Zeno line: Difference between revisions
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The '''Zeno line''' is the name given to a line along which the [[compressibility factor]] is unity <ref> | The '''Zeno line''' is the name given to a line along which the [[compressibility factor]] is unity <ref>D. Ben-Amotz and D. R. Herschbach, "Correlation of the Zeno (Z=1) line for supercritical fluids with vapor-liquid rectilinear diameters", Israel Journal of Chemistry '''30''' pp. 59-68 (1990)</ref> | ||
:<math>Z:= \frac{pV}{Nk_BT}=1</math> | :<math>Z:= \frac{pV}{Nk_BT}=1</math> | ||
==Batchinsky law== | |||
The Batchinsky law <ref>[http://dx.doi.org/10.1002/andp.19063240205 A. Batschinski "Abhandlungen über Zustandsgleichung; Abh. I: Der orthometrische Zustand", Annalen der Physik '''19''' pp. 307-309 (1906)]</ref>, derived from the [[van der Waals equation of state]], states that: | |||
:<math>\frac{\rho}{\rho_B} + \frac{T}{T_B} = 1</math> | |||
where <math>\rho_B</math> is the value of the density obtained by the extrapolating the coexistence curve into the low temperature region beyond the [[triple point]], and <math>T_B</math> is the [[Boyle temperature]], which is <math>a/bR</math>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1021/j100184a053 Jiasai Xu and Dudley R. Herschbach "Correlation of Zeno line with acentric factor and other properties of normal fluids", Journal of Physical Chemistry '''96''' pp. 2307-2312 (1992)] | *[http://dx.doi.org/10.1021/j100184a053 Jiasai Xu and Dudley R. Herschbach "Correlation of Zeno line with acentric factor and other properties of normal fluids", Journal of Physical Chemistry '''96''' pp. 2307-2312 (1992)] | ||
*[http://dx.doi.org/10.1021/jp001344e Michael C. Kutney, Matthew T. Reagan, Kenneth A. Smith, Jefferson W. Tester, and Dudley R. Herschbach "The Zeno (Z = 1) Behavior of Equations of State: An Interpretation across Scales from Macroscopic to Molecular", Journal of Physical Chemistry B '''104''' pp. 9513-9525 (2000)] | *[http://dx.doi.org/10.1021/jp001344e Michael C. Kutney, Matthew T. Reagan, Kenneth A. Smith, Jefferson W. Tester, and Dudley R. Herschbach "The Zeno (Z = 1) Behavior of Equations of State: An Interpretation across Scales from Macroscopic to Molecular", Journal of Physical Chemistry B '''104''' pp. 9513-9525 (2000)] | ||
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*[http://dx.doi.org/10.1021/jp808817p E. M. Apfelbaum and V. S. Vorob’ev "Correspondence between the Critical and the Zeno-Line Parameters for Classical and Quantum Liquids", Journal of Physical Chemistry B '''113''' pp. 3521-3526 (2009)] | *[http://dx.doi.org/10.1021/jp808817p E. M. Apfelbaum and V. S. Vorob’ev "Correspondence between the Critical and the Zeno-Line Parameters for Classical and Quantum Liquids", Journal of Physical Chemistry B '''113''' pp. 3521-3526 (2009)] | ||
*[http://dx.doi.org/10.1063/1.3151982 E. M. Apfelbaum and V. S. Vorob'ev "The confirmation of the critical point-Zeno-line similarity set from the numerical modeling data for different interatomic potentials", Journal of Chemical Physics 130, 214111 (2009)] | *[http://dx.doi.org/10.1063/1.3151982 E. M. Apfelbaum and V. S. Vorob'ev "The confirmation of the critical point-Zeno-line similarity set from the numerical modeling data for different interatomic potentials", Journal of Chemical Physics 130, 214111 (2009)] | ||
*[http://dx.doi.org/10.1021/jp911897k V. L. Kulinskii "Simple Geometrical Interpretation of the Linear Character for the Zeno-Line and the Rectilinear Diameter", Journal of Physical Chemistry B '''114''' pp. 2852-2855 (2010)] | |||
[[category: equations of state]] | [[category: equations of state]] | ||
Latest revision as of 16:31, 6 October 2010
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The Zeno line is the name given to a line along which the compressibility factor is unity [1]
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z:= \frac{pV}{Nk_BT}=1}
Batchinsky law[edit]
The Batchinsky law [2], derived from the van der Waals equation of state, states that:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\rho}{\rho_B} + \frac{T}{T_B} = 1}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_B} is the value of the density obtained by the extrapolating the coexistence curve into the low temperature region beyond the triple point, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_B} is the Boyle temperature, which is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a/bR} .
References[edit]
- ↑ D. Ben-Amotz and D. R. Herschbach, "Correlation of the Zeno (Z=1) line for supercritical fluids with vapor-liquid rectilinear diameters", Israel Journal of Chemistry 30 pp. 59-68 (1990)
- ↑ A. Batschinski "Abhandlungen über Zustandsgleichung; Abh. I: Der orthometrische Zustand", Annalen der Physik 19 pp. 307-309 (1906)
Related reading
- Jiasai Xu and Dudley R. Herschbach "Correlation of Zeno line with acentric factor and other properties of normal fluids", Journal of Physical Chemistry 96 pp. 2307-2312 (1992)
- Michael C. Kutney, Matthew T. Reagan, Kenneth A. Smith, Jefferson W. Tester, and Dudley R. Herschbach "The Zeno (Z = 1) Behavior of Equations of State: An Interpretation across Scales from Macroscopic to Molecular", Journal of Physical Chemistry B 104 pp. 9513-9525 (2000)
- E. M. Apfelbaum, V. S. Vorob'ev, and G. A. Martynov "Triangle of Liquid−Gas States", Journal of Physical Chemistry B 110 pp. 8474-8480 (2006)
- E. M. Apfelbaum, V. S. Vorob’ev and G. A. Martynov "Regarding the Theory of the Zeno Line", Journal of Physical Chemistry A 112 pp. 6042-6044 (2008)
- E. M. Apfelbaum and V. S. Vorob′ev "A New Similarity Found from the Correspondence of the Critical and Zeno-Line Parameters", Journal of Physical Chemistry B 112 pp. 13064–13069 (2008)
- E. M. Apfelbaum and V. S. Vorob’ev "Correspondence between the Critical and the Zeno-Line Parameters for Classical and Quantum Liquids", Journal of Physical Chemistry B 113 pp. 3521-3526 (2009)
- E. M. Apfelbaum and V. S. Vorob'ev "The confirmation of the critical point-Zeno-line similarity set from the numerical modeling data for different interatomic potentials", Journal of Chemical Physics 130, 214111 (2009)
- V. L. Kulinskii "Simple Geometrical Interpretation of the Linear Character for the Zeno-Line and the Rectilinear Diameter", Journal of Physical Chemistry B 114 pp. 2852-2855 (2010)