Calculation of thermodynamic parameters of combustion products of propellants under constant volume conditions using the virial equation of state. Influence of values of virial coefficients

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.

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Regions of applicability of the virial equation of state with different numbers of virial coefficients

Combustion Explosion and Shock Waves ◽

10.1007/bf00742493 ◽

1970 ◽

Vol 6 (3) ◽

pp. 243-246

Author(s):

A. A. Antanovich ◽

M. A. Plotnikov ◽

G. Ya. Savel'ev

Keyword(s):

Equation Of State ◽

Virial Coefficients ◽

Virial Equation ◽

Virial Equation Of State

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

Canadian Journal of Physics ◽

10.1139/p86-125 ◽

1986 ◽

Vol 64 (6) ◽

pp. 677-684 ◽

Cited By ~ 37

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.

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

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc2009113 ◽

2010 ◽

Vol 75 (4) ◽

pp. 447-462 ◽

Cited By ~ 17

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%.

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