Zeno line

The Zeno line is the name given to a line along which the compressibility factor is unity

$Z:={\frac {pV}{Nk_{B}T}}=1$

Batchinsky law

The Batchinsky law , derived from the van der Waals equation of state, states that:

${\frac {\rho }{\rho _{B}}}+{\frac {T}{T_{B}}}=1$

where $\rho _{B}$ is the value of the density obtained by the extrapolating the coexistence curve into the low temperature region beyond the triple point, and $T_{B}$ is the Boyle temperature, which is $a/bR$.

References

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)