Maximilians-Universität München. Lorenz's result can be interpreted as the limit of an infinite number of Carnot processes operating in series across the temperature ranges of the source and sink.

Coefficient of performance

The Carnot COP of a heat pump operating between a constant source temperature $T_{C}$ and a constant sink temperature $T_{H}$ is

$\mathrm {COP} _{\mathrm {Carnot} }={\frac {T_{H}}{T_{H}-T_{C}}}.$

For external streams with approximately constant heat capacity, the Lorenz COP replaces the constant temperatures with the logarithmic mean temperatures of the sink and source:

$\mathrm {COP} _{\mathrm {Lorenz} }={\frac {{\bar {T}}_{H}}{{\bar {T}}_{H}-{\bar {T}}_{C}}}$

where, for a sink heated from inlet temperature $T_{H,i}$ to outlet temperature $T_{H,o}$ and a source cooled from $T_{C,i}$ to $T_{C,o}$,

${\bar {T}}_{H}={\frac {T_{H,o}-T_{H,i}}{\ln \!\left({\frac {T_{H,o}}{T_{H,i}}}\right)}}\qquad {\bar {T}}_{C}={\frac {T_{C,i}-T_{C,o}}{\ln \!\left({\frac {T_{C,i}}{T_{C,o}}}\right)}}$

with all temperatures on an absolute scale. When the source and sink temperatures are constant (no temperature glide), the logarithmic mean temperatures reduce to $T_{H}$ and $T_{C}$ and the Lorenz COP reduces to the Carnot COP, so the Carnot cycle is the isothermal special case of the Lorenz cycle.

Because the Lorenz cycle exchanges heat reversibly with the gliding streams, its COP exceeds the Carnot COP evaluated at the most demanding stream temperatures.

Applications

The Carnot cycle is the ideal reversible cycle operating between two thermal reservoirs at fixed temperatures. In many practical heat-pump and refrigeration applications, however, the external fluids do not remain at fixed temperatures. A stream supplying heat to an evaporator may cool as heat is removed, while a stream heated by a condenser may warm as heat is added. The Lorenz cycle accounts for these finite temperature changes by replacing the fixed Carnot reservoir temperatures with thermodynamic mean temperatures.

This distinction is important in applications involving large temperature glides. In such cases, a Carnot comparison based only on inlet or outlet temperatures can understate or overstate the theoretical maximum performance. The Lorenz cycle provides a comparison based on the full temperature profile of the heat source and heat sink.

The Lorenz cycle is used in the analysis of heat-pump systems for industrial process heat, district heating, and other applications involving sensible heat streams . It is also used in studies of heat pumps employing working fluids or mixtures that exhibit temperature glide during evaporation or condensation, including zeotropic refrigerant mixtures.

See also

• Carnot cycle
• Coefficient of performance
• Exergy
• Heat pump and refrigeration cycle
• Temperature glide
• Zeotropic mixture

References

This page will be placed in the following categories if it is moved to the article namespace.

Categories:

• Thermodynamic cycles
• Heat pumps
• Refrigerators