Some Simple Isothermal Equations of State

J. ROSS MACDONALD

doi:10.1103/RevModPhys.38.669

Access by Xinjiang University

Some Simple Isothermal Equations of State

J. ROSS MACDONALD

Texas Instruments Incorporated, Dallas, Texas 75222

PDF

Rev. Mod. Phys. 38, 669 – Published 1 October, 1966

DOI: https://doi.org/10.1103/RevModPhys.38.669

Abstract

Previous work on the Tait equation of state, usually applied to liquids, is discussed together with a review of work on a closely related simple equation arising both from the theory of finite strain and from microscopic considerations. The latter equation has been primarily used for fitting hydrostatic compression pressure-volume data for solids. A detailed discussion of methods for assessing goodness-of-fit of data to equations of state is presented along with an analysis of ways to help decide which of two similar equations is the more applicable for given data. Nonlinear least squares fitting of the above two-parameter equations of state is carried out for the first time using published $P - V - T$ data for water, a very compressible hydrocarbon liquid, zinc, lithium, sodium, potassium, and rubidium and the results compared with those of previous analyses of these data. Careful fitting of the present type can lead to new conclusions and insights not so apparent from less careful fitting of the present equations or from fitting with other equations. For most of the materials and data considered here the finite-strain equation was found to be superior to the Tait equation. Reasons are advanced, however, why both equations should be primarily considered only as empirical, with theoretical justifications for them applicable only over limited pressure-volume ranges.

References (36)

J. R. Macdonald and c. A. Barlow, Jr., J. Chem. Phys. 36, 3062 (1962)
J. R. Macdonald, J. Chem. Phys. 40, 1792 (1964)
J. J. Gilvarry, J. Appl. Phys. 28, 1253 (1957)
F. D. Murnaghan, Finite Deformation of an Elastic Solid (John Wiley & Sons, Inc., New York, 1951), Chap. 4 Proc. Natl. Acad. Sci. 30, 244 (1944)
J. J. Gilvarry, Phys. Rev. 102, 331 (1956)
J. J. Gilvarry, Phys. Rev. 102, 325 (1956)
Yu. N. Ryabinin, Z. Tekh. Fiz. 30, 739 (1960) [English transl.: Soviet Phys.—Tech. Phys. 5, 693 (1960)]
M. A. Cook and L. A. Rogers, J. Appl. Phys. 34, 2330 (1963)
J. C. Slater, Introduction to Chemical Physics (McGraw-Hill Book Company, Inc., New York, 1939), p. 239, Eqs. (4.3), (4.5)
P. Gombas, Ann. Phys. (Leipzig) 9, 70 (1951)
Yu. N. Ryabinin, Fiz. Metal. i Metalloved. 9, 312 (1960)
[O. L. Anderson, J. Phys. Chem. Solids 27, 547 (1966)]
R. Ginell and T. J. Quigley, J. Phys. Chem. Solids 26, 1157 (1965)
R. Simha and S. T. Hadden, J. Chem. Phys. 25, 702 (1956)
V. S. Nanda and R. Simha, J. Chem. Phys. 41, 1884 (1964)
W. G. Cutler, R. H. McMickle, W. Webb, and R. W. Schiessler, J. Chem. Phys. 29, 727 (1958)
V. S. Nanda and R. Simha, J. Chem. Phys. 41, 3870 (1964)
R. Ginell, J. Chem. Phys. 34, 1249, 2174 (1961)
R. Ginell, J. Chem. Phys. 35, 1776 (1961)
R. GinellHandbuch der Experimentalphysik, W. Wien and F. Harms, Eds. (Academische Verlagsgesellschaft M. B. H., Leipzig, 1926-1937), Vol. 8, part 2, pp. 224-228
A. Zeitlin, Annotated Bibliography on High-Pressure Technology (Butterworths, Washington, 1964)
D. W. Marquardt, J. Soc. Ind. Appl. Math. 2, 431 (1963)
L. J. Hudleston, Trans. Faraday Soc. 33, 97 (1937) D. M. Newitt and K. E. Weale, J. Chem. Soc. 1951, 3092
P. W. Bridgman, J. Chem. Phys. 3, 597 (1935)
R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 63, 898 (1941)
P. W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 55-70, 71-87 (1948)
T. W. Richards, J. Am. Chem. Soc. 37, 1643 (1915)
R. I. Beecroft and C. A. Swenson, J. Phys. Chem. Solids 18, 329 (1961)
C. E. Monfort and C. A. Swenson, J. Phys. Chem. Solids 26, 291 (1965)
C. A. Swenson, J. Phys. Chem. Solids 27, 33 (1966)
L. Knopoff in High Pressure Physics and Chemistry, I, R. S. Bradley, Ed. (Academic Press Inc., New York, 1963)
L. J. Briggs, J. Appl. Phys. 21, 721 (1950)
N. E. Dorsey, Properties of Ordinary Water-Substance (Reinhold Publishing Corp., New York, 1940), p. 181
A. Wohl, Z. Physik. Chem. 99, 234 (1921)
R. E. Gibson and J. F. Kincaid, J. Am. Chem. Soc. 60, 511 (1938)
R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 61, 2515 (1939)

[c1] J. R. Macdonald and c. A. Barlow, Jr., J. Chem. Phys. 36, 3062 (1962)

[c2] J. R. Macdonald, J. Chem. Phys. 40, 1792 (1964)

[c3] J. J. Gilvarry, J. Appl. Phys. 28, 1253 (1957)

[c4] F. D. Murnaghan, Finite Deformation of an Elastic Solid (John Wiley & Sons, Inc., New York, 1951), Chap. 4 Proc. Natl. Acad. Sci. 30, 244 (1944)

[c5] J. J. Gilvarry, Phys. Rev. 102, 331 (1956)

[c6] J. J. Gilvarry, Phys. Rev. 102, 325 (1956)

[c7] Yu. N. Ryabinin, Z. Tekh. Fiz. 30, 739 (1960) [English transl.: Soviet Phys.—Tech. Phys. 5, 693 (1960)]

[c8] M. A. Cook and L. A. Rogers, J. Appl. Phys. 34, 2330 (1963)

[c9] J. C. Slater, Introduction to Chemical Physics (McGraw-Hill Book Company, Inc., New York, 1939), p. 239, Eqs. (4.3), (4.5)

[c10] P. Gombas, Ann. Phys. (Leipzig) 9, 70 (1951)

[c11] Yu. N. Ryabinin, Fiz. Metal. i Metalloved. 9, 312 (1960)

[c12] [O. L. Anderson, J. Phys. Chem. Solids 27, 547 (1966)]

[c13] R. Ginell and T. J. Quigley, J. Phys. Chem. Solids 26, 1157 (1965)

[c14] R. Simha and S. T. Hadden, J. Chem. Phys. 25, 702 (1956)

[c15] V. S. Nanda and R. Simha, J. Chem. Phys. 41, 1884 (1964)

[c16] W. G. Cutler, R. H. McMickle, W. Webb, and R. W. Schiessler, J. Chem. Phys. 29, 727 (1958)

[c17] V. S. Nanda and R. Simha, J. Chem. Phys. 41, 3870 (1964)

[c18] R. Ginell, J. Chem. Phys. 34, 1249, 2174 (1961)

[c19] R. Ginell, J. Chem. Phys. 35, 1776 (1961)

[c20] R. GinellHandbuch der Experimentalphysik, W. Wien and F. Harms, Eds. (Academische Verlagsgesellschaft M. B. H., Leipzig, 1926-1937), Vol. 8, part 2, pp. 224-228

[c21] A. Zeitlin, Annotated Bibliography on High-Pressure Technology (Butterworths, Washington, 1964)

[c22] D. W. Marquardt, J. Soc. Ind. Appl. Math. 2, 431 (1963)

[c23] L. J. Hudleston, Trans. Faraday Soc. 33, 97 (1937) D. M. Newitt and K. E. Weale, J. Chem. Soc. 1951, 3092

[c24] P. W. Bridgman, J. Chem. Phys. 3, 597 (1935)

[c25] R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 63, 898 (1941)

[c26] P. W. Bridgman, Proc. Am. Acad. Arts Sci. 76, 55-70, 71-87 (1948)

[c27] T. W. Richards, J. Am. Chem. Soc. 37, 1643 (1915)

[c28] R. I. Beecroft and C. A. Swenson, J. Phys. Chem. Solids 18, 329 (1961)

[c29] C. E. Monfort and C. A. Swenson, J. Phys. Chem. Solids 26, 291 (1965)

[c30] C. A. Swenson, J. Phys. Chem. Solids 27, 33 (1966)

[c31] L. Knopoff in High Pressure Physics and Chemistry, I, R. S. Bradley, Ed. (Academic Press Inc., New York, 1963)

[c32] L. J. Briggs, J. Appl. Phys. 21, 721 (1950)

[c33] N. E. Dorsey, Properties of Ordinary Water-Substance (Reinhold Publishing Corp., New York, 1940), p. 181

[c34] A. Wohl, Z. Physik. Chem. 99, 234 (1921)

[c35] R. E. Gibson and J. F. Kincaid, J. Am. Chem. Soc. 60, 511 (1938)

[c36] R. E. Gibson and O. H. Loeffler, J. Am. Chem. Soc. 61, 2515 (1939)

Reviews of Modern Physics

Export citation

Export citation

Some Simple Isothermal Equations of State

Abstract

References (36)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation