Isochoric Heat-Capacity Measurements for Pure Methanol in the Near-Critical and Supercritical Regions

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,ρ_S) 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,ρ_S) 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 ( and B ₀).     

Isochoric Heat Capacity of Heavy Water at Subcritical and Supercritical Conditions

The heat capacity of heavy water was measured in the temperature range from 294 to 746 K and at densities between 52 and 1105 kg·m^–3 using a high-temperature, high-pressure adiabatic calorimeter. The measurements were performed at 14 liquid and 9 vapor densities between 52 and 1105 kg·m^–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 (0.97T/T _c1.03 and 0.75/_c1.25), the uncertainty is 4.5%. The original C _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, 0.8T/T _c1.5 and 0.35/_c1.65. 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.     

Isochoric Heat Capacity Measurements for 0.5 H2O+0.5 D2O Mixture in the Critical Region

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 kgm^–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 kgm^–3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, T _{C, this work}=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (T _{C, IAPWS}=647.096 K) adopted by IAPWS.     

Experimental Study of the Critical Behavior of the Isochoric Heat Capacity of Aqueous Ammonia Mixture

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.     

Isochoric Heat Capacity of CO2 + n-Decane Mixtures in the Critical Region

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- and two-phase isochoric heat capacities, temperatures (T _S), and densities (ρ_S) 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 (ρ_C), 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 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.     

Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point

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 () 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 – _S measurements for D₂O near the critical point.     

Experimental Study of the Isochoric Heat Capacity of Diethyl Ether (DEE) in the Critical and Supercritical Regions

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 (A₀⁺ and A₀^- ){({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 (A₀⁺ /A₀^- = 0.521){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.     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Crossover equation of state of normal hexane in the critical region

The coefficients of the basic crossover equation of state of n-hexane are determined in the critical region from experimental P, , T and C_p, P, T data. In the reduced density and temperature ranges 0.35_c1.65 and 0.982T/T_c1.23 the root mean square errors of the calculated pressure, isobaric heat capacity, and isochoric heat capacity were 0.115%, 4.87%, and 3.04%, respectively.Academician M. D. Millionshchikov Petroleum Institute, Grozny, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp.185–191, August, 1993.     

PVT Measurements for Pure Ethanol in the Near-Critical and Supercritical Regions

The PVT properties of pure ethanol were measured in the near-critical and supercritical regions. Measurements were made using a constant-volume piezometer immersed in a precision thermostat. The uncertainty of the density measurements was estimated to be 0.15%. The uncertainties of the temperature and pressure measurements were, respectively, 15 mK and 0.05%. Measurements were made along various near-critical isotherms between 373 and 673 K and at densities from 91.81 to 497.67 kg · m⁻³. The pressure range was from 0.226 to 40.292 MPa. Using two-phase PVT results, the values of the saturated-liquid and -vapor densities and the vapor pressure for temperatures between 373.15 and 513.15 K were obtained by means of an analytical extrapolation technique. The measured PVT data and saturated properties for pure ethanol were compared with values calculated from a fundamental equation of state and correlations, and with experimental data reported by other authors. The values of the critical parameters (T _C,P _C,ρ _C) were derived from the measured values of saturated densities and vapor pressure near the critical point. The derived values of the saturated densities near the critical point for ethanol were interpreted in term of the “complete scaling” theory.     

Volumetric (PVT) and Calorimetric (C V VT) Measurements for Pure Methanol in the Liquid Phase

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 kgm^–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.     

Theoretical Study of Specific Heat,Density of States,Free Energy,and Critical Field of High Temperature Cuprate Superconductors Based on Intra and Interlayer Interactions

The role of attractive interlayer and intralayer interactions in layered high T _c cuprate superconductors have been investigated using a one-band two layer tight binding Hamiltonian. Self-consistent equations for the superconducting order parameter (Δ) and critical temperature (T _c ) are derived using double time Green’s functions and equation of motion method. The expression for excitonic type correlation (γ _c ), specific heat, density of states, free energy, and critical field are obtained. The interlayer interactions play an important role in the enhancement of T _c in layered high T _c cuprates. The oxygen isotope effect is also analyzed. The agreement between theoretical and experimental results for the system YBa_2−x La _x Cu₃O₇ (0≤x≤0.5) is quite satisfactory.      

Isochoric Heat Capacity Measurements for Light and Heavy Water 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 C_V 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 T_S() on measured isochores. The uncertainty of the phase-transition temperature measurements is about ±0.02 K. The measured C_V data for D₂O and H₂O are compared with values predicted from a recent developed parametric crossover equation of state and IAPWS-95 formulation.     

Isochoric Specific Heat Capacity of Difluoromethane (R32) and a Mixture of 51.11 mass% Difluoromethane (R32) + 48.89 mass% Pentafluoroethane (R125)

The isochoric heat capacity (c _v ) 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 c _v ’s agree well with those of other researchers in the measurement range of the present study.     

Viscosity and density of the ternary mixture heptane+methylcyclohexane+1-methylnaphthalene

The dynamic viscosity η and the density ρ of the ternary mixture heptane (mole fractionx ₁)+methylcyclohexane (mole fractionx ₂) + 1-methylnaphthalene (mole fractionx ₃) were measured as a function of temperatureT (303.15, 323.15, and 343.15 K) and pressureP(≤100 MPa). The experimental results correspond to 378 values of η and ρ. With reference to the 54 values previously published on pure substances and 378 values for the three associated binaries. the system is globally described by 810 experimental values for various values ofP, T, and compositon.     

Structure and properties of polyethyleneterephthalate crystallized by annealing in the highly oriented state

The structure of polyethyleneterephthalate bristles drawn about five times in the amorphous state and subsequently crystallized at temperatures between 100 and 260‡ C has been studied by means of small-angle X-ray scattering. In addition density, heat of fusion and wide-angle scattering behaviour were measured. For comparison, similar experiments were carried out with undrawn samples. The results showed that the degree of crystallinity of PET cannot be calculated from density data on the basis of a simple two-phase model, since the effective densitiesρ _c ^* andρ _a ^* of the crystalline and amorphous regions depend strongly on crystallization and drawing conditions. With rising crystallization temperature the size of the mosaic blocks building up the crystalline layers and their longitudinal mutual order increase whereas the volume fraction of the crystalline region is only rather slightly effected by the annealing temperature. The difference between the effective densityρ _c ^* and the “X-ray density”ρ _c of the crystalline layers is supposed to be caused by lattice vacancies in the boundaries of the mosaic blocks.     

Quench-condensed indium-hydrogen films. II. Changes in electric and superconducting characteristics near the metal-insulator transition

Electrical and superconducting properties of indium films condensed in a H₂ atmosphere (pressurep _{H 2}=6×10⁻⁶ to 1.4×10⁻⁴ Torr) onto a substrate cooled with liquid helium are investigated. As hydrogen content is increased, a continuous increase in residual resistivity ρ* is observed, permitting systematic study of the resistance vs. temperature dependenceR(T) and the superconducting transition temperatureT _c on approaching the metal-insulator transition (MIT). With regard to ρ*, four regimes of conductivity can be observed: (1) conductivity with a positive temperature resistance coefficient (TRC), (2) conductivity with a small, constant, negative TRC, (3) conductivity under weak localization with ΔR (T) ∼ln T or type corrections, (4) hopping conductivity.T _c rises continuously with ρ* and reaches its peak (∼5.2K) in the second regime. A further increase of ρ* leads to a decrease ofT _c and complete suppression of superconductivity. The experimental dependenceR(T) is compared with theory. TheT _c variation on approaching the MIT and the relation between Mooij's rule and the superconducting properties are discussed.     

He4 State Equation Below 0.8 K

This work develops the Helmholtz potential A(ρ, T) for He⁴ below 0.8 K. Superfluid terms, related to temperature and momentum gradients, are neglected with negligible loss of accuracy in the derived state properties (specific heats, first sound velocity, expansivity, compressibility, etc.). Retained terms are directly related to a bulk fluid compressibility plus phonon and roton excitations in this quantum fluid. The bulk fluid compressibility is found from the empirical equation c₁³ ≈ c₁₀³ + b; P, where c₁ is the velocity of first sound, P is the pressure, and c₁₀ and b are constants; this empirical equation is found to apply also to other helium temperature ranges and to other fluids. The phonon excitations lead to a single temperature-dependent term in A(ρ ,T) up to 0.3 K, with only two more terms added up to 0.8 K. The roton potential, negligible below about 0.3 K, is a single term first derived 60 years ago but little used in more recent work. The final A(ρ ,T) is shown to fit available experimental specific heat data to about ±2% or better. The magnitude of the pressure-independent Gruneisen parameter below 0.3 K is typical of highly compressed normal liquids. Extension of the equation above 0.8 K is hampered by lack of data between 0.8 and 1.2 K     

Specific heat studies in Ho-Ba-CuO superconductors: Fermionic and bosonic contributions

The specific heats of superconducting HoBa₂Cu₃O_7-δ (T _c≅ 92 K) have been theoretically investigated in the temperature domain 70 ≤T ≤110 K. The bosonic (phonons) contribution to the specific heat is estimated from Debye model in the harmonic approximation for high temperature expansion (T > θ_D/2π) using the moments of the phonon density of states. The fermionic constituent as the electronic specific heat is deduced using a suitable trial function above and belowT _c. As a next step the contribution of specific heat by charge oscillations (plasmons) are obtained. The theoretical results from bosonic and fermionic terms are then compared with the experimental results. We find that the specific heats from electronic as well as plasmon term are only a fraction of lattice specific heat and in particular, plasmons do not influence the thermal conduction significantly. The implications of the above analysis are discussed.