Living anionic polymerization: Difference between revisions

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{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}
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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 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]], and accommodates the [[exergy]] destruction occurring as heat is transferred irreversibly.
 
Endoreversible thermodynamics was discovered in simultaneous work by Novikov<ref name="Novikov1958">I. I. Novikov. ''The Efficiency of Atomic Power Stations''. Journal Nuclear Energy II, 7:125–128, 1958. translated from Atomnaya Energiya, 3 (1957), 409.</ref> and Chambadal,<ref name="Chambadal1957">Chambadal P (1957) ''Les centrales nucléaires''. Armand Colin, Paris, France, 4 1-58</ref> although sometimes mistakenly attributed to Curzon & Ahlborn. <ref name="Curzon1975">F.L. Curzon and B. Ahlborn, American Journal of Physics, vol. 43, pp. 22–24 (1975)</ref>
 
== Novikov engine ==
 
[[File:NovikovEngine.png|500px|thumb|right|Novikov engine showing irreversible heat transfer between T_H and T_iH, coupled to a [[Carnot cycle]] operating between T_iH and T_C.<ref name="Wagner2008"/>]]
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,<ref name="Bejan1996">A Bejan, J. Appl. Phys., vol. 79, pp. 1191–1218, 1 Feb. 1996 http://dx.doi.org/10.1016/S0035-3159(96)80059-6</ref> which is the '''Chambadal-Novikov efficiency''':
 
::<math>\eta = 1 - \sqrt{\frac{T_L}{T_H}}</math>
 
In the limit of infinitesimally small power output, the standard Carnot result for efficiency is recovered.<ref name="Wagner2008"/> For some typical cycles, the above equation (note that [[absolute temperature]]s must be used) gives the following results:<ref name="Curzon1975"/><ref name="Callan1985">Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed. ed.). John Wiley & Sons, Inc.. ISBN 0-471-86256-8.</ref>
 
<!-- copied from [[Heat engine]]: -->
{| class="wikitable"
! ''Power Plant'' !! <math>T_c</math> (°C) !! <math>T_h</math> (°C) !! <math>\eta</math> (Carnot) !! <math>\eta</math> (Endoreversible) !! <math>\eta</math> (Observed)
|-
! [[West Thurrock]] ([[United Kingdom|UK]]) [[Fossil fuel power plant|coal-fired power plant]]
| 25 || 565 || 0.64 || 0.40 || 0.36
|-
! [[CANDU reactor|CANDU]] ([[Canada]]) [[nuclear power plant]]
| 25 || 300 || 0.48 || 0.28 || 0.30
|-
! [[Larderello]] ([[Italy]]) [[Geothermal power|geothermal power plant]]
| 80 || 250 || 0.33 || 0.178 || 0.16
|}
 
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.<ref name="Lavenda2007">B. H. Lavenda, Am. J. Phys., vol. 75, pp. 169-175 (2007)</ref>  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 Thomson <ref name="Thomson1853">W. Thomson, Phil. Mag. (Feb. 1853)</ref> 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 <math>\sqrt{T_HT_L}</math> so that the efficiency  is the Carnot efficiency for an engine working between <math>T_H</math> and <math>\sqrt{T_HT_L}</math>.
 
<!-- following text copied from [[Heat engine]], and further edited -->
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.<ref name="Wagner2008">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</ref> It is also introduced by Hoffman et al.<ref>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.</ref><ref name="Hoffman1997">K. H. Hoffmann, J. M. Burzler, and S. Schubert. Endoreversible Thermodynamics. J. Non-Equilib. Thermodyn., 22(4):311–355, 1997.</ref> A thorough discussion of the concept, together with many applications in engineering, is given in the book by Hans Ulrich Fuchs.<ref name="Fuchs2011">H. U. Fuchs, ''The Dynamics of Heat'' (2nd ed.), chapter 9. Graduate Texts in Physics, Springer 2011, ISBN 978-1-4419-7603-1</ref>
 
== References ==
 
{{Reflist}}
 
{{DEFAULTSORT:Endoreversible Thermodynamics}}
[[Category:Thermodynamics]]

Latest revision as of 13:45, 8 April 2014

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