DOI: 10.1063/1.1696618. Equation of State in the Neighborhood of the Critical Point

Equation of State in the Neighborhood of the Critical Point

10.1063/1.1696618

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by Φ being a constant. It is suggested that in a real fluid Φ(x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of Φ (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant-volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).

Bibliography

Widom, B. (1965). Equation of State in the Neighborhood of the Critical Point. The Journal of Chemical Physics, 43(11), 3898â3905.

Authors 1

B. Widom (first)

References 15 Referenced 1,131

10.1139/v54-017 / Can. J. Chem. (1954)
10.1063/1.1733766 / J. Chem. Phys. (1963)
10.1103/PhysRev.87.410 / Phys. Rev. (1952)
{'key': '2024020900350624700_r4'}
{'key': '2024020900350624700_r5'}
10.1103/PhysRevLett.13.713 / Phys. Rev. Letters (1964)
{'key': '2024020900350624700_r7'}
10.1063/1.1726135 / J. Chem. Phys. (1964)
{'key': '2024020900350624700_r9', 'first-page': '303', 'volume': '13', 'year': '1964', 'journal-title': 'Phys. Rev. Letters'} / Phys. Rev. Letters (1964)
10.1103/PhysRev.65.117 / Phys. Rev. (1944)
10.1103/PhysRev.136.A1599 / Phys. Rev. (1964)
10.1063/1.1733076 / J. Chem. Phys. (1962)
{'key': '2024020900350624700_r13', 'first-page': '842', 'volume': '39', 'year': '1963', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1963)
{'key': '2024020900350624700_r14', 'first-page': '183', 'volume': '2', 'year': '1957', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. (1957)
10.1103/PhysRevLett.14.623 / Phys. Rev. Letters (1965)

Dates

Type	When
Created	20 years, 7 months ago (Jan. 9, 2005, 3:01 a.m.)
Deposited	1 year, 6 months ago (Feb. 8, 2024, 7:35 p.m.)
Indexed	5 hours, 25 minutes ago (Aug. 23, 2025, 9:40 p.m.)
Issued	59 years, 8 months ago (Dec. 1, 1965)
Published	59 years, 8 months ago (Dec. 1, 1965)
Published Print	59 years, 8 months ago (Dec. 1, 1965)

Funders 0

None

BibTeX

@article{Widom_1965, title={Equation of State in the Neighborhood of the Critical Point}, volume={43}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1696618}, DOI={10.1063/1.1696618}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Widom, B.}, year={1965}, month=dec, pages={3898–3905} }

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