Isochoric Specific Heat in the Dual Model of Liquids

Fabio Peluso

doi:10.3390/liquids1010007

Abstract

We continue in this paper to illustrate the implications of the dual model of liquids (DML) by deriving the expression for the isochoric specific heat as a function of the collective degree of freedom available at a given temperature and analyzing its dependence on temperature. Two main tasks have been accomplished. First, we show that the expression obtained for the isochoric specific heat in the DML is in line with the experimental results. Second, the expression has been compared with the analogous one obtained in another theoretical dual model of the liquid state, the phonon theory of liquid thermodynamics. This comparison allows providing interesting insights about the number of collective degrees of freedom available in a liquid and the value of the isobaric thermal expansion coefficient, two quantities that are related to each other in this framework.

Highlights

The first part is the process in which the lattice particle collides with the liquid particle and transfers to it momentum and energy, a fraction of which is transformed in the kinetic energy of the liquid particle, and the remaining in the potential energy of its internal Degrees of Freedom (DoF)
CVH < mCV, which represents in turn an upper limit for CVH, providing the maximum thermal energy that can be stored into the harmonic DoF of icebergs
The same trend holds for the speed of sound, which manifests a positive dispersion versus frequency (PSD), while the opposite is true for the viscosity

Summary

Introduction

The value obtained experimentally for the speed of sound in liquid water [25,26,27,32]. If the anharmonic interaction described by the Lagrangian (i.e., the wave-packet–liquid particle interaction in the DML) has a double-well (or multi-well) form, the field can move from one minimum to another (tunnel effect) in addition to oscillating in a single well This motion is analogous to diffusive particle jumps in the liquid and represents a possible origin for the viscosity. The relaxation time is one of the key points of both models, and because the only common argument of PLT and DML is the assumption that thermal energy in liquids is transported by means of collective lattice excitations, both harmonic and anharmonic, the mutual agreement shows that both of them look at the model of the liquid state in the same way from different observation points. Their comparison with the expressions of CV provided by the DML and the PLT is not straightforward

Isochoric Specific Heat in the DML and the PLT Models

DML Comparison with Other Recent Liquid Models

Further Discussion and Conclusions