An optical method for measuring PVT data, critical constants, virial coefficients, and molecular parameters of GeH4

1983 ◽  
Vol 61 (7) ◽  
pp. 1060-1063
Author(s):  
D. Balzarini ◽  
A. Rosenberg ◽  
P. Palffy-Muhoray
Keyword(s):  
Refractive Index ◽  
Equation Of State ◽  
Optical Method ◽  
Virial Coefficients ◽  
Virial Equation ◽  
Density Range ◽  
Lennard Jones ◽  
Pvt Data ◽  
Virial Equation Of State ◽  
Critical Constants

An optical method has been developed for measuring PVT data for a fluid. The method consists of measuring the refractive index as a function of density and temperature and, separately, as a function of pressure and temperature. The results are combined to yield PVT data. Germane has been studied. Isotherms have been measured in the temperature range 293 to 323 K and the density range 0.07 to 0.7 g cm−3. The data in the critical region are analyzed to obtain the critical constants Pc = 48.8 atm, ρc = 0.522 g cm−3, and Tc = 38.97 C ± 0.2. The data at lower densities are fitted to a virial equation of state to obtain the second and third coefficients. The values at 312.15 K are B = −2.37 cm3 g−1 and C = 1.99 cm6 g−2. The data are analyzed to yield the Lennard–Jones parameters ε/K = 230 ± 15 deg and σ = 4.6 ± 0.2 Å.

The equation of state of the two-dimensional Lennard–Jones fluid

1986 ◽  
Vol 64 (6) ◽  
pp. 677-684 ◽  
Author(s):  
M. Rami Reddy ◽  
Seamus F. O'Shea
Keyword(s):  
Equation Of State ◽  
Virial Coefficients ◽  
Nonlinear Least Squares ◽  
Virial Equation ◽  
Two Dimensional ◽  
Marquardt Method ◽  
Lennard Jones ◽  
Virial Equation Of State ◽  
First Time ◽  
Critical Constants

By combining pressure and energy data from the virial equation of state, through fifth virial coefficients, with the second and third virial coefficients themselves and the results of computer-simulation calculations, we have constructed an equation of state for the two-dimensional Lennard–Jones fluid for 0.45 ≤ T* ≤ 5 and 0.01 ≤ ρ* ≤ 0.8. The fitted data include some in the metastable region, and, therefore, the equation of state also describes "van der Waals loops" including unstable regions. The form used is a modified Benedict–Webb–Rubin equation having 33 parameters including one nonlinear one. The fitting was done using a nonlinear least squares algorithm based on a Levenberg–Marquardt method. A total of 211 simulation points, 97 reported here for the first time, were used in the fitting, and the overall standard deviation is less than 2% for both energy and pressure. Second and third virial coefficients derived from the fit in the supercritical region are in excellent agreement with exact values. The critical constants derived from the fit are in reasonable agreement with published estimates.

The effect of truncation and shift on virial coefficients of Lennard–Jones potentials

2010 ◽  
Vol 75 (4) ◽  
pp. 447-462 ◽  
Author(s):  
Katherine R. S. Shaul ◽  
Andrew J. Schultz ◽  
David A. Kofke
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Virial Coefficients ◽  
Expansion Method ◽  
Virial Equation ◽  
Critical Temperatures ◽  
Lennard Jones ◽  
Virial Equation Of State ◽  
Yield Values ◽  
Fifth Order

We present virial coefficients of up to fifth order computed by Mayer-sampling Monte Carlo for several truncated-and-shifted Lennard–Jones potentials. We employ these coefficients within the virial equation of state to compute vapor-branch spinodals and critical points for each potential considered. We find that truncation distances of 5.0σ and higher yield values in significantly better agreement with those of the unmodified potential than those resulting from the more commonly used truncation distances of 2.5 and 3.0σ. We also employ these virial coefficients to examine the perturbed virial expansion method of Nezbeda and Smith for estimating the critical point. We find that the first-order perturbation performs well in characterizing the effect of potential truncation on the critical point for the truncation distances considered, with errors in critical temperatures ranging from –3 to +2% and errors in critical densities about constant at –22%. Addition of higher-order terms to the perturbation treatment brings it closer to the behavior given by the virial equation of state, which at fifth order underestimates the critical temperatures by 2 to 4% and the critical densities by 20 to 30%.

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

Exponential Virial Equation of State

1968 ◽  
Vol 49 (9) ◽  
pp. 4032-4036 ◽  
Author(s):  
Kenneth E. Starling
Keyword(s):  
Equation Of State ◽  
Virial Equation ◽  
Virial Equation Of State
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