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We respond to recent articles (Int. J. Thermophysics 39 139 2018, ibid.40 21 2019) that seek to deny the veracity of the empirical discovery and thermodynamic description of a gas-liquid supercritical mesophase. These IJT articles are misleading because they are based upon a false premise that the mesophase is a hypothetical concept. There is no "mesophase hypothesis" as wrongly stated in the title of article IJT, 40 21, 2019. Unlike the critical point continuity hypothesis of van der Waals (1873), or the universal critical point scaling hypothesis advocated by Anisimov and Sengers, and others since 1965, the supercritical mesophase is an empirical entity. If a hypothetical van der Waals fluid with the properties of a critical-state point with divergent isochoric heat capacity, and with the scaling properties of "universality" theory, were to exist, it could be used to vitiate the second law of thermodynamics. By contrast, the supercritical mesophase, discovered originally from computer experiments, is an empirically established equilibrium fluid region, of two-state systems of gas plus liquid, within a single Gibbs phase; the properties of which are determined by the laws of thermodynamics. Here, we provide a phenomenological definition of the gas-liquid supercritical mesophase that accords with the body of compelling experimental results over a 150-year period since van der Waals including modern computer experiments info:eu-repo/semantics/publishedVersion

Heat capacities Cv, Cp, and sound velocity W of carbon dioxide are calculated on the basis of a new thermal combined equation of state (EoS) with a low number of regulated constants. This equation includes a new regular EoS with 11 coefficients, a scaling EoS with six coefficients, and a regular transition function containing two adjustable parameters. Calculating results for thermodynamic properties of CO2 in the regular behavior range of up to 200 MPa correspond to the accuracy level of modern practical equations of state with large numbers of determined constants. This makes it possible to calculate the properties of CO2 in the critical region, taking into account the achievements of scaling theory. To determine the constants of the calculated equations, only p,ρ,T-data for CO2 were used. The experimental and tabular data on Cv, Cp, S, H, and W were not involved except isochoric heat capacity Cv in the ideal gas state. These data were used to compare the calculated results with the experimental and tabulated values. The universal critical exponents were taken in accordance with the three-dimensional Ising model. The average errors in describing the thermal properties of CO2 do not exceed errors: rms error is 0.93 % in pressure and max deviation in Cv is 10 %. Divergences in the critical region relate to application of the scaling equation of state, in contrast to the regular equations. The comparison was made with calculated Cv, Cp using the current crossover EoSs for CO2.

It is shown that the meso-phase hypothesis of Woodcock L. V. fails to describe quantitatively and qualitatively the isochoric and isobaric heat capacities, speed of sound, long wavelength limit of the structural factor, isothermal compressibility, density fluctuations, Joule-Thompson coefficient and isothermal throttling coefficient of argon in the meso-phase region. It is also shown that VdW-EOS can describe qualitatively the excess Gibbs energy and rigidity of argon near critical point., Comment: arXiv admin note: text overlap with arXiv:1810.02699

It is shown that: (1) the expressions for the isochoric (CV) and isobaric (CP) heat capacities of liquid and gas, coexisting in phase equilibrium, the heat capacities at saturation of liquid and gas (Cσ) and the heat capacity Cλ used in the article “On the Interpretation of Near-Critical Gas–Liquid Heat Capacities, L. V. Woodcock, Int. J. Thermophys. (2017) 38, 139” are incorrect; (2) the conclusions of the article based on the comparison of the incorrect CV, CP and Cλ with experimental data are also incorrect; (3) the lever rule cannot be used to define CV and CP in the two-phase coexistence region; (4) a correct expression for the isochoric heat capacity describes well the experimental data; (5) there is no misinterpretation of near-critical gas–liquid heat capacity measurements in the two-phase coexistence region; (6) there are no proofs in the article that: (a) the divergence of CV is apparent; (b) it has not been established experimentally that the thermodynamic properties of fluids satisfy scaling laws with universal critical exponents asymptotically close to a single critical point of the vapor–liquid phase transition; and (c) there is no singular critical point on Gibbs density surface. We obtained the relations connecting the isochoric heat capacity in the two-phase region with thermodynamic properties at saturation of homogeneous liquid and gas which can be used to verify the equation of state.

An equation of state is developed for the Lennard-Jones model fluid, truncated and shifted at $$r_{\mathrm{c}} = 2.5\sigma $$ . The underlying dataset contains thermodynamic properties at 706 state points including pressure, residual internal energy, first volume derivative of the residual internal energy, and residual isochoric heat capacity as a function of temperature and density. The equation of state is explicit in terms of the Helmholtz energy, allowing the determination of any thermodynamic property by differentiation. It is valid for temperatures $$0.6

New measurements are reported for the isochoric heat capacity of the ionic liquid substance 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]). These measurements extend the ranges of our earlier study [N.G. Polikhronidi et al., Phys. Chem. Liq. 52, 657 (2014)] by 5 % of the compressed liquid density and by 75 kelvins. An adiabatic calorimeter was used to measure one-phase (CV1) liquid and two-phase (CV2) liquid + vapor isochoric heat capacities, densities (ρS ), and phase-transition temperatures (TS ) of the ionic liquid (IL) substance. The combined expanded uncertainty of the density ρ and isochoric heat capacity CV measurements at the 95 % confidence level with a coverage factor of k = 2 is estimated to be 0.15 % and 3 %, respectively. Measurements are concentrated in the immediate vicinity of the liquid + vapor phase transition curve, in order to closely observe phase transitions. The present measurements and those of our earlier study are analyzed together, and are presented in terms of thermodynamic properties (TS, ρS, CV1 and CV2) evaluated at saturation and in terms of key derived thermodynamic properties Cp, CS, [Formula: see text], and [Formula: see text] on the liquid + vapor phase transition curve. A thermodynamic relation by Yang and Yang is used to confirm the internal consistency of measured two-phase heat capacities CV2, which are observed to fall perfectly on a line as a function of specific volume at a constant temperature. The observed linear behavior is exploited to evaluate contributions to the quantity CV2 = f(V,T) from chemical potential [Formula: see text] and from vapor pressure [Formula: see text]. The physical nature and specific details of the temperature and specific volume dependence of the two-phase isochoric heat capacity and some features of the other derived thermodynamic properties of IL at liquid saturation curve are considered in detail.

PVT properties were measured for hydrogen by the Burnett method in the temperature range from 353 K to 473 K and at pressures up to 100 MPa. In the present Burnett method, the pressure measurement was simplified by using an absolute pressure transducer instead of a differential pressure transducer, which is traditionally used. The experimental procedures become easier, but the absolute pressure transducer is set outside the constant temperature bath because of the difficulty of its use in the bath, and the data acquisition procedure is revised by taking into account the effects of the dead space in the absolute pressure transducer. The measurement uncertainties in temperature, pressure, and density are 20 mK, 28 kPa, and 0.07 % to 0.24 % (k = 2), respectively. Based on the present data and other experimental data at low temperatures, a virial equation of state (EOS) from 220 K to 473 K and up to 100 MPa was developed for hydrogen with uncertainties in density of 0.15 % (k = 2) at P ≤ 15 MPa, 0.20 % at 15 MPa 40 MPa, and this EOS shows physically reasonable behavior of the second and third virial coefficients. Isochoric heat capacities were also calculated from the virial EOS and were compared with the latest EOS of hydrogen. The calculated isochoric heat capacities agree well with the latest EOS within 0.5 % above 300 K and up to 100 MPa, while at lower temperatures, as the pressure increases, the deviations become larger (up to 1.5 %).

Second-order thermodynamic derivative properties, such as isobaric thermal molar expansions, isothermal and adiabatic molar compressibilities, and isochoric molar heat capacities of (ethanol, decan-1-ol, 2-methyl-2-butanol) + heptane mixtures at pressures up to 100 MPa and in the temperature range from 293.15 K to 318.15 K were derived from experimental speed-of-sound u(T, p), density ρ(T, p = 0.1 MPa), and isobaric heat-capacity Cp(T, p = 0.1 MPa) data using appropriate thermodynamic relations. Excess values for the given properties were calculated according to the criterion of thermodynamic ideality of a mixture (Douheret et al., Chem. Phys. Chem. 2, 148 (2001)), i.e., assuming that the chemical potential of component i in the ideal liquid mixture is equal to the chemical potential of component i in the mixture of perfect gases. The deviations from ideality for the mixtures under test have been explained in terms of the self-association of alcohols in solution which produces a strong departure from random mixing, the change in the non-specific interactions during mixing, and the packing effects.

Two- and one-phase liquid and vapor isochoric heat capacities (C V ρ T relationship) of diethyl ether (DEE) in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were carried out in the temperature range from 347 K to 575 K for 12 liquid and 5 vapor densities from 212.6 kg·m−3 to 534.6 kg·m−3. The expanded uncertainties (coverage factor k = 2, two-standard deviation estimate) for values of the heat capacity were 2% to 3% in the near-critical region, 1.0% to 1.5% for the liquid isochores, and 3% to 4% for the vapor isochores. The uncertainties of density (ρ) and temperature (T) measurements were 0.02% and 15 mK, respectively. The values of the internal energy, U(T, V), and second temperature derivative of pressure, (∂2 P/∂T 2) ρ , were derived using the measured C V data near the critical point. The critical anomaly of the measured C V and derived values of U(T, V) and (∂2 P/∂T 2) ρ in the critical and supercritical regions were interpreted in terms of the scaling theory of critical phenomena. The asymptotic critical amplitudes \({({A_0^+} {\rm and} {A_0^- )}}\) of the scaling power laws along the critical isochore for one- and two-phase C V were calculated from the measured values of C V . Experimentally derived values of the critical amplitude ratio for \({C_{V} \left({A_0^+ /A_0^- = 0.521}\right)}\) are in good agreement with the values predicted by scaling theory. The measured C V data for DEE were analyzed to study the behavior of loci of isothermal and isochoric C V maxima and minima in the critical and supercritical regions.

A relation for the distribution function of clusters in a liquid, earlier proposed by the authors, allows one to find the number of particles in a cluster and its dependence on state parameters and to find the frequencies of IR-spectra of organic liquids. The authors have improved the method of finding the number of particles contained in a cluster. The proposed modification of the cluster theory allows one to estimate the energy of clusters, to reveal features of their structure, and to calculate the basic thermophysical properties of liquids, such as the difference of isobaric and isochoric heat capacities, the dynamic viscosity, and other properties. The authors have determined the cluster component of full absorption of ultrasonic waves, the cluster relaxation time, and the dimer formation energy for liquid noble gases and organic liquids. The comparison of the obtained results with experimental data demonstrates the reasonableness of the proposed model for prediction of thermophysical and acoustic properties of liquids.

The isochoric heat capacity (cv) of R-410A [a mixture of 49.81 mass% difluoromethane (HFC-32) + 50.19 mass% pentafluoroethane (HFC-125)] and 1,1,2,2-tetrafluoroethyl-2,2,2-trifluoroethylether (HFE-347pcf2) was measured at temperatures from 277 K to 400 K and at pressures up to 30 MPa. The reported density measurements for R-410A and HFE-347pcf2 are in the single-phase region and cover a density range above 0.92 g·cm−3 and 1.33 g·cm−3, respectively. The measured data of R-410A are compared with data reported by other researchers. Also, the measured data of R-410A are examined with an available equation of state. As a result, it is found that the present cv data for R-410A agree well with those by other researchers and the calculated values with the equation of state in the measurement range except near the critical isochore.

The isochoric heat capacity of a NH3 + H2O (0.2607 mole fraction of ammonia) mixture has been measured in the near- and supercritical regions. Measurements were made in the single- and two-phase regions including the coexistence curve using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. Measurements were made along 38 liquid and vapor isochores in the range from 120.03 kg · m−3 to 671.23 kg · m−3 and at temperatures from 478 K to 634 K and at pressures up to 28 MPa. Temperatures at the liquid–gas phase transition curve, T S(ρ), for each measured density (isochore) and the critical parameters (T C and ρ C) for the 0.2607 NH3 + 0.7393 H2O mixture were obtained using the quasi-static thermograms technique. The expanded uncertainty of the heat-capacity measurements at the 95 % confidence level with a coverage factor of k = 2 is estimated to be 2 % to 3 % in the near-critical and supercritical regions, 1.0 % to 1.5 % in the liquid phase, and 3 % to 4 % in the vapor phase. Uncertainties of the density, temperature, and concentration measurements are estimated to be 0.06 %, 15mK, and 5×10−5 mole fraction, respectively. An unusual behavior of the isochoric heat capacity of the mixture was found near the maxcondetherm point (in the retrograde region). The value of the Krichevskii parameter was calculated using the critical properties data for the mixture and vapor-pressure data for the pure solvent (H2O). The derived value of the Krichevskii parameter was used to analyze the critical behavior of the strong (C P , K T ) and weakly (C V ) singular properties in terms of the principle of isomorphism of critical phenomena in binary mixtures. The values of the characteristic parameters (K 1, K 2), temperatures (τ 1, τ 2), and the characteristic density differences (Δρ 1, Δρ 2) were calculated for the NH3 + H2O mixture by using the critical-curve data.

The isochoric heat capacity (cv) of difluoromethane (R32) and a mixture of 51.11 mass% R32 + 48.89 mass% pentafluoroethane (R125) was measured at temperatures from 268 K to 328 K and at pressures up to 30 MPa. The reported density measurements are in the single-phase region and cover a range of ρ > 800 kg · m−3. The measured data are compared with results measured by other researchers. Also, the measured data are examined with available equations of state. As a result, it is found that the measured cv’s agree well with those of other researchers in the measurement range of the present study.

The density (300–363 K, up to 3.5 MPa) and speed of sound (293–373 K, 7.5–480 kPa) in gaseous R-404a have been studied by an isochoric piezometer method and an ultrasonic interferometer, respectively. The pressures of the saturated vapor along the dew line were measured from 298 to 330 K. The experimental uncertainties of the temperature, pressure, density, and speed-of-sound measurements were estimated to be within ±20 mK, ±1.5 kPa, ±0.15%, and ±(0.1–0.2)%, respectively. On the basis of the obtained data, the isobaric molar heat capacity of R-404a was calculated for the ideal-gas state. An eight-coefficient Benedict–Webb–Rubin equation of state has been developed for the gaseous phase of R-404a.

The density of gaseous and liquid 1,1,1,2,3,3-hexafluoropropane (HFC-236ea) and the speed of sound in liquid HFC-236ea have been studied by a γ-attenuation technique, an ultrasonic interferometer, and an isochoric piezometer method over the temperature range of 263–423 K at pressures up to 4.05 MPa. The purity of the samples used throughout the measurements is 99.68 mol%. The pressures of the saturated vapor were measured over the same temperature range. The experimental uncertainties of the temperature, pressure, density, and speed-of-sound measurements were estimated to be within ±20 mK, ±1.5 kPa, ±(0.05–0.30)%, and ±(0.05–0.10)%, respectively.

Isochoric heat-capacity measurements for pure methanol are presented as a function of temperature at fixed densities between 136 and 750 kg·m−3. The measurements cover a range of temperatures from 300 to 556 K. The coverage includes the one- and two-phase regions, the coexistence curve, the near-critical, and the supercritical regions. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat-capacity measurements are estimated to be 2–3% depending on the experimental density and temperature. Temperatures at saturation, T S(ρ), for each measured density (isochore) were measured using a quasi-static thermogram technique. The uncertainty of the phase-transition temperature measurements is 0.02 K. The critical temperature and the critical density for pure methanol were extracted from the saturated data (T S,ρS) near the critical point. For one near-critical isochore (398.92 kg·m−3), the measurements were performed in both cooling and heating regimes to estimate the effect of thermal decomposition (chemical reaction) on the heat capacity and phase-transition properties of methanol. The measured values of C V and saturated densities (T S,ρS) for methanol were compared with values calculated from various multiparametric equations of state (EOS) (IUPAC, Bender-type, polynomial-type, and nonanalytical-type), scaling-type (crossover) EOS, and various correlations. The measured C V data have been analyzed and interpreted in terms of extended scaling equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitudes ( $$A_0^\pm$$ and B 0).

Thermodynamic properties of liquid 1-tetradecene have been calculated using a grid algorithm based on sound-speed data, obtained in a previous study over a wide range of temperatures and pressures. Since additional information such as densities and isobaric heat capacities at atmospheric pressure are needed for these calculations, the most reliable literature data and those obtained on the basis of structure–property correlations in the homologous series of 1-alkenes were used. Detailed tables, containing values of sound speed, density, isobaric, and isochoric heat capacities, isobaric expansion coefficient, isothermal compressibility, enthalpy, and entropy in the range of temperatures from 303 to 433 K and at pressures from 0.1 to 100 MPa, are given.

The isochoric heat capacity of two binary (CO2+n-decane) mixtures (0.095 and 0.178 mole fraction of n-decane) have been measured with a high- temperature, high-pressure, nearly constant volume adiabatic calorimeter. Measurements were made at nineteen near-critical liquid and vapor densities between 87 and 658 kg·m−3 for the composition of 0.095 mole fraction n-decane and at nine densities between 83 and 458 kg·m−3 for the composition of 0.178 mole fraction n-decane. The range of temperatures was 295 to 568 K. These temperature and density ranges include near- and supercritical regions. The measurements were performed in both one- and two-phase regions including the vapor + liquid coexistence curve. The uncertainty of the heat- capacity measurements is estimated to be 2% (coverage factor k=2). The uncertainty in temperature is 15 mK, and that for density measurements is 0.06%. The liquid and vapor one- $$(C_{V1}^{\prime}, C_{V1}^{\prime \prime})$$ and two-phase $$(C_{V2}^{\prime}, C_{V2}^{\prime \prime})$$ isochoric heat capacities, temperatures (T S), and densities (ρS) at saturation were measured by using the well-established method of quasi-static thermograms for each filling density. The critical temperatures (T C), the critical densities (ρC), and the critical pressure (P C) for the CO2+n-decane mixtures were extracted from the isochoric heat-capacity measurements on the coexistence curve. The observed isochoric heat capacity along the critical isochore of the CO2+n-decane mixture exhibits a renormalization of the critical behavior of C V X typical for mixtures. The values of the characteristic parameters (K 1, K 2), temperatures (τ1 ,τ2), and the characteristic density differences $$(\Delta \bar{\rho}_1, \Delta \bar{\rho}_2)$$ were estimated for the CO2+n-decane mixture by using the critical-curve data and the theory of critical phenomena in binary mixtures. The ranges of conditions were defined on the T-x plane for the critical isochore and the ρ-x plane for the critical isotherm, for which we observed renormalization of the critical behavior for the isochoric heat capacity.

The isochoric heat capacity (c v ) and pressure–volume–temperature-composition (pvTx) properties were measured for propane + isobutane mixtures in the liquid phase and in the supercritical region. The expanded uncertainty (k = 2) of temperature measurements is estimated to be ±13 mK, and that of pressure measurements is ±8 kPa. The expanded relative uncertainty for c v is ±3.2% for the liquid phase, increasing to ±4.8% for near-critical densities. The expanded uncertainty for density is estimated to be ±0.16%. The present measurements for {xC3H8 +(1−x)i-C4H10} with x = 0.0, 0.498, 0.756, and 1.0, were obtained at 659 state points at temperatures from 270 to 420 K and at pressures up to 30 MPa. The experimental data were compared with a published equation of state.

The isochoric heat capacity of pure methanol in the temperature range from 482 to 533 K, at near-critical densities between 274.87 and 331.59 kg· m−3, has been measured by using a high-temperature and high-pressure nearly constant volume adiabatic calorimeter. The measurements were performed in the single- and two-phase regions including along the coexistence curve. Uncertainties of the isochoric heat capacity measurements are estimated to be within 2%. The single- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. The critical temperature (Tc = 512.78±0.02K) and the critical density (ρc = 277.49±2 kg · m−3) for pure methanol were derived from the isochoric heat-capacity measurements by using the well-established method of quasi-static thermograms. The results of the CVVT measurements together with recent new experimental PVT data for pure methanol were used to develop a thermodynamically self-consistent Helmholtz free-energy parametric crossover model, CREOS97-04. The accuracy of the crossover model was confirmed by a comprehensive comparison with available experimental data for pure methanol and values calculated with various multiparameter equations of state and correlations. In the critical and supercritical regions at 0.98Tc≤ T ≤ 1.5Tc and in the density range 0.35ρc ≤ ρ leq 1.65 ρc, CREOS97-04 represents all available experimental thermodynamic data for pure methanol to within their experimental uncertainties.

Thermal conductivity has been previously obtained from molecular dynamics (MD) simulations using either equilibrium (EMD) simulations (from Green--Kubo equations) or from steady-state nonequilibrium (NEMD) simulations. In the case of NEMD, either boundary-driven steady states are simulated or constrained equations of motion are used to obtain steady-state heat transfer rates. Like their experimental counterparts, these nonequilibrium steady-state methods are time consuming and may have convection problems. Here we report a new transient method developed to provide accurate thermal conductivity predictions from MD simulations. In the proposed MD method, molecules that lie within a specified volume are instantaneously heated. The temperature decay of the system of molecules inside the heated volume is compared to the solution of the transient energy equation, and the thermal diffusivity is regressed. Since the density of the fluid is set in the simulation, only the isochoric heat capacity is needed in order to obtain the thermal conductivity. In this study the isochoric heat capacity is determined from energy fluctuations within the simulated fluid. The method is valid in the liquid, vapor, and critical regions. Simulated values for the thermal conductivity of a Lennard-Jones (LJ) fluid were obtained using this new method over a temperature range of 90 to 900 K and a density range of 1–35 kmol · m-3. These values compare favorably with experimental values for argon. The new method has a precision of ±10%. Compared to other methods, the algorithm is quick, easy to code, and applicable to small systems, making the simulations very efficient.

A thermodynamic study at atmospheric pressure on the ethanol + n-dodecane and ethanol + n-tridecane binary systems near their liquid-liquid critical points has been carried out. To this end, densities and speeds of sound were determined in the temperature range from 288.15 to 308.15 K, whereas differential scanning calorimetry was used to obtain isobaric heat capacities per unit volume from 288.15 to 303.15 K as well as liquid-liquid equilibrium curves. All these results for the mentioned properties were obtained over the complete composition range. They were used to obtain molar volumes, isentropic compressibilities, isobaric thermal expansivities, isothermal compressibilities, isochoric heat capacities, and the excess quantities of all these properties. An untypical behavior of the excess heat capacities at the lowest measuring temperatures resulting from the critical behavior of the isobaric heat capacity is observed. No clear anomalies for the excess volumetric properties are detected.

PVTx relationships for a H2O + CH3OH mixture (0.36 mole fraction of methanol) were measured in a range of temperatures from 373 to 673 K and pressures between 0.042 and 90.9 MPa. The density ranged from 37.76 to 559.03 kg · m−3. Measurements were made with a constant-volume piezometer surrounded by a precision thermostat. The temperature inside the thermostat was maintained uniform within 5 mK. The volume of the piezometer (32.68 ± 0.01 cm3) was previously calibrated from well-established PVT values of pure water (IAPWS), and was corrected for both temperature and pressure expansions. Uncertainties of the density, temperature, and pressure measurements are estimated to be 0.16%, 30 mK, and 0.05%, respectively. The uncertainty in composition is 0.001 mole fraction. The method of isochoric and isothermal break points was used to extract the phase transition temperatures, pressures, and densities for each measured isochore and isotherm. The values of the critical temperature, pressure, and density of the mixture were also determined from PVTx measurements in the critical region.

A Helmholtz free energy equation of state for the fluid phase of hydrogen sulfide has been developed as a function of reduced temperature and density with 23 terms on the basis of selected measurements of pressure–density–temperature (P, ρ, T), isobaric heat capacity, and saturation properties. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from the triple point temperature (187.67 K) to 760 K at pressures up to 170 MPa. The uncertainty in density calculation of the present equation of state is 0.7% in the liquid phase, and that in pressure calculation is 0.3% in the vapor phase. The uncertainty in saturated vapor pressure calculation is 0.2%, and that in isobaric heat capacity calculation is 1% in the liquid phase. The behavior of the isobaric heat capacity, isochoric heat capacity, speed of sound, and Joule–Thomson coefficients calculated by the present model shows physically reasonable behavior and those of the calculated ideal curves also illustrate the capability of extending the range of validity. Graphical and statistical comparisons between experimental data and the available thermodynamic models are also discussed.

A fundamental equation of state for pentafluoroethane was established on the basis of not only assessment of the experimental data but also by introducing parameters for virial coefficients having a theoretical background in statistical thermodynamics. The equation of state has a range of validity for temperatures from the triple point up to 500 K and pressures up to 70 MPa. The estimated uncertainties of the equation are 0.1% for the vapor pressure, 0.15% in density for the saturated-liquid phase, 0.5% in density for the saturated-vapor phase, 0.1% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.5% in density for the supercritical region, 0.01% in speed of sound for the gaseous phase, 0.9% in speed of sound for the liquid phase, 0.5% in isobaric specific heat for the liquid phase, and 1.2% in isochoric specific heat for the liquid phase. The derived specific heats in the gaseous phase are close to the values from the virial equation of state with the second and third virial coefficients derived from intermolecular potential models and precise speed-of-sound measurements.

Isochoric heat capacity and PVTx properties of an aqueous methanol solution (0.50 mass fraction or 0.36 mole fraction of methanol) were measured in the liquid phase with a twin-cell adiabatic calorimeter. Temperatures ranged from 333 to 422 K, and pressures ranged to 20 MPa. The calorimetric cell (70 cm3 capacity) was surrounded by adiabatic thermal shielding (high vacuum) and a steel-sheathed electric heater wound tightly on its surface. By combining the various sources of experimental uncertainty using a root-sum-of-squares formula, the relative uncertainty of C V is estimated to be 2%. The uncertainties of the density, temperature (absolute), and pressure measurements are, respectively, about 0.1%, 40 mK, and ±7 kPa. The measured densities were used to calculate excess molar volumes that were compared with values calculated with a reliable model by Simonson et al. Good agreement within ±0.008 cm3ċmol−1 (or ±0.03% of the density) was found between measured values of excess molar volume and those calculated from the model. Values of saturated liquid densities were determined by extrapolating experimental P-T data to the saturation curve.

Volumetric (PVT) and calorimetric (C V VT) properties of pure methanol were measured in the liquid phase with a twin-cell adiabatic calorimeter. Temperatures were measured in a range from 314 to 411 K, densities between 699.3 and 775.6 kg⋅m−3, and pressures to 20 MPa. The calorimetric cell (70 cm3 capacity) was surrounded by adiabatic thermal shielding (high vacuum). The sample pressures were measured by means of a quartz crystal transducer to within an uncertainty of about ±7 kPa. The relative uncertainty of C V was estimated to be 2%, with a coverage factor k = 2, by combining the various sources of experimental uncertainty using a root-sum-of-squares formula. The results for pure methanol were compared with other recent measurements performed with a second high-temperature, high-pressure adiabatic calorimeter. Deviations of less than 3% were found between the earlier C V data and the present results for pure methanol. The uncertainty of the density measurements was estimated to be 0.2% (k = 2). The measured densities and isochoric heat capacities were compared with values calculated with an IUPAC equation of state. Agreement of density was within 0.088% and that for isochoric heat capacity was within 0.95%. Values of vapor pressure were determined by extrapolating experimental P–T data to the saturated temperature along a fixed isochore. In the temperature range of this study, decomposition of methanol was not observed.

A new fundamental thermodynamic equation of state for difluoromethane was developed by considering the intermolecular potential behavior for improving the reliability in the gaseous phase. Reliable second and third virial coefficients are introduced in accordance with the principle of a unified relation of the intermolecular potential energy and the fundamental equation of state. The fundamental equation of state is able to provide reliable thermodynamic properties even at low temperatures or in the region near saturation where precise and accurate experimental data are not available. The estimated uncertainties of calculated properties from the equation of state are 0.07% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.35% in pressure for the supercritical region, 0.07% in vapor pressure, 0.2% in saturated-liquid density, 0.7% in saturated-vapor density, 0.01% in speed of sound for the gaseous phase, 0.7% in speed of sound for the liquid phase, and 0.6% in isochoric specific heat for the liquid phase. The equation is valid for temperatures from the triple point to 450 K and pressures up to 72 MPa.

A grid algorithm based on sound speed data, was used to calculate the thermodynamic properties of liquid n-dodecane. The density, isobaric expansion coefficient, isothermal compressibility, isobaric and isochoric heat capacities, enthalpy, and entropy of liquid n-dodecane were calculated in the range of temperatures from 293 to 433 K and pressures from 0.1 to 140 MPa. Coefficients of the Tait equation were determined in the above-identified range of parameters. A table of the thermodynamic properties of n-dodecane is presented.

Highly accurate thermodynamic property models for binary and ternary hydrocarbon mixtures containing propane, n-butane, and isobutane have been developed. In the present model, reliable equations of state explicit in Helmholtz free energy for these three hydrocarbons that have already been developed by the present authors have been adapted. The excess term used to represent the contribution of mixing was optimized for each binary mixture by using the available experimental thermodynamic property data including PρTx, isochoric heat capacity, and saturation properties (bubble-point pressures, mole fractions in the vapor phase, and saturated vapor- and liquid-densities) as input data. A generalized correction for the three binary mixtures, besides the ideal mixing, consists of only four terms in its functional form, the structure of which was determined by simultaneous optimization to the input data for the three binary mixtures by employing a stepwise regression analysis. The “bank of terms,” that is a matrix of candidate terms applied for the regression, was carefully prepared through detailed observation of the nonideal mixing representation of the experimental data of the three binary mixtures. No additional adjustable parameters were used in the present model for the ternary propane/n-butane/isobutane mixture. Based on comparisons with the available experimental data and values from the developed equations of state, the present models for the three binary and the ternary hydrocarbon mixtures accurately represent most of the reliable experimental data. In addition, the graphical tests of the derived thermodynamic properties show that the models, including that for the ternary mixture, provide a physically sound representation of all the thermodynamic properties over the entire fluid phase.

The isochoric heat capacity C V of an equimolar H2O+D2O mixture was measured in the temperature range from 391 to 655 K, at near-critical liquid and vapor densities between 274.05 and 385.36 kg⋅m−3. A high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter was used. The measurements were performed in the one- and two-phase regions including the coexistence curve. The uncertainty of the heat-capacity measurement is estimated to be ±2%. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from the experimental data for each measured isochore. The critical temperature and the critical density for the equimolar H2O+D2O mixture were obtained from isochoric heat capacity measurements using the method of quasi-static thermograms. The measurements were compared with a crossover equation of state for H2O+D2O mixtures. The near-critical isochoric heat capacity behavior for the 0.5 H2O+0.5 D2O mixture was studied using the principle of isomorphism of critical phenomena. The experimental isochoric heat capacity data for the 0.5 H2O+0.5 D2O mixture exhibit a weak singularity, like that of both pure components. The reliability of the experimental method was confirmed with measurements on pure light water, for which the isochoric heat capacity was measured on the critical isochore (321.96 kg⋅m−3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, TC, this work=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (TC, IAPWS=647.096 K) adopted by IAPWS.

The density and speed of sound in gaseous and liquid 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) have been studied by a γ-attenuation technique, an ultrasonic interferometer, and an isochoric piezometer method over the temperature range of 273 to 383 K at pressures up to 3.5 MPa. The purity of the samples used throughout the measurements are 99.99 mol%. The pressures of the saturated vapor were measured over the same temperature range. The experimental uncertainties of the temperature, pressure, density, and speed of sound measurements were estimated to be within ±20 mK, ±1.5 kPa, ±0.2%, and ±(0.15–0.2)%, respectively. On the basis of the obtained data, the isobaric molar heat capacity of HFC-227ea was calculated for the ideal-gas state.

Isochoric heat capacity measurements of D2O are presented as a function of temperature at fixed densities of 319.60, 398.90, 431.09, and 506.95 kg·m−3. The measurements cover a range of temperatures from 551 to 671 K and pressures up to 32 MPa. The coverage includes one- and two-phase states and the coexistence curve near the critical point of D2O. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat capacity measurements are estimated to be 2 to 3%. Temperatures at saturation T S (ρ) were measured isochorically using a quasi-static thermogram method. The uncertainty of the phase transition temperature measurements is about ±0.02 K. The measured C V data for D2O were compared with values predicted from a parametric crossover equation of state and six-term Landau expansion crossover model. The critical behavior of second temperature derivatives of the vapor pressure and chemical potential were studied using measured two-phase isochoric heat capacities. From measured isochoric heat capacities and saturated densities for heavy water, the values of asymptotic critical amplitudes were estimated. It is shown that the critical parameters (critical temperature and critical density) adopted by IAPWS are consistent with the T S –ρ S measurements for D2O near the critical point.

The isochoric heat capacity was measured for D2O at a fixed density of 356.075 kg·m−3 and for H2O at 309.905 kg·m−3. The measurements cover the range of temperatures from 623 to 661 K. The measurements were made with a high-temperature, high-pressure, adiabatic calorimeter with a nearly constant inner volume. The uncertainty of the temperature is 10 mK, while the uncertainty of the heat capacity is estimated to be 2 to 3%. Measurements were made in both the two-phase and the one-phase regions. The calorimeter instrumentation also enables measurements of PVT and the temperature derivative (∂P/∂T)V along each measured isochore. A detailed discussion is presented on the experimental temperature behavior of CV in the one- and two-phase regions, including the coexistence curve near the critical point. A quasi-static thermogram method was applied to determine values of temperature at saturation TS(ρ) on measured isochores. The uncertainty of the phase-transition temperature measurements is about ±0.02 K. The measured CV data for D2O and H2O are compared with values predicted from a recent developed parametric crossover equation of state and IAPWS-95 formulation.

Deuteron solid-state NMR techniques at high pressure are used to study the chain dynamics in the amorphous polymer atactic polypropylene. The arrest of the structural relaxation above the glass-transition temperature Tgis investigated using one- and two-dimensional deuteron NMR spectra. The slow reorientation of the main chain segments is identified with the α-process observed in mechanical relaxation experiments. On approaching the glass transition, the time scale of the collective motion of the main chain becomes longer very rapidly at decreasing temperatures. Along isobars, at pressure values up to 5 kbar, the temperature dependence of the logarithmic average correlation time is very well described by a Vogel–Fulcher function. The motion of the main chain is strongly dependent on the pressure, while its character is determined mainly by the distance to Tg. The introduction of the equation of state allows the investigation of the dynamic behavior on isothermal and isochoric paths on approaching Tg. It is found that along an isotherm the mobility as a function of the density is also of the Vogel–Fulcher form.

Experimental PVTx property data have been used to develop a thermodynamic model of the gas-phase PVTx properties for R-32/125/143a in terms of a truncated virial equation of state. It is developed on the basis of the experimental PVTx property data which were obtained by a group of the present authors. The present model represents the input data with a high reproducibility, i.e., within ±0.2% in pressure for each pure component, ±0.25% for binary mixtures except for R-32/143a, and ±0.3% for ternary mixtures. The present model covers a temperature range of 300 to 380K, pressures up to 4.5MPa, and densities up to 2.5 molċdm−3 at any composition of the present ternary system. The uncertainty of the present model is considered being within ±0.3% in pressure and ±0.3% in the second virial coefficient. The thermodynamic behaviors of the specific isobaric heat capacity, isochoric heat capacity, and speed of sound are also discussed, in addition to the examination of the temperature dependence of the second and third virial coefficients.

A thermophysical property databank for technically important gases and liquids has been created. It provides users with data for nearly 30 substances: monatomic and diatomic gases, air, water and steam, carbon dioxide, ammonia, some hydrocarbons, and refrigerants. The coefficients of the equations of state and equations for calculating transport properties, the ideal-gas functions, the saturated vapor pressure, and the melting pressure are provided for each substance. The system of programs allows the calculation of the compressibility factor, density, enthalpy, entropy, isochoric and isobaric specific heats, speed of sound, Joule–Thomson coefficient, viscosity, and thermal conductivity and some other properties. These values can be determined in the single-phase and two-phase regions and on the phase-equilibrium lines at temperatures from the triple point up to 500 to 1500 K and at pressures up to 100 MPa (for monatomic and diatomic gases, up to 2500 to 3000 K and 300 MPa). Properties can be calculated for the following nine combinations of independent variables: T, ρ; T, p; T, s; T, x; p, ρ; p, h; p, s; p, x; and h, s. The software of the databank has a modular structure and permits an increase in the number of substances, properties, and independent variables.

The thermal expansion coefficients and isobaric heat capacities of fluorite-type compounds have been estimated using the Morse potential and the Debye model. The Born repulsion parameters of various compounds, which are necessary for determining the parameters of the Morse potential, have been determined empirically for elements belonging to every period of the periodic table. Using the parameters thus determined, the Debye temperature, the thermal expansion coefficient, and the Gruneisen constant of fluorite-type compounds have been calculated and then the isochoric and the isobaric heat capacities have been calculated over a wide range of temperatures. The calculated thermal expansion coefficients and isobaric heat capacities thus obtained are in good agreement with experimental values except for the anomalous temperature regions due to vacancy formation and phase transitions.

Molar heat capacities at a constant volume (C v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C (2) v), saturated liquid (C σ or C′ x ), and single-phase (C v) molar heat capacities. The C σ data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T tr) and the enthalpy of fusion (Δ fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2σ level) for C v is estimated to be 0.7%, for C (2) v it is 0.5%, and for C σ it is 0.7%.

The p–ρ–T relationships were measured for binary refrigerant mixtures by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K, while pressures extended up to 35 MPa. Measurements were conducted on compressed gas and liquid samples with the following mole fraction compositions: 0.4997 R32+0.5003 R134a, 0.3288 R32+0.6712 R134a, 0.4996 R32+0.5004 R125, 0.5001 R125+0.4999 R134a, and 0.5000 R125+0.5000 R143a. Most published p–ρ–T data are in good agreement with this study. The uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p

In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.

The p–ρ–T relationships were measured for 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 176 to 380 K for R123 and from 104 to 400 K for R124, while pressures extended up to 35 MPa. Measurements were conducted on compressed liquid samples. Most published p–ρ–T data are in good agreement with this study. The uncertainty is 0.03 K for temperature and 0.01% for pressure at p>3 MPa and 0.05% at p

Densities, isentropic compressibilities, and isobaric molar heat capacities were determined over the whole composition range for nitromethane+(2-butanol or isobutanol) at atmospheric pressure and at the temperatures 288.15, 293.15, 298.15, and 308.15 K. These results allowed us to obtain isobaric thermal expansivities, isothermal compressibilities, and isochoric molar heat capacities at the temperature 298.15 K. The excess quantities for the given properties were obtained. In addition, liquid–liquid phase separation temperatures were also determined, locating upper critical solution temperatures near the experimental temperatures. The variation of the properties among isomers is discussed. Also, the effect of the nonrandomness of the mixtures expected near the critical point is discussed.

The two-phase isochoric heat capacity of nitrogen tetroxide was measured in the temperature range from 261.74 K to the critical temperature (431.072 K) at densities between 201.21 and 1426.5 kg·m−3 using a high-temperature and high-pressure adiabatic calorimeter. The measurements were performed in the two-phase region for 26 isochores (15 liquid and 11 vapor densities) including the coexistence curve and critical region. Uncertainties of the measurements are estimated to be 2%. The original temperatures and C V data were converted to the ITS-90. The liquid and vapor two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. From measured (T S, ρ S, C′ V2, C″ V2) data, the values of second temperature derivatives of vapor-pressure d 2 P S/dT 2 and chemical potential d 2 μ/dT 2 were derived using the Yang–Yang relation. The results were compared with values calculated from other vapor-pressure equations. The values of saturated densities and critical parameters derived in calorimetric experiments were compared with literature data. The unusual temperature behavior of d 2 P S/dT 2 and d 2 μ/dT 2 was found at low temperatures around 351 K and near the critical point.

The p–ρ–T relationships and constant volume heat capacity Cv were measured for ternary refrigerant mixtures by isochoric methods with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K for p–ρ–T and from 203 to 345 K for Cv, while for both data types pressures extended to 35 MPa. Measurements of p–ρ–T were carried out on compressed gas and liquid samples with the following mole fraction compositions: 0.3337 R32+0.3333 R125+0.3330 R134a and 0.3808 R32+0.1798 R125+0.4394 R134a. Measurements of Cv were carried out on liquid samples for the same two compositions. Published p–ρ–T data are in good agreement with this study. For the p–ρ–T apparatus, the uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p

Measurements of the molar heat capacity at constant volume C v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, ρ, T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, ρ, T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C v predictions with measurements was found. Published C v(ρ, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.

Studies of the thermodynamic properties of trifluoroiodomethane (CF3I) are presented in this paper. The vapor–liquid coexistence curve of CF3I was measured by visual observation of the meniscus. The critical temperature and the critical density of CF3I were determined by considering not only the level where the meniscus disappeared but also the intensity of the critical opalescence. The correlation of the saturated density in the critical region was developed, and the exponent of the power law β was determined. Correlations of the saturated vapor and liquid densities and the enthalpy of vaporization for CF3I were also developed. The vapor pressure of CF3I was measured at temperatures ranging from below the normal boiling point to the critical point, and a vapor pressure equation for CF3I was developed, from which the normal boiling point of CF3I was determined. The gaseous PVT properties of CF3I were measured with a Burnett/isochoric method, and a gaseous equation of state for CF3I was developed. The speed of sound of gaseous CF3I was measured with a cylindrical, variable-path acoustic interferometer operating at 156.252 kHz, and the ideal-gas heat capacity and second acoustic virial coefficient were calculated. A correlation of the second virial coefficient for CF3I was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with the result based on PVT measurements. The surface tension of CF3I was measured with a differential capillary rise method (DCRM), and the temperature dependence of the results was successfully represented to within ±0.13 mN·m−1 using a van der Waals correlation.

The heat capacity of heavy water was measured in the temperature range from 294 to 746 K and at densities between 52 and 1,105 kg{center_dot}m{sup {minus}3} using a high-temperature, high-pressure adiabatic calorimeter. The measurements were performed at 14 liquid and 9 vapor densities between 52 and 1,105 kg{center_dot}m{sup {minus}3}. Uncertainties of the measurements are estimated to be within 3% for vapor isochores and 1.5% for the liquid isochores. In the region of the immediate vicinity of the critical point (0.97 {le} T/T{sub c} {le}1.03 and 0.75 {le}p/p{sub c} {le}1.25), the uncertainty is 4.5%. The original C{sub v} data were corrected and converted to the new ITS-90 temperature scale. A parametric crossover equation of state was used to represent the isochoric heat capacity measurements of heavy water in the extended critical region, 0.8 {le} T/T{sub c} {le}1.5 and 0.35 {le}p/p{sub c} {le}1.65. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and saturation densities were extracted from experimental data for each measured isochore. Most of the experimental data are compared with the Hill equation of state, and the overall statistics of deviations between experimental data and the equation of state are given.

An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m−3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.

A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P–ρ–T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.