Balance Equations — The Conservation Laws

  • Peter Glansdorff
Part of the International Centre for Mechanical Sciences book series (CISM, volume 74)


Let us consider an extensive variable defined by the volume integral (*)
Assuming the boundary surface Ω at rest, we follow the time change of (2.1). This may be split into two parts:
where deI denotes the variation due to the exchange with the external world, and dlI the source of the quantity I inside the system. A conservation law for the variable I implies:
As an example, let us consider the first law of thermodynamics, which expresses the conservation of energy (I = E).


Heat Flux Balance Equation Entropy Production Local Equilibrium Extensive Variable 
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  1. [1]
    P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure Stability and Fluctuations, Wiley, Interscience, London, 1971.MATHGoogle Scholar
  2. [2]
    Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford, 1961.MATHGoogle Scholar
  3. [3]
    J.C. Legros, Thèse de doctorat, Chimie Physique, Université Libre de Bruxelles, 1971.Google Scholar

Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Peter Glansdorff
    • 1
  1. 1.Université Libre, BruxellesBelgium

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