The Thermodynamic Properties of Liquid Argon

Abstract

The thermodynamic properties and equation-of-state data of liquid argon are interpreted in terms of a partition function previously derived. This partition function has a part due to vibratory motion of the atoms in the liquid and a part due to translational motion. The vibratory part contains the Debye characteristic temperature Θ for the solid, evaluated for a certain interatomic distance a0 which appears as a parameter in the partition function. a0 is interpreted as the average interatomic distance between nearest neighbors in the liquid, and is a function of a, the latter being defined as (2½V/N)⅓, where V is the molal volume and N Avogadro's number. With V set equal to the molal volume of the liquid at its normal melting point, a0 is assigned a value which appears reasonable from the atomic distribution curves obtained by x-ray studies of the liquid. With this value of a0, the partition function for this fixed value of V gives reasonably good values of the entropy over a large range of temperatures. A small, entirely reasonable change in the partition function improves the agreement with the experimental data. The parameters in the partition function have been evaluated for other values of V by using equation-of-state data. This leads to a calculation of the specific heats of saturated liquid argon over a range of temperatures. The agreement with experimental data is not exceedingly close, but is probably within experimental error. A calculation is also made of the free energies of the solid and liquid phases along the melting curve. They are found to be equal to within reasonably close limits. The application to various values of V leads to the evaluation of a0 as a function of a. The experimental curve for (∂S/∂V)T plotted against V appears to show a change of slope near the value of V characteristic of the liquid at its normal melting point. There is also a change in slope of the curve for da0/da vs. a, at the corresponding value of a. These facts are interpreted in terms of the atomic distribution curves, which appear to indicate a change in structure of the liquid which starts near the same value of V or a. The liquid appears to change from a distorted face-centered structure to a distorted body-centered structure as the volume increases. Information about the potential energy of liquid argon is obtained from the experimental data by application of the partition function. It is found that the potential energy of the liquid can be rather effectively correlated with the potential energy of the solid. Finally, certain peculiarities of the equation-of-state data are believed to indicate a pre-freezing phenomenon, in which particles containing appreciable numbers of atoms and having the structure of the solid, appear in the liquid. A state of this sort can be stabilized by the entropy of mixing of the solid particles with the liquid.