Law of corresponding states
The law of corresponding states is an empirical law which encapsulates the finding that the equations of state for many real gases are remarkably similar when they are expressed in terms of reduced temperatures (), pressures, () and volumes (), where the subscript represents the value of the property at the critical point. This law was first described by Johannes Diderik van der Waals in his 1873 thesis, and forms the subject of a paper by him in 1913 .
- There is negligible difference between Fermi–Dirac statistics and Bose–Einstein statistics for the system (i.e. the system behaves classically).
- The effect of quantisation of the translational degrees of freedom is negligible (i.e. the system behaves classically).
- The molecules are spherically symmetrical, either actually or by virtue of rapid and free rotation.
- The intramolecular degrees of freedom are assumed to be completely independent of the volume per molecule.
- The potential energy will be taken as a function only of the various intermolecular distances.
- The potential energy for a pair of molecules can be written as where is the intermolecular distance, and and are characteristic constants, and is a universal function.
(for pressure measured in atmospheres, and volume in cm3mole-1)
where is the Boyle temperature.
where is the triple point.
- Johannes Diderik van der Waals "The law of corresponding states for different substances", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 15 II pp. 971-981 (1913)
- Kenneth S. Pitzer "Corresponding States for Perfect Liquids", Journal of Chemical Physics 7 pp. 583-590 (1939)
- E. A. Guggenheim "The Principle of Corresponding States", Journal of Chemical Physics 13 pp. 253-261 (1945)
- Kenneth S. Pitzer, David Z. Lippmann, R. F. Curl Jr., Charles M. Huggins, Donald E. Petersen "The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization", Journal of the American Chemical Society 77 pp. 3433-3440 (1955)
- Massimo G. Noro and Daan Frenkel "Extended corresponding-states behavior for particles with variable range attractions", Journal of Chemical Physics 113 2941-2944 (2000)
- J. de Boer and A. Michels "Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium", Physica 5 pp. 945-957 (1938)
- Patrick Grosfils and James F. Lutsko "Dependence of the liquid-vapor surface tension on the range of interaction: A test of the law of corresponding states", Journal of Chemical Physics 130 054703 (2009)
- Hong Wei Xiang "The Corresponding-States Principle and its Practice", Elsevier Science (2005) ISBN 0-444-52062-7
- L. A. Bulavin and V. L. Kulinskii "Generalized principle of corresponding states and the scale invariant mean-field approach", Journal of Chemical Physics '133 134101 (2010)
- P. Orea, A. Romero-Martínez, E. Basurto, C. A. Varga and G. Odriozola "Corresponding states law for a generalized Lennard-Jones potential", Journal of Chemical Physics 143 024504 (2015)