Linear Thermodynamics and Phenomenological Coefficients
It results from the equilibrium equalities (3.14), that in its neighbourhood, the link between the flows Jα and the forces Xα may be assumed to be linear: (4.1) Such relations are called phenomenological laws, where the Lαβ denote the phenomenological coe
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L E C T URE S - No. 74
PETER GLANSDORFF UNIVERSITE LIBRE,
ßRUXELLES
THBRMODYNAMICS IN CONTEMPORARY DYNAMICS
LECTURES HELD AT THE DEPARTMENT
OF MECHANICS OF SOLIDS JULY 1971
UDINE 1971
SPRINGER-VERLAG WIEN GMBH
Thia work ia IUqect to copyright All rights are reserved. whether the whole or part oi the material ia concemed speeifically those oi translation, reprinting, re-use oi illustrations, broadcasting, reproduction by photocopying machine or simüar means, and storage in data banks.
©
1972 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien-New York in 1972
ISBN 978-3-211-81177-1 DOI 10.1007/978-3-7091-2844-2
ISBN 978-3-7091-2844-2 (eBook)
PREFACE The notes which foZZow correspond to the 12 Zectures given at CISM in Udine, during the summer course of 1971. The first part represents a summary of the monograph pubZished with my coZZeague PRIGOGINE under the titZe: "Thermodynamics theory of Structure, StabiZity and FZuctuations" (G. WiZey Interscience, London, N.Y., 1971). A french edition of the same monograph has been pubZished about the same time in Paris, by MASSON ET CIE, under the titZe of "Stl'UCture, StabiZite et FZuctuations". This summary shouZd enabZe the reader to grasp the interest for a non Zinear thermodynamics of irreversibZe phenomena, i.e. those who occur far from equiZibrium. Indeed, it is within this range that instabiZities can be expected, which in turn are susceptibZe to give birth to some space 0'1' time order in the system (Zimit cycZe, etc ... ). Several examples iZZustrate this importan~ generaZization of cZassicaZ thermodynamics, as weZZ as its extension to hydrodynamics, by ta king into account the convective effects aZong with dissipative phenomena, usuaZZy considered aZone. The second part is devoted to originaZ new contributions which are not incZuded in the above monograph. In this respect, Zet us mention on the theoreticaZ aide, the demonstration of the convergence of the iteration method used together with the ZocaZ
Prefaae
4
in order to determine approximate soZutions when the exaat soZution aannot be expeated. On the other hand~ from the standpoint of praatiaaZ exampZes~ Zet us underZine the next appZiaation treated in Chap. XI~ and devoted to an extension of the Benard probZem~ to a two aomponent system. Numerous graphs and numeriaaZ data due to Dr. J.C. LEGROS are therein estabZished.
potentiaZ~
Udine~
JuZy 1971
1. Introduction.
In the notes which follow, the reader will dis-
tinguish two parts: 10) Sections which constitute a short summary of the laws ofnon linear thermodynamies, extensively developed in arecent monograph (P. Glansdorff and I. Prigogine, "Thermodynamic Theory of Structure Stabili ty and Fluctuations ", j. Wiley, Interscience, London, N. Y. 1971, or the French edition: "Structure, Stabilite et Fluctuations", Masson, Paris, 1971). 20) Sections which present a detailed account of new applications.
The most important is related to the stability of a two component fluid layer, heated from below. Numerous numerical results
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