Thermodynamics pp 101-129 | Cite as


  • Gianni Astarita


A phase is defined as a part of a body within which the local state is a smooth function of position (the gradient of any state variable is finite at all points). A multiphase system is therefore a body which contains surfaces of discontinuity for the state; such surfaces are called interfaces. The principle of action and reaction forbids pressure to be discontinuous at interfaces, and so pressure is continuous even in multiphase systems, except for the effect of surface tension on curved interfaces. There is no fundamental law of physics which forbids temperature discontinuities, but in heat transfer theory the usual assumption of a continuous temperature distribution has been generally successful, and therefore that assumption is retained here (see the literature section in this regard).


Free Enthalpy Liquid Crystal Dynamic Surface Tension Smectic Phase Internal State Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. “For each hotness there is some body whose latent heat at that hotness fails to vanish for some volume.” This is called the “Thermometric axiom”; and, since it has to do with latent heat, it seems appropriate that it should have been formulated by J. B. Boyling [Proc. R. Soc. London 329, 35 (1972)].CrossRefGoogle Scholar
  2. The idea that a one-component system has in principle properties which are continuous through the phase change, embodied in Figure 4.1.1, is originally due to Van der Waals, Die Continuitat des Gasformingen und Flussigen Zustandes, J. A. Barth, Leipzig (1881).Google Scholar
  3. The question of pressure and temperature being continuous across an interface between two phases presents some subtlety. For instance, shock waves in gases are phenomena where both temperature and pressure are discontinuous; however, the discontinuity travels through the gas and is sustained by a nonequilibrium phenomenon. The point is discussed in detail in any book on gas dynamics. Discontinuities of temperature, chemical potential, and velocity can also occur in nonequilibrium phenomena; the whole question is discussed in a recent review paper by G. Astarita and R. Ocone, Adv. Chem. Eng. (to be published).Google Scholar
  4. Phase equilibria are discussed in all thermodynamics textbooks. For the case of mixtures, a very complete discussion is given by M. B. King, Phase Equilibria in Mixtures, Pergamon Press, Oxford (1969).Google Scholar
  5. Phase equilibria in continuous mixtures have been discussed in a number of papers; the recent one by S. K. Shibata, S. I. Sandler, and R. A. Behrens, Chem. Eng. Sci. 42, 1977 (1987) is a good guide to the relevant literature.CrossRefGoogle Scholar
  6. The possibility of heterogeneous isomerization equilibria has been considered by H. S. Caram and L. E. Scriven, Chem. Eng. Sci. 31, 163 (1976); see alsoCrossRefGoogle Scholar
  7. G. Astarita, Chem. Eng. Sci. 31, 1224 (1976), and the literature cited in these papers.CrossRefGoogle Scholar
  8. A comparatively recent review on liquid crystals is to be found in G. W. Gray and P. A. Winsor (Eds.), Liquid Crystals and Plastic Crystals, Ellis Horwood, Chichester (1974).Google Scholar
  9. Special transitions are discussed by H. B. Callen, Thermodynamics, Wiley, New York (1960).Google Scholar
  10. L. Tisza, Phase Transformations in Solids, Chapter 1, Wiley, New York (1951).Google Scholar
  11. K. Denbigh, The Principles of Chemical Equilibrium, Cambridge University Press, Cambridge (1964). The specific case of the rubber-glass transition in polymers is discussed in detail byGoogle Scholar
  12. R. N. Haward, The Physics of Glassy Polymers, Applied Science Publ., London (1973). The literature which deals specifically with the problem of predicting inequalities such as π ≥ 1 is extremely confusing, and much of it is best left unread.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Gianni Astarita
    • 1
    • 2
  1. 1.University of DelawareNewarkUSA
  2. 2.University of NaplesNaplesItaly

Personalised recommendations