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)] | ||
*[http://dx.doi.org/10.1021/jp057327c 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)] | *[http://dx.doi.org/10.1021/jp057327c 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)] | ||
*[http://dx.doi.org/10.1021/jp802999z 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)] | |||
*[http://dx.doi.org/10.1021/jp8066487 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)] | *[http://dx.doi.org/10.1021/jp8066487 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)] | ||
*[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]
Batchinsky law[edit]
The Batchinsky law [2], derived from the van der Waals equation of state, states that:
where is the value of the density obtained by the extrapolating the coexistence curve into the low temperature region beyond the triple point, and is the Boyle temperature, which is .
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)