Endoreversible thermodynamics

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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^[1] and Chambadal^[2], although sometimes mistakenly attributed to Curzon & Ahlborn ^[3].

Novikov engine

Novikov engine showing irreversible heat transfer between T_H and T_iH, coupled to a Carnot cycle operating between T_iH and T_C^[4].

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^[5], which is the Chambadal-Novikov efficiency:

$\eta = 1 - \sqrt{\frac{T_L}{T_H}}$

In the limit of infinitesimally small power output, the standard Carnot result for efficiency is recovered^[4]. For some typical cycles, the above equation (note that absolute temperatures must be used) gives the following results^[3][6]:

Power Plant	Tc (°C)	Th (°C)	η (Carnot)	η (Endoreversible)	η (Observed)
West Thurrock (UK) coal-fired power plant	25	565	0.64	0.40	0.36
CANDU (Canada) nuclear power plant	25	300	0.48	0.28	0.30
Larderello (Italy) geothermal power plant	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 engine

An introduction to endoreversible thermodynamics is given in the thesis by Katharina Wagner^[4]. It is also introduced by Hoffman et al.^[7][8]. A thorough discussion of the concept, together with many applications in engineering, is given in the book by Hans Ulrich Fuchs^[9].

References

1. ^ I. I. Novikov. The Efficiency of Atomic Power Stations. Journal Nuclear Energy II, 7:125–128, 1958. translated from Atomnaya Energiya, 3 (1957), 409.
2. ^ Chambadal P (1957) Les centrales nucléaires. Armand Colin, Paris, France, 4 1-58
3. ^ ^{a b} F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22–24 (1975)
4. ^ ^{a b c} M.Sc. Katharina Wagner, A graphic based interface to Endoreversible Thermodynamics, TU Chemnitz, Fakultät für Naturwissenschaften, Masterarbeit (in English). http://archiv.tu-chemnitz.de/pub/2008/0123/index.html
5. ^ A Bejan, J. Appl. Phys., vol. 79, pp. 1191–1218, 1 Feb. 1996 http://dx.doi.org/10.1016/S0035-3159(96)80059-6
6. ^ Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed. ed.). John Wiley & Sons, Inc.. ISBN 0-471-86256-8.
7. ^ K. H. Hoffmann. An introduction to endoreversible thermodynamics. Atti dell Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali, pages 1–19, 2007.
8. ^ K. H. Hoffmann, J. M. Burzler, and S. Schubert. Endoreversible Thermodynamics. J. Non-Equilib. Thermodyn., 22(4):311–355, 1997.
9. ^ H. U. Fuchs, The Dynamics of Heat (sec. ed.), chapter 9. Graduate Texts in Physics, Springer 2011, ISBN 978-1-4419-7623-1