On isochoric heat capacity of fluids at high temperatures

I.H. Umirzakov

Physica A: Statistical Mechanics and its Applications, 2020, vol. 539, issue C

Abstract: As known, the isochoric heat capacity Cv of many atomic and molecular substances in liquid and supercritical fluid states decreases with increasing temperature at high temperatures. It is shown that: such a behavior of Cv is related to a decrease of the contribution of interactions of atoms with each other to Cv with increasing temperature; such a behavior of Cv takes place for atomic substances when the fluctuations of the total kinetic energy increase with increasing temperature faster than that of the total potential energy; such a behavior of Cv can be described by the density independent radial distribution function of non-ideal dilute gas consisting of atoms interacting with each other via an additive potential which is equal to the sum of a spherically symmetrical pair interaction potentials over of all pairs of particles; the pair potential can be equal to: the potential of soft spheres, bounded potential, non-positive potential, the sum of the potential of hard spheres and bounded or non-positive or attractive potential, and the sum of the repulsive potential of soft spheres and attractive London potential; the above conclusions are valid for molecular substances if the isochoric heat capacity of the molecular ideal gas does not depend on temperature; the radial distribution function of non-ideal dilute gas can describe the above behavior of Cv for argon in liquid and supercritical states; the Carnahan–Starling equation of state for the hard spheres with temperature dependent diameter gives a good quantitative description of the isochoric heat capacity of argon if the diameter is defined using the Lennard-Jones potential. The equation to define the Frenkel line of molecular substances on the (temperature, density)-plane is established. The explicit expressions to define the Frenkel line are derived. It is shown that the existence of the Frenkel line established from the condition Cv−Cv,ig=k∕2, where Cv,ig is the isochoric heat capacity of an ideal gas, does not mean that the solid-like and liquid-like states exist in liquids, and the transition from Cv>2k to Cv<2k across the Frenkel line is the transition from the solid-like states to liquid-like ones.

Keywords: Isochoric heat capacity; Liquid; Fluid; Argon; Interaction potential; Radial distribution function; Frenkel line (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:539:y:2020:i:c:s0378437119316668

DOI: 10.1016/j.physa.2019.122941

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