The phase rule by the mathematician and physicist Gibbs 1 was commented by Fuller 2 in this way:
The chemist Willard Gibbs developed the phase rule dealing with liquid, gaseous, and crystalline states of substances, apparently not realizing that his phase rule employed the same generalized mathematics as that of Euler’s topological vertexes, faces, and edges [1].
Keywords
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Fuller, R.B., Applewhite, E.J.: Synergetics. Explorations in the Geometry of Thinking. Macmillan Publishing Co. Inc., New York (1975)
Tauch, D., Russel, C.: Glass-ceramics with zero thermal expansion in the system bao/al2o3/b2o3. J. Non-Cryst. Solids 351(27–29), 2294–2298 (2005)
Gibbs, J.W.: On the equilibria of heterogenous substances. In: The Collected Works, vol. 1. Yale University Press, New Haven, CT (1948 [reprinted])
Johnson, W.C.: On the inapplicability of Gibbs phase rule to coherent solids. Metall. Mater. Trans. A 22(1), 1093–1097 (1991)
Li, D.: Curvature effects on the phase rule. Fluid Phase Equilib. 98, 13–34 (1994)
Shapiro, A.A., Stenby, E.H.: Thermodynamics of the multicomponent vapor-liquid equilibrium under capillary pressure difference. Fluid Phase Equilib. 178(1–2), 17–32 (2001)
Cromwell, P.R.: Polyhedra. Cambridge University Press, Cambridge (1999)
Schläfli, L.: Gesammelte mathematische Abhandlungen. Birkhäuser, Basel (1950). Edited by Steiner-Schläfli-Komitee der Schweizerischen Naturforschenden Gesellschaft
Tverberg, H.: How to cut a convex polytope into simplices. Geometriae Dedicata 3(2), 239–240 (1974)
Michon, G.P., Anderson, S.E.: Counting polyhedra. [electronic] http://home.att.net/∼numericana/data/polyhedra.htm (2001)
Weisstein, E.W.: Polyhedral graph. From MathWorldA Wolfram Web Resource: [electronic] http://mathworld.wolfram.com/PolyhedralGraph.html (2004)
Klochko, M.A.: Analogy between phase rule and the Euler theorem for polyhedrons. Izvest. Sectora Fiz.-Khim. Anal., Inst. Obshei. i Neorg. Khim., Akadd. Nauk SSSR 19, 82–88 (1949)
Levin, I.J.: The phase rule and topology. J. Chem. Educ. 23, 183–185 (1946)
Mindel, J.: Gibbs’ phase rule and Euler’s formula. J. Chem. Educ. 39, 512–514 (1962)
Morikawa, T., Newbold, B.T.: Analogous odd-even parities in mathematics and chemistry. Himi_ (Chemistry) 12(6), 445–450 (2003)
Radhakrishnan, T.P.: Euler’s formula and phase rule. J. Math. Chem. 5, 381 (1990)
Rüdel, O.: The phase rule and the boundary law of Euler. Z. Elektrochem. 35, 54 (1929)
Wildeboer, G., Plath, P.J.: Euler’sche Polyederformel und Gibbs’sche Phasenregel. Commun. Math. Comput. Chem. (MATCH) 7, 163–175 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fink, J.K. (2009). The Phase Rule. In: Physical Chemistry in Depth. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01014-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-01014-9_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01013-2
Online ISBN: 978-3-642-01014-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)