Isobaric Thermal Expansion Research Articles

Study of tetraalkylammonium salts in acetonitrile solutions: Transport properties, density, thermal expansion and phase transitions

The electrical conductivity of binary solutions of tetraethylammonium trifluoromethanesulfonate ([TEA][OTf]), tetraethylammonium tetrafluoroborate ([TEA][BF4]) and spiro-(1,1′)-bipyrrolidinium tetrafluoroborate ([SBP][BF4]) in acetonitrile was measured at atmospheric pressure in the temperature range of 293.15–348.15 K for different salt mole fractions. The highest electrical conductivities of the acetonitrile solutions of [TEA][BF4], [SBP][BF4] and [TEA][OTf] were 96 ± 7, 94.5 ± 0.5 and 71.6 ± 0.5 mS·cm−1, respectively, at 348.15 K. The activation energy of the conductivity for nonassociating electrolytes was calculated using the Arrhenius equation, and the activation energy of the ionic conductivity of glass-forming liquids was calculated using the Vogel-Fulcher-Tamman equation. The cation and anion diffusion coefficients in the [TEA][OTf], [TEA][BF4] and [SBP][BF4] solutions in acetonitrile were determined by the robust pulsed-gradient stimulated echo sequence technique. Experimental density data were used to calculate the isobaric thermal expansion coefficients in the temperature range of 293.15–348.15 K. The thermophysical properties (the temperatures and heats of the phase transitions and the melting temperatures) of the pure salts and their binary solutions in acetonitrile were determined by differential scanning calorimetry.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set.

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρliq and vaporization enthalpies ΔHvap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κT, the isobaric thermal-expansion coefficient αP, the isobaric heat capacity cP, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔGwat, and the free energy of solvation ΔGche in cyclohexane. For the target properties ρliq and ΔHvap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κT, αP, ϵ, D, and ΔGche; and less accurate results in terms of cP and ΔGwat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Enthalpy, heat capacity and thermal expansivity measurements of MgSiO3 akimotoite: Reassessment of its self-consistent thermodynamic data set

Enthalpy, isobaric heat capacity (CP) and thermal expansivity (α) of MgSiO3 akimotoite were re-determined by drop-solution calorimetry, differential scanning calorimetry and high-temperature powder X-ray diffraction measurement, respectively. From the obtained α, thermal Grüneisen parameter of MgSiO3 akimotoite was constrained to be 1.3. Using isochoric heat capacity by lattice vibrational model calculation and the Grüneisen relation equation, α and CP above maximum measurement temperature and the temperature derivative of isothermal bulk modulus were optimized by the least squares fitting to an existing P–V–T dataset which makes these parameters self-consistent. The obtained thermodynamic data set for MgSiO3 akimotoite was used to calculate the akimotoite–bridgmanite phase equilibrium boundary in MgSiO3 and high-pressure phase relations in Mg2SiO4. The result shows the stability field of the phase assemblage of MgSiO3 akimotoite + MgO below about 1400 K and around 23 GPa, suggesting the phase transition from ringwoodite to bridgmanite + ferropericlase via akimotoite + ferropericlase in cold subducted slabs.

Influence of MgO concentration and water content on thermal conductivity enhancement of nanofluids based on deep eutectic solvent (choline chloride:glycerol)

The development and extensive studies on cost-effective and eco-friendly nanofluids with efficacious thermophysical properties are essential regarding the ever-increasing concerns about environmental hazards. Thus, the present research intended to offer novel green nanofluids based on a two-step method for the dispersion of magnesium oxide (MgO) nanoparticles in two binary DESs and four ternary DESs. The binary DESs were composed of choline chloride (ChCl) and glycerol (Gly) in 1:2 and 1:5 M ratios, and the four ternary DESs consisted of ChCl, Gly, and water in 1:2:1 1:2:2, 1:5:1, and 1:5:2 M ratios. Dynamic light scattering analyzed the stability of samples for several days. Moreover, a comprehensive experimental analysis of thermophysical characteristics of DESs and DES-based nanofluids was executed by defining specific classifications, including type of base solvents, MgO mass concentration (1, 5, and 10 wt%), and temperature range (283.15 to 333.15 K). In addition, the isobaric thermal expansivities were calculated by empirical data. The experimental findings revealed that adding nanoparticles and water content in DES structure caused an augment in thermal conductivity. Around 4–21% increase in thermal conductivity was observed for nanofluids made up of binary DESs, and around 10% for those made up of ternary DESs. Furthermore, DES-based nanofluids showed an average 1.2% drop in density versus temperature, while around 3% enhancement was achieved for 5 wt% MgO suspended in 1ChCl:2Gly. Based on comparisons with the most relevant nanofluids reported in the previous studies, it was determined that the nanofluids presented in the current study were superior. Eventually, it was demonstrated that the nanofluid of 10 wt% MgO in binary 1ChCl:5Gly mixture achieved the highest thermal conductivity (0.304 W.m-1K−1) can be considered as a high-potential candidate for heat transfer purposes.

Prigogine-Defay ratio and its change with fictive temperature approaching the ideal glass transition

According to equilibrium thermodynamic theory, a liquid of zero configurational entropy would undergo an Ehrenfest type second order transition to another disordered structure at a temperature T2 known as the ideal glass transition temperature, but glass formation prevents one from observing it. The heat capacityCp, isothermal compressibility, κT, and isobaric thermal expansion coefficient, αp, change by an amount Δ at the Ehrenfest temperature, TEH=T2, and also at the glass transition temperature Tg. The Ehrenfest ratio RE at TEHorT2, ΔCp,EHΔκT,EHTEHVEH(Δαp,EH)2≡1. In contrast, experimentally determined Prigogine-Defay ratio, ∏P−D at Tg, ΔCpΔκTTV(Δαp)2>1, where V is the volume at the respective temperatures. Angell and Sichina [Ann. N. Y. Acad. Sci. 279 (1976) 53-67] discussed how ∏P−D would change to RE if a liquid could be cooled slowly enough to reach T2. After critically reviewing the basic aspects of RE and of experimental and theoretical values of ∏P−D, we use generic variations of ΔCp, ΔκT, ΔαP and V with the fictive temperature, Tf, and the extrapolated values of these quantities for o-terphenyl at T=T2, and calculate RE and ∏P−D. We find that RE<∏P−D, thus contributing to Angell-Sichina's discussion of the unique structure of the low temperature disordered phase. We then consider how ∏P−D would change if the entropy of a liquid were extrapolated such that it did not violate the third law of thermodynamics and there was no need for the conjecture of an Ehrenfest transition.

The mixing properties, IR analysis and quantum chemical calculations of trimethoxylsilane derivatives with ethanol, 1-butanol, 1-pentanol and 1-octanol

The density, viscosity and speed of sound of trimethoxylsilane derivatives with ethanol, 1-butanol, 1-pentanol and 1-octanol have been measured at 298.15, 303.15, 308.15, 313.15 K, 318.15 and 323.15 K, respectively. The excess molar volume, viscosity deviation, excess Gibbs energy of activation of viscous flow, isobaric thermal expansivity and isentropic compressibility deviation were calculated from these results. The Redlich–Kister equation was used for the correlation. The calculated excess properties have been discussed according to the possible interactions formed between the molecules in the mixture using equimolar attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy. In all of the compositions and experimental temperature ranges studied, the excess molar volumes were found to be negative for vinyl trimethoxy silane and phenyl trimethoxy silane with ethanol. This may be attributed to the close accumulation of molecules and easier formation of cross-association structures between the alkoxysilane molecules. However, the excess molar volume of the binary mixture of vinyl trimethoxy silane and phenyl trimethoxy silane with n-butanol, n-pentanol, and n-octanol was positive. Hydrogen bond fracture may play a leading role in this process. The excess molar volumes of the binary system comprised of trifluoropropyl trimethoxy silane with ethanol and 1-octanol were all positive. This may be attributed to the influence of steric hindrance, which makes it difficult for trifluoropropyl trimethoxy silane to form a cross-association structure with alcohol molecules.

An experimental study of novel nanofluids based on deep eutectic solvents (DESs) by Choline chloride and ethylene glycol

In this work, the preparation and characterization of some new nanofluids based on deep eutectic solvents (DESs) consisting of a hydrogen bond acceptor, ethylene glycol (EG), and a hydrogen bond donor, choline chloride (ChCl), as well as water, are presented. The nanofluids were designed by the dispersion of spherical MgO nanoparticles in four different DESs, ChCl:EG (molar ratio of 1:2), 1ChCl:5EG, 1ChCl:2EG:2Water, and 1ChCl:5EG:2Water. The stability of nanofluids was carried out by measuring size distribution for five days, which discovered the best results obtained with nanofluids of dispersed MgO in DES 1ChCl:5EG. Thermophysical properties (thermal conductivity and density) were measured and the influence of nanoparticles’ mass fraction, temperature, and water content all were examined. The acquired outcomes revealed that the trend of density was reducing by increment in temperature since for pure base fluids and DES-based nanofluids 1.3% decrement were recorded, averagely (the decline in density was sharper in the case of DES 1ChCl:5EG and its based nanofluids). The thermal conductivity was almost constant during the range of 283.15–333.15 K. It confirmed that the thermal conductivities of prepared nanofluids based on DESs with water were higher in comparison to the ones based on DESs without water and nanoparticles concentration could promote thermal conductivity. The greatest enhancement was gained at 10 wt% of MgO suspended in DES 1ChCl:2EG. The isobaric thermal expansivity was also determined at different temperatures. Eventually, the general conclusions were drawn and concerning the results, the MgO/DES 1ChCl:2EG 10 wt% nanofluids was introduced as the most efficient.

Solvation properties of 1-butyl 2, 3-dimethyl imidazolium chloride ionic liquid in aqueous and aqueous glycine solutions at different temperatures using volumetric and compressibility parameters

Volumetric and compressibility approaches were employed in this investigation to analyse the intermolecular interactions of 1-Butyl-2,3-dimethyl imidazolium chloride in aqueous, in 0.05 mol.kg−1 aqueous glycine and 0.1095 mol.kg−1 aqueous glycine solutions over the concentration range 0.01 to 0.13 mol.kg−1 at different temperatures i.e., T= (288.15,293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure by measuring density(ρ) and speed of sound(u) data. Various thermophysical parameters such as apparent molar volume of solute(Vϕ), limiting apparent molar volume of solute(Vϕ0), transfer limiting apparent molar volume of soluteΔtrVϕ0, Hepler's constant (∂2Vϕ0/∂T2), isentropic compressibility (κS), apparent molar isentropic compression of solute (KS,ϕ), partial molar isentropic compression of solute(KS,ϕ0) and partial molar isentropic compression of transfer of solute ΔtrKS,ϕ0 have been calculated using the corresponding thermophysical data at studied temperatures. In addition, the temperature dependence of apparent molar volume of solute has been used to determine isobaric expansivity or thermal expansion coefficient(α), apparent molar expansivity of solute Eϕ and limiting apparent molar expansivity solute Eϕ0 parameters of binary and ternary systems. The findings were described in terms of solute–solute and solute–solvent interactions.

Density, viscosity, surface tension, and spectral analysis of polyethylene glycol 300 + 1,2-Propylenediaminebinary liquid mixture

At T = 293.15 ∼ 318.15 K, the density (ρ), viscosity (η), and surface tension (γ) data of polyethylene glycol 300 (PEG300) and 1,2-propane diamine (1,2-PDA) binary liquid mixture in the entire composition range were systemically measured. Meanwhile, the influence of different temperatures on the physical properties of the binary liquid mixture was deeply discussed. The values of ρ and η of PEG300 were compared with the reported values of ρ and η of different linear alcohols under the same experimental conditions. It was found that the values of ρ and η of linear alcohols were related to the number of carbon chains. Under isothermal conditions, the values of ρ and η increased with the number of carbon chains. After that, excess molar volume (VmE), excess viscosity (ηE), surface tension deviation (Δγ), excess Gibbs energy of activation of viscous flow (ΔG∗E), and molar isobaric thermal expansion (Ep,m) of PEG (1) + 1,2-PDA (2) binary mixture were calculated. The η values were fitted with four semi-empirical formulas, and the VmE, ηE, and Δγ values were fitted with Redlich-Kister (R-K) equation. IR, UV, FLS, and Raman spectral technologies were used to further prove the interaction among different molecules of the liquid mixture.

Simultaneous compressed liquid viscosity and density measurements of n-alkanes at temperatures between (291 and 353) K and pressures up to 50 MPa

Compressed liquid density (ρ) and dynamic viscosity (η) were simultaneously measured for pure liquid n-alkanes (n-hexane, n-heptane, n-octane, n-nonane, and n-decane) in the temperature range from (291 to 353) K and pressure up to 50 MPa by an experimental system using a coil capillary tube viscometer (CCTV) coupled with a vibrating tube densimeter (VTD). The reliability and validation of this measuring system were verified by determining and comparing both dynamic viscosity and density data of ethanol published in the international literature. The maximum viscosity deviation was 8 μPa ∙ s for viscosity and 0.87 kg ∙ m−3 for density. The measurements were carried out with a relative expanded uncertainty (k=2) of 1.00 % for the measurements of dynamic viscosity and 0.20 % for the measurements of density considering the impurities of the chemical compounds). Both dynamic viscosity and density data were represented using two empirical models, obtaining a maximum deviation of 2.49 % for the dynamic viscosity and 0.12 % for the density with the experimental data. Finally, the isothermal compressibility and isobaric thermal expansivity were calculated from the empirical models at the reported conditions.

Synthesis and Characterization of Fluorinated Phosphonium Ionic Liquids to Use as New Engineering Solvents

In this work, a set of novel fluorinated ionic liquids (FILs), based on different tetra-alkyl-phosphonium cations with perfluorobutanesulfonate and perfluoropentanoate anions, were synthesized and characterized in order to check their suitability to apply as engineering solvents. Thermophysical and thermal properties were both determined between 293.15 and 353.15 K, and the molecular volumes and free volumes and the coefficients of isobaric thermal expansion were determined from experimental values of refractive index and density. Lastly, the Walden plot was used to evaluate the ionicity of the novel FILs. The cytotoxicity of these compounds was also determined using the human hepatocellular carcinoma cells (HepG2) and the human colon carcinoma cells (Caco-2). Finally, the results were all discussed with the aim of understanding the behaviour of these compounds, considering the influence of the anion and the hydrogenated alkyl chain length. In summary, the new FILs synthesized in this work present adequate properties for their application in different industrial processes. Most of these compounds are liquid at room temperature with high decomposition temperatures. All phosphonium-based FILs have lower densities than conventional ionic liquids and common organic solvents, and the viscosity depends directly on the selected anion. Furthermore, the ionicity of FILs based on the sulfonate anion is higher than those based on the carboxylate anion. Finally, the phosphonium-based FILs have no significant effect on cellular viability at lower concentrations.

Determination of Density, Isobaric Thermal Expansivity Coefficient and Isothermal Compressibility Coefficient Correlations for n-Dodecane and n-Nonane, as a Function of Temperature and Pressure

Determination of Density, Isobaric Thermal Expansivity Coefficient and Isothermal Compressibility Coefficient Correlations for n-Dodecane and n-Nonane, as a Function of Temperature and Pressure

High pressure thermophysical characteristics of butyl caprate and butyl laurate as fully biorenewable components of biodiesel fuel

The butyl-based fatty acid esters can be considered as fully biorenewable components of biodiesel fuel due to the possibility of synthesis from biobutanol and vegetable or animal oils. For this reason in this work high pressure thermophysical properties of butyl caprate (butyl decanoate) and butyl laurate (butyl dodecanoate) used for optimization spray characteristics in diesel injection systems are studied. The speed of sound was measured at temperatures from 293 to 318 K and pressures from 0.1 to 101 MPa. The speed of sound, density, isobaric heat capacity, viscosity, surface tension were measured under atmospheric pressure and at the temperatures from the range of 273 to 363 K. The effect of temperature and pressure on density, isentropic and isobaric compressibilities, isobaric heat capacity, and isobaric thermal expansion was determined by the acoustic method. The results obtained show that differences between density and isentropic compressibility of esters can be compensated by temperature and/or pressure. Comparison of thermophysical properties of butyl caprate and butyl laurate with characteristics for diesel, biodiesel composed of fatty acids methyl esters of rapeseed oil, neat methyl and ethyl esters shows that they can be considered as promising fuel additives in this regard.

Thermophysical properties of chloropropanes in liquid phase: Experiments and simulations

In this work, the properties of liquid 1-chloropropane, 2-chloropropane and 1,3-dichloropropane are investigated. The Span–Wagner equation of state (EoS) is used to improve the existing thermophysical properties as a function of the temperature and pressure of these chloropropanes. For 1-chloropropane and 2-chloropropane, the thermophysical properties are compared with Molecular Dynamics simulation results performed in the range of temperature 293.15–373.15 K and the range of pressure 0.1–200 MPa. In addition, for both monochloropropanes, the isobaric thermal expansion coefficient obtained from Span–Wagner EoS and MD simulations is compared with the one obtained from the recently proposed Daridon’s method.

Ferrocene based ionic liquid: synthesis, structure, transport properties and mechanism of thermal degradation

Doping with transition metals is a promising way to expand the industrial applications of ionic liquids (ILs). This study reports the synthesis, structure and physicochemical properties of a novel butyl-dimethyl-(ferrocenylmethyl)ammonium bis(trifluoromethanesulfonyl)imide ([BDFA][NTf2]) IL. The thermo-gravimetric analysis combined with mass spectrometry of evolved gases demonstrated the high thermal stability of [BDFA][NTf2] up to 500 K. The thermal degradation of [BDFA][NTf2] at higher temperatures is a multi-step process accompanied by the cation destruction through the Hofmann elimination reaction and the subsequent transformations, such as fragmentation of the products of thermal degradation of the [NTf2]-anion and the direct interaction between these products. The glass transition and melting temperatures of [BDFA][NTf2] measured by the differential scanning calorimetry are 229 and 320 K, respectively. The electrical conductivities and densities of binary mixtures of [BDFA][NTf2] with acetonitrile (AN) were measured in the temperature range of 293 – 348 K at atmospheric pressure. The isobaric thermal expansion coefficients were calculated from the experimental data. The conductivity – temperature dependences were analyzed using the Arrhenius and Vogel-Fulcher-Tammann equations. The activation energy of ion transport and limiting conductivity increased with the IL mole fraction in AN.

Thermodynamic study of the aqueous pseudo-binary mixtures of betaine-based deep eutectic solvents at T = (293.15 to 313.15) K

ABSTRACT This work investigates physicochemical properties of betaine/propylene glycol (Bet/PG) and betaine/ethylene glycol (Bet/EG) DESs in water by measuring their densities in neat state and aqueous mixtures over the entire composition range at T = (288.15–318.15) K under atmospheric pressure (≈ 85 kPa). The obtained values of density were used to compute the excess molar volumes (), molar volume (V m), apparent molar volume (), limiting apparent molar expansibility () and the isobaric thermal expansion coefficient (). The solute-solvent interactions in the investigated solutions are evaluated on the basis of these important physicochemical properties. The results indicated that two studied DESs act as a structure-making solute in water over the whole temperature range using Hepler’s constant. Finally, the experimental densities were correlated with some models including Jouyban-Acree, Jouyban-Acree-van’t Hoff, modified Jouyban-Acree-van’t Hoff, Redlich-Kister and Emmerling. The Redlich-Kister expression and Jouyban-Acree model were also used for representation of values.

Polarisation of water under thermal fields: the effect of the molecular dipole and quadrupole moments.

The investigation of the behaviour of water under thermal fields is important to understand thermoelectricity of solutions, aqueous suspensions, bioelectric effects or the properties of wet materials under spatially inhomogeneous temperature conditions. Here we discuss the response of bulk water to external thermal fields using non-equilibrium molecular dynamics simulations, and five widely used forcefields: TIP4P/2005, TIP4P/2005f, OPC, SPC/E and TIP3P. These models all show the thermal polarisation (TP) effect in bulk water, namely the build-up of an electrostatic field induced by the temperature gradient. The strength of this effect is ∼0.1-1 mV K-1 at near-standard conditions for all forcefields, supporting the generality of TP. Moreover, all the models predict a temperature inversion of the polarisation field, although the inversion temperatures vary significantly across different models. We rationalise this result by deriving theoretical equations that describe the temperature inversion as a balance of the isobaric thermal expansion, dipole orientation in the thermal field and the ratio of the molecular dipole/quadrupole moments. Lower ratios lead to higher inversion temperatures. Based on our results, we conclude that the accuracy of the forcefields describing the TP effect decreases as, TIP4P/2005 ∼ TIP4P/2005f ∼ OPC > SPC/E > TIP3P. At coexistence conditions, the inversion temperature is expected to be around 400 K. Furthermore, we establish a correlation between the TP inversion temperature and the temperature corresponding to the minimum of the liquid-vapour surface potential of water.

Viscosity and Density Measurements on Liquid n-Heptadecane at High Pressures

This article reports novel measurements of the viscosity, η, of liquid n-heptadecane at pressures up to 70 MPa, along six isotherms between 303 and 358 K. The experiments were carried out using a vibrating wire viscometer operated in the forced mode. The 303 and 313 K isotherms have a restricted range of pressures to avoid eventual solidification. The present measurements have an uncertainty less than U(η) = 0.015·η with a confidence level of 0.95. Complementary measurements of the density, ρ, were performed with the same ranges of temperature and pressure, using a DMA HP Anton Paar U-tube densimeter, with a DMA 5000 instrument as a reading unit. The overall maximum uncertainty is U(ρ) = 0.002·ρ with a confidence level of 0.95. The article provides a correlation of the viscosity of compressed liquid n-heptadecane with the molar volume, constructed by means of a scheme based on a modified hard-sphere theory, which describes the experimental data within ca. 1%. A program is provided in the Supporting Information to promptly perform interpolation of the viscosity as a function of temperature and pressure. The isothermal compressibility and the isobaric thermal expansivity were calculated from the density. Viscosity–pressure coefficients have also been determined from the viscosity.

Linear isotherm regularities of liquid gallium under pressure

Several new regularities in liquid gallium have been obtained from both the available experimental data and calculated thermodynamic properties along the isothermal lines with the equation of state (EoS) of a power law form. The quantity Z−1V3 is linearly proportional to V3 for all isotherms at high temperatures. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT derived from the available experimental data and EoS of a power law form are observed to be linear with respect to V−3 with the temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity (LIR) EoS. By using the analytical expression from the LIR EoS, the calculated isobaric thermal expansion coefficient, isochoric heat capacity, isobaric heat capacity, Grüneisen parameter, and Anderson–Grüneisen parameter show quite different behavior with pressure at a constant temperature compared with those values from EoS of a power law form. In addition, analytical expressions of thermodynamic properties of liquid gallium are derived from the LIR EoS, such as adiabatic bulk modulus, sound velocity, entropy, internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy, which have the same tendency with pressure at a constant temperature as the numerically integrated values from EoS of a power law form.

Isochoric Specific Heat in the Dual Model of Liquids

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.