  Recent research shows that liquids and dense supercritical fluids support
high frequency shear waves. Here, we proposed a general heat capacity model of
supercritical fluids using the latest theoretical findings (the liquid phonon
theory). In this theory, heat capacity cv of supercritical fluids is only
related to the infinite-frequency shear modulus, Debye relaxation time and
minimal length of the longitudinal mode in supercritical fluids rather than the
system-specific structure and interactions. The present model quantitatively
explains the heat capacities in the liquid-like region and the gas-like region
above the critical point. At the same time, the heat capacities of 6
supercritical fluids (including monatomic fluids Ar, Ne and molecular fluids
N2, CO, CO2, CH4) over a wide range of temperatures and pressures were
calculated using the present model, yielding a high accuracy with no
free-fitting parameters. This model has two advantages: (1) The contribution of
intramolecular vibrations was considered, which makes the model applicable to
molecular fluids and high temperature region; (2) This method starts from the
quasi-harmonic Debye model. Thus, it does not require any adjustable parameters
and thermal expansion coefficients. Furthermore, the present cv model of the
rigid liquid-like supercritical region in this paper can be extended to liquid
phase of molecular fluids.
