Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures

A Monte Carlo method for the evaluation of equilibrium thermodynamic properties of a system of interacting particles is described. The classical configurational partition function at a given density is calculated from the estimated value of the weight function γ(Φ), up to a factor that is independent of temperature; γ(Φ)dΦ is the fraction of all accessible configurations of N particles confined to a fixed volume for which the total potential energy has a value between Φ and Φ+dΦ. The weight function is found to vary approximately as (Φ—Φ0)n, where Φ0 and n are constants; n increases roughly linearly with density. The method is applied to the calculation of thermodynamic properties of gaseous argon at four densities in the temperature range between −100° and 150°C. A Lennard‐Jones potential function is used and though the agreement with experiment is good there is evidence of inadequacy in the Leonnard‐Jones model. All calculations are made for N=32.

[1]  I. R. Mcdonald,et al.  Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method , 1967 .

[2]  R. Tolman,et al.  The Principles of Statistical Mechanics. By R. C. Tolman. Pp. xix, 661. 40s. 1938. International series of monographs on physics. (Oxford) , 1939, The Mathematical Gazette.

[3]  Marshall N. Rosenbluth,et al.  Further Results on Monte Carlo Equations of State , 1954 .

[4]  F. R. Parker,et al.  Recent monte carlo calculations of the equation of state of Lenard-Jones and hard sphere molecules , 1958 .

[5]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[6]  A. Rotenberg.  Monte Carlo Equation of State for a Mixture of Hard Spheres , 1965 .

[7]  F. R. Parker,et al.  Monte Carlo Equation of State of Molecules Interacting with the Lennard‐Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature , 1957 .

[8]  E. Smith,et al.  Thermodynamic properties of mixtures of hard sphere molecules by Monte Carlo methods , 1963 .

[9]  A. Rotenberg.  Equation of State of Hard Spheres at Very High Density , 1965 .

[10]  B. Alder,et al.  Melting Curve at High Pressure , 1966 .

[11]  A. Michels,et al.  Isotherms of argon between 0°c and 150°c and pressures up to 2900 atmospheres , 1949 .

[12]  A. Rotenberg.  Monte Carlo Equation of State for Hard Spheres in an Attractive Square Well , 1965 .

[13]  J. Levelt,et al.  Thermodynamic properties of argon at temperatures between 0°C and −140°C and at densities up to 640 amagat (pressures up to 1050 atm.) , 1958 .

[14]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[15]  W. W. Wood,et al.  Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres , 1957 .

[16]  J. Benson,et al.  EXISTENCE OF TWO PHASES IN ONE-DIMENSIONAL CLASSICAL FLUIDS , 1966 .