Endoreversible thermodynamics is a subset of irreversible

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...

aimed at making more realistic assumptions about

heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy ( heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conducti ...

than are typically made in reversible thermodynamics. It gives an 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 A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodyna ...

, and accommodates the

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, reaching maximum entropy. When the surroundings are the reservoir, exergy is the pot ...

destruction occurring as heat is transferred irreversibly. Endoreversible thermodynamics was discovered in simultaneous work by Novikov and Chambadal,Chambadal P (1957) ''Les centrales nucléaires''. Armand Colin, Paris, France, 4 1-58 although sometimes mistakenly attributed to Curzon & Ahlborn.

Novikov engine

An equation for the efficiency of a semi-ideal

heat engine In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower stat ...

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: ::

\eta = 1 - \sqrt

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 temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...

s must be used) gives the following results:Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed. ed.). John Wiley & Sons, Inc.. . As shown, the endoreversible efficiency much more closely models the observed data. However, such an engine violates Carnot's principle which states that work can be done any time there is a difference in temperature. The fact that the hot and cold reservoirs are not at the same temperature as the working fluid they are in contact with means that work can and is done at the hot and cold reservoirs. The result is tantamount to coupling the high and low temperature parts of the cycle, so that the cycle collapses.B. H. Lavenda, Am. J. Phys., vol. 75, pp. 169-175 (2007) In the Carnot cycle there is strict necessity that the working fluid be at the same temperatures as the heat reservoirs they are in contact with and that they are separated by adiabatic transformations which prevent thermal contact. The efficiency was first derived by William ThomsonW. Thomson, Phil. Mag. (Feb. 1853) in his study of an unevenly heated body in which the adiabatic partitions between bodies at different temperatures are removed and maximum work is performed. It is well known that the final temperature is the geometric mean temperature

\sqrt

so that the efficiency is the Carnot efficiency for an engine working between

T_H

and

\sqrt

. Due to occasional confusion about the origins of the above equation, it is sometimes named the Chambadal–Novikov–Curzon–Ahlborn efficiency.

References

{{DEFAULTSORT:Endoreversible Thermodynamics Thermodynamics

Novikov engine

See also

References