Endoreversible thermodynamics
Encyclopedia
Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer
than are typically made in reversible thermodynamics
. It gives a upper bound on the energy that can be derived from a real process that is lower than that predicted by Carnot for a Carnot cycle
, and accommodates the exergy
destruction occurring as heat is transferred irreversibly.
Endoreversible thermodynamics was discovered in simultanenous work by Novikov and Chambadal, although sometimes mistakenly attributed to Curzon & Ahlborn .
An equation for the efficiency of a semi-ideal heat engine
operating at maximum power output in which heat transfer is irreversible but other components are ideal can be shown to have the following form, which is the Chambadal-Novikov efficiency:
In the limit of infinitesimally small power output, the standard Carnot result for efficiency is recovered. For some typical cycles, the above equation (note that absolute temperatures must be used) gives the following results:
As shown, the endoreversible efficiency much more closely models the observed data.
Due to occasional confusion about the origins of the above equation, it is sometimes named the Chambadal-Novikov-Curzon-Ahlborn efficiency.
An introduction to endoreversible thermodynamics is given in the thesis by Katharina Wagner. It is also introduced by Hoffman et al.. A thorough discussion of the concept, together with many applications in engineering, is given in the book by Hans Ulrich Fuchs.
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...
than are typically made in reversible thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
. It gives a upper bound on the energy that can be derived from a real process that is lower than that predicted by Carnot for a Carnot cycle
Carnot cycle
The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...
, and accommodates the exergy
Exergy
In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its...
destruction occurring as heat is transferred irreversibly.
Endoreversible thermodynamics was discovered in simultanenous work by Novikov and Chambadal, although sometimes mistakenly attributed to Curzon & Ahlborn .
Novikov engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...
operating at maximum power output in which heat transfer is irreversible but other components are ideal can be shown to have the following form, which is the Chambadal-Novikov efficiency:
In the limit of infinitesimally small power output, the standard Carnot result for efficiency is recovered. For some typical cycles, the above equation (note that absolute temperatures must be used) gives the following results:
| Power Plant |  (°C) |  (°C) |  (Carnot) |  (Endoreversible) |  (Observed) |
|---|---|---|---|---|---|
| West Thurrock West Thurrock West Thurrock is a traditional Church of England parish and town in Thurrock, Essex, England, located 17.5 miles east south-east of Charing Cross, London.-Location:... (UK United Kingdom The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages... ) coal-fired power plant Fossil fuel power plant A fossil-fuel power station is a power station that burns fossil fuels such as coal, natural gas or petroleum to produce electricity. Central station fossil-fuel power plants are designed on a large scale for continuous operation... |
25 | 565 | 0.64 | 0.40 | 0.36 |
| CANDU CANDU reactor The CANDU reactor is a Canadian-invented, pressurized heavy water reactor. The acronym refers to its deuterium-oxide moderator and its use of uranium fuel... (Canada Canada Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean... ) nuclear power plant Nuclear power plant A nuclear power plant is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity.Nuclear power plants are usually... |
25 | 300 | 0.48 | 0.28 | 0.30 |
| Larderello Larderello Larderello is a frazione of the comune of Pomarance, in Tuscany in central Italy. It is a geologically active area, renowned for its geothermal productivity.- Geography :... (Italy Italy Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and... ) geothermal power plant Geothermal power Geothermal energy is thermal energy generated and stored in the Earth. Thermal energy is the energy that determines the temperature of matter. Earth's geothermal energy originates from the original formation of the planet and from radioactive decay of minerals... |
80 | 250 | 0.33 | 0.178 | 0.16 |
As shown, the endoreversible efficiency much more closely models the observed data.
Due to occasional confusion about the origins of the above equation, it is sometimes named the Chambadal-Novikov-Curzon-Ahlborn efficiency.
See also
Heat engineHeat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...
An introduction to endoreversible thermodynamics is given in the thesis by Katharina Wagner. It is also introduced by Hoffman et al.. A thorough discussion of the concept, together with many applications in engineering, is given in the book by Hans Ulrich Fuchs.