Abstract:The slopes of isochors and isotherms as they cross the unit compressibility line are found to constitute a corresponding property for many fluids over a wide range of densities extending from dilute gases to compressed liquids. This correspondence is represented by a simple function, and its consequences for equations of state are examined. In particular, a new interrelation among the virial coefficients is derived. The interrelation is tested for the Lennard-Jones 12,6 intermolecular potential, and the agreem… Show more
“…The slopes of reduced isotherms and isochores intersecting the VC line at the same point are equal to each other, and by eq 2 (dZ/d6)j = (dZ/d5)e = AB5/(1 -)2 = AB(1 -6)/ 2 (5) at unit Z. This result has been observed to hold, possibly to within experimental error, for a number of dilute gases, dense gases, and liquids (Holleran and Sinka, 1971). It was for this reason that the sum of powers on the 6 and (1 -5) factors in eq 2 was set at -2.…”
An equation of state is presented which is consistent with the experimental observations that the unit-compressibility T vs. d line for many fluids is straight, the ratio of (Z -1) for different fluids at equal reduced temperatures and densities is nearly constant, and the slopes of isotherms and isochores at the unit compressibility line are simply related to the temperature of the isotherm. The equation is applied to gaseous methane, and with six constants reproduces the data of Douslin, Harrison, Moore, and McCullough to within the reported experimental error with an average deviation of 0.02%.
“…The slopes of reduced isotherms and isochores intersecting the VC line at the same point are equal to each other, and by eq 2 (dZ/d6)j = (dZ/d5)e = AB5/(1 -)2 = AB(1 -6)/ 2 (5) at unit Z. This result has been observed to hold, possibly to within experimental error, for a number of dilute gases, dense gases, and liquids (Holleran and Sinka, 1971). It was for this reason that the sum of powers on the 6 and (1 -5) factors in eq 2 was set at -2.…”
An equation of state is presented which is consistent with the experimental observations that the unit-compressibility T vs. d line for many fluids is straight, the ratio of (Z -1) for different fluids at equal reduced temperatures and densities is nearly constant, and the slopes of isotherms and isochores at the unit compressibility line are simply related to the temperature of the isotherm. The equation is applied to gaseous methane, and with six constants reproduces the data of Douslin, Harrison, Moore, and McCullough to within the reported experimental error with an average deviation of 0.02%.
“…Although the linearity of the Z = 1 contour was discovered by Batschinski in 1906, it appears to have been forgotten until nearly six decades later. Beginning in the early 1960s, researchers at the University of Karlsruhe, the Odessa Institute of Marine Engineering, and several Russian institutes discussed the Zeno line extensively, − related it to other thermodynamic properties, − and incorporated it in the development of various thermodynamic models. , Independently, during the late 1960s, Holleran and co-workers − proposed several useful applications for the Z = 1 contour. Among the diverse names used are orthometric condition, ideal-gas curve, and unit compressibility line; we have adopted the term Zeno line 1,2 to “emphasize the paradoxical character of its arrowlike linearity.” 1 Experimental Zeno lines for pure H 2 O, CO 2 , and CH 4 .…”
Section: Introductionmentioning
confidence: 99%
“…Beginning in the early 1960s, researchers at the University of Karlsruhe, the Odessa Institute of Marine Engineering, and several Russian institutes discussed the Zeno line extensively, [7][8][9] related it to other thermodynamic properties, [10][11][12] and incorporated it in the development of various thermodynamic models. 13,14 Independently, during the late 1960s, Holleran and co-workers [15][16][17][18] proposed several useful applications for the Z ) 1 contour. Among the diverse names used are orthometric condition, idealgas curve, and unit compressibility line; we have adopted the term Zeno line 1,2 to "emphasize the paradoxical character of its arrowlike linearity."…”
The regularity exhibited by fluids along the contour of the unit compressibility factor in the temperaturedensity plane, where Z t PV/RT ) 1, is explored as a means for testing and improving the volumetric equations of state. For a wide range of pure fluids, this contour, known as the Zeno line, has been empirically observed to be nearly linear from the Boyle temperature of the low-density vapor to around the triple point in the liquid region. The Z ) 1 contour thus offers a quantitative criterion for interpreting intermolecular interactions. For H 2 O, CH 4 , and CO 2 , experimental results are compared with predictions from macroscopic PVT equations of state and with predictions from NVT molecular simulations. Reasonably straight Zeno lines result from commonly used macroscopic EOS models, such as the Redlich-Kwong-Soave (RKS) and the Peng-Robinson (PR). Although quantitative agreement between predicted and experimental Zeno behavior was not exact, the general trends suggest that these macroscopic models adequately capture the dynamic balance that exists between repulsive and attractive forces along the Zeno contour. From molecular dynamics simulations, the Lennard-Jones, the Simple Point Charge (SPC), and the extended SPC/E models of pure H 2 O also yielded Zeno lines close to experimentally measured values over a wide range of densities. Density-scaled radial distribution functions indicate that the degree of long-range ordering was nearly invariant along the Zeno line, but hydration numbers and cluster sizes varied markedly.
“…is applied to the Z = 1 curve where eq 1 holds, Holleran and Sinka (1971) showed that eq also holds for points on this curve, simply denoted as the UC line.…”
The unit compressibility line is analyzed at a nonzero pressure point of intersection with the inversion curve, assuming that the unit compressibility line is linear in the T-d plane. It is shown that this assumption requires both the inversion curve and an isotherm to have local zero slopes at the intersection point viewed in the compressibility factor vs. pressure plane, results not observed in Z, P representations of properties.
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