# Difference between revisions of "Zeno line"

Carl McBride (talk | contribs) m (Added Batchinsky law) |
Carl McBride (talk | contribs) m (→Batchinsky law) |
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:<math>Z:= \frac{pV}{Nk_BT}=1</math> | :<math>Z:= \frac{pV}{Nk_BT}=1</math> | ||

==Batchinsky law== | ==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> states that: | + | 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> | :<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]]. | 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]]. | ||

+ | |||

==References== | ==References== | ||

<references/> | <references/> |

## Revision as of 14:42, 6 October 2010

The **Zeno line** is the name given to a line along which the compressibility factor is unity ^{[1]}

## Batchinsky law

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.

## References

- ↑ 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)