On isochoric heat capacity of fluids at high temperatures

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.