Isochoric Specific Heat in the Dual Model of Liquids

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 function of the collective degrees of freedom available at a given temperature and analyzing its dependence on temperature. Two main tasks will be 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 will be compared with the analogous one obtained in another theoretical dual model of the liquid state, the Phonon Theory of Liquid Thermodynamics. This comparison will allow to get interesting insights about the number of collective degrees of freedom available in a liquid and on the value of the isobaric thermal expansion coefficient, two quantities that are related to each other in this framework.

Mesoscopic Collective Dynamics in Liquids and the Dual Model

“…We will return on the calculation of V C in Section 3.3, where an expression for V C is determined in the frame of DML. In a separate paper [54] the dependence on temperature of V C is analysed and it is shown that the theoretical expression obtained in the DML is in line with the experimental results; besides, its comparison with the analogous one obtained in the PLT model allows to get interesting insights about the number of collective degrees of freedom available in a liquid and on the value of the isobaric thermal expansion coefficient. A limitation of the PLT is that this model only deals with intermolecular modes and neglect intramolecular ones; DML tries to cover this gap with the aid of the parameter ' m ', accounting for the statistical number of DoF actually excited at the considered thermodynamic state (see Eq.…”

“…( 20), that deserves a dedicated analysis because it has many interesting consequences. In a separate paper [54] it has been compared with the expression given by PLT model [11,[29][30][31][32][33][34][35][36][37][38] for the same physical quantity. The Authors calculate an expression for the harmonic and anharmonic contributions to the specific heat within a liquid phonon theory based on the concept of liquid relaxation time introduced by Maxwell [8].…”

“…The above behaviour is due, among others, to the variation vs temperature of m, 0  dT dm . The reader is addressed to [54] for an accurate and dedicated analysis.…”

“…DML provides also a comparison with some results obtained by independent research groups on the dynamics and thermodynamics of liquid media (liquid specific heat, thermal conductivity, sound velocity, capability of transporting momentum, etc.). In a separate paper [54] a direct comparison is made between the expressions for the specific heat arrived at in the two models, DML and PLT. This comparison provides interestingly the minimum and maximum numerical values of the number of collective DoF involved in the exchange of energy and momentum, m , and of its derivative with respect to Temperature, dT dm .…”

“…This is a fundamental point of the DML. In a separate paper [54], this argument is deeply discussed and limits for dT dm and m are deduced and analysed.…”