Equation of State of Overpressurized Liquid 4He at Zero Temperature

No Heading In recent experiments, Balibar and collaborators have been able to produce metastable superfluids ⁴He up to 163 ± 20 bar, a pressure much higher than the freezing point (25 bar). Interpretation of some of their experimental data requires the knowledge of the equation of state of bulk ⁴He in this high-pressure regime. As this is not experimentally known, they extrapolate to these high pressures using analytical fits to the well-known equation of state in the stable regime. Using the same theoretical analysis that allowed in the past to reproduce accurately the equation of state of liquid ⁴He in the stable domain, we present now extended results for this equation of state up to 350 bar. Our calculations, based on the diffusion Monte Carlo method, show some significant differences with the proposed extrapolations, which could be relevant for future experiments.PACS numbers: 67.40.–w, 67.80.–s     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

Dielectric Properties of Liquid Pentafluoroethane (HFC-125)

This paper reports measurements of the static relative permittivity of HFC-125 in the liquid phase, performed by using the direct capacitance method at 10 kHz, for temperatures from 214 to 304 K and pressures up to 16 MPa. The repeatability of the measurements was found to be of the order of ±0.7×10^–3and the uncertainty is estimated to be better than ±0.72×10^–2. We provide a complete set of tables of experimental data as a function of temperature, pressure, and density, which cover the dielectric property needs for most engineering applications. The data obtained were used to establish dielectric equations of state as a function of density and temperature and as a function of pressure and temperature. To study the dependence of the relative permittivity on temperature, pressure and density, we have applied various molecular theories of polar liquids. The apparent dipole moment obtained was*=2.482 D.     

Thermal conductivity andPVT measurements of pentafluoroethane (refrigerant HFC-125)

By means of the transient and steady-state coaxial cylinder methods, the thermal conductivity of pentafluoroethane was investigated at temperatures from 187 to 419 K and pressures from atmospheric to 6.0 MPa. The estimated uncertainty of the measured results is ±(2–3)%. The operation of the experimental apparatus was validated by measuring the thermal conductivity of R22 and R12. Determinations of the vapor pressure andPVT properties were carried out by a constant-volume apparatus for the temperature range 263 to 443 K, pressures up to 6 MPa, and densities from 36 to 516 kg m^–3. The uncertainties in temperature, pressure, and density are less than ±10 mK, ±0.08%, and ±0.1%, respectively.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Saturated liquid densities and bubble-point pressures of the binary HFC 152a+HCFC 142b system

Forty-eight sets of the saturated liquid densities and bubble-point pressures of the binary HFC 152a + HCFC 142b system were measured with a magnetic densimeter coupled with a variable-volume cell. The measurements obtained at four compositions, 20, 40, 60, and 80 wt%, of HFC 152a cover a range of temperatures from 280 to 400 K. The experimental uncertainties in temperature, pressure, density, and composition were estimated to be within ±15mK, ±20kPa, ±0.2%, and between –0.14 and ±0.01 wt% HFC 152a (–0.01 and + 0.14 wt% HCFC 142b), respectively. The purities of the samples were 99.9 wt% for HFC 152a and 99.8 wt% for HCFC 142b. A binary interaction parameter, k _ij , in the Peng-Robinson equation of state was determined as a function of temperature for representing the bubble-point pressures. On the other hand, two constant binary-interaction parameters, k _ij and l _ij , were introduced into the mixing rule of the Hankinson-Brobst-Thomson equation for representing the saturated liquid densities.     

The specific heat capacity and thermal conductivity of normal liquid3He

By observing the diffusion of a heat pulse along a 10-cm column of normal liquid³He with the aid of two vibrating wire thermometers, it has been possible to measure the heat capacityC and thermal conductivityK of the liquid in the temperature range fromT _C to 10 mK and at pressures of 0.21, 4.39, 9.97, 20.01, and 29.32 bar. By using a Pt NMR thermometer, an LCMN thermometer, and a³He melting curve thermometer calibrated using the melting curve given by Greywall in 1983, a temperature scale has been established and (1) it has been shown that this melting curve is consistent in the temperature range 5–22 mK with the Korringa law for the Pt thermometer with a Korringa constant of 29.8±0.2 sec mK, (2) departures have been observed from the Curie-Weiss law for LCMN at low temperatures, and (3) values of the superfluid transition temperature have been obtained that are about 4% lower than the Helsinki values. The measured heat capacities agree well with those of Greywall, but values ofKT are higher than those of Greywall and show more temperature dependence below 10 mK. The implications for the present results of the very different melting curve given by Greywall in 1985 are discussed in an Appendix.     

The effect of pressure on the melting temperature and lamellar thickness of trans-1,4-polyisoprene crystallized at pressures of 1 bar to 3 kbar

The melting temperatures of both low-melting form and high-melting form trans-1,4-polyisoprene crystals grown at 1 bar pressure have been determined as a function of pressure. Equilibrium melting temperatures have been determined for specimens crystallized at pressure. All the melting temperatures increase by approximately 15 K kbar^–1. Lamellar thicknesses have been measured by both thin film transmission electron microscopy and via low-angle X-ray studies over the pressure range 1 bar to 3.0 kbar. The two methods of measurements give good agreement. Crystals of a given thickness melt at a given temperature, at 1 bar pressure, independent of temperature or pressure of crystallization. Crystals of a given thickness are formed at a given supercooling independent of the pressure of crystallization. At a given crystallization temperature the thickness of crystals formed decreases with increasing pressure. Crystals of the same form grow, at all pressures studied, by the same basic mechanism. Chain-extended type crystals were not formed.     

A thermodynamic property formulation for cyclohexane

A formulation for the thermodynamic properties of cyclohexane is presented. The equation is valid for single-phase and saturation states from the melting line to 700 K at pressures up to 80 MPa. It includes a fundamental equation explicit in reduced Helmholtz energy with independent variables of reduced density and temperature. The functional form and coefficients of the ancillary equations were determined by weighted linear regression analyses of evaluated experimental data. An adaptive regression algorithm was used to determine the final equation. To ensure correct thermodynamic behavior of the Helmholtz energy surface the coefficients of the fundamental equation were determined with multiproperty fitting, Pressure-density-temperature (P-p-T) and isobaric heat capacity (C _p -P-T) data were used to develop the fundamental equation, SaturationP-p-T values, calculated from the estimating functions, were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Separate functions were used for the vapor pressure, saturated liquid density, saturated vapor density. ideal-gas heat capacity. and pressure on the melting curve, Comparisons between experimental data and values calculated using the fundamental equation are given to verify the accuracy of the formulation. The formulation given here may be used to calculate densities within ±0.1 %, heat capacities to within ±2 %. and speed of sound to within ± 1 %, except near the critical point.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

An experiment to detect vacancies and their possible Bose-Einstein condensation in solid 4He

Using a capacitive pressure gauge, the pressure of a constant-volume ⁴He-sample was measured in the temperature range 1.5–120 mK, at pressures of 25.3 bar (on the melting curve) and 26.0 bar. A gradual pressure change occurring as a consequence of the ideal gas behavior of vacancies, or a pressure anomaly corresponding to a Bose-Einstein condensation of the vacancies, was not observed. Within the sensitivity of the pressure gauge (2 Pa), this result sets upper limits to the density of zero-point vacancies.Department of Physics, University of Florida, Gainesville, Florida 32611.     

Thermodynamic properties by levitation calorimetry — V. High-temperature heat content of liquid gallium

The heat content (enthalpy) of liquid gallium relative to the supercooled liquid state at 298.15 K has been measured by levitation calorimetry over the temperature range 1412–1630 K. Thermal energy increments were determined using an aluminum block calorimeter of conventional design. The sharp decrease of C _p with increasing temperature observed just above the melting point does not persist up to the high temperatures of the present work. When combined with recent laser-flash calorimetry results from the literature, the present work indicates that C _p is 26.46 ± 0.71 J · g-atom^–1 · K^–1 over the temperature range 587–1630 K.Paper presented at the Japan-United States Joint Seminar on Thermophysical Properties, October 24–26, 1983, Tokyo, Japan.     

Measurements of Gaseous PVTx Properties and Saturated Vapor Densities of Refrigerant Mixture R-125+R-143a

The experimental PVTx properties of a binary refrigerant mixture, R-125 (pentafluoroethane)+R-143a (1,1,1-trifluoroethane), have been measured for a composition of 50 mass% R-125 by a constant-mass method coupled with an expansion procedure in a range of temperatures from 305 to 400 K, pressures from 1.5 to 6.1 MPa, and densities from 92 to 300 kg·m^–3. The experimental uncertainties of the present measurements are estimated to be within ±7.2 mK in temperature, ±3.0 kPa in pressure, ±0.12 kg·m^–3 in density, and ±0.040 mass% in composition. The sample purities are 99.953 mass% for R-125 and 99.998% for R-143a. Seven saturated vapor densities and dew point pressures of the R-125+R-143a system were determined, on the basis of rather detailed PVTx properties measured in the vicinity of the saturation boundary as well as the thermodynamic behavior of isochores near saturation. The second and third virial coefficients for temperatures from 330 to 400 K were also determined.     

Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa

A thermodynamic property formulation for standard dry air based upon experimental P––T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.     

Thermal conductivities of new refrigerants R125 and R32 measured by the transient hot-wire method

Thermal conductivity measurements are reported for the new refrigerants pentafluoroethane (R125) and dilluoromethane (R32), which are suggested to replace chlorodifluoroethane (R22) as components of a mixture. Transient hot-wire experiments were performed which cover both the liquid and the vapor states at temperatures and pressures ranging fromt = –40 to 90°C and fromp = 1 to 60 bar. Uncertainties keep within 1.6% for liquid and 2.0% for vapor states, The results are correlated with density and temperature. In addition, temperature-dependent correlations are presented for practical calculations for (i) saturated liquid, (ii) saturated vapor, and (iii) dilute gas (which approximately equals the vapor state at ambient pressure). Finally, the results are compared with data from the literature and also with the respective thermal conductivities of R22.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

NMR study of 3He bubbles in phase-separated solid 3He –4He mixtures

³ He droplets embedded in a solid ⁴ He matrix have been studied by NMR and pressure measurements. One feature of the experiment is that the mixture crystals, of ³ He concentration 1%, are grown under constant pressure conditions to minimise the formation of defects. A number of sample pressures below 34 bar have been studied. Isotopic phase separation and the melting of the bubbles are clearly observed. Measurements of T₁ , T₂ and magnetisation give detailed information on the structure of the droplets. At an initial sample pressure of 28.3 bar preliminary measurements of the T₁ of the liquid bubbles show a temperature dependence of the form (A+ B/T²)^–1. This indicates that the expected relaxation in the liquid is augmented by a constant contribution, probably from the surface of the droplets.     

Thermal conductivity of water and 2-n-butoxyethanol and their mixtures in the temperature range 305–350 K at pressures up to 150 MPa

The thermal conductivity of binary liquid mixtures of water and 2-n-butoxyethanol has been measured within the temperature range 305–350 K at pressures up to 150 MPa. The measurements have been carried out with a transient hotwire instrument suitable for electrically conducting liquids and have an estimated accuracy of ±0.3%. The liquid mixture has a closed-loop solubility and reveals a lower critical solution temperature for a mole fraction of 2-n-butoxyethanol of 0.0478 at a temperature of 322.25 K. The results of the measurements reveal a small, but discernible, enhancement of the thermal conductivity of the solution at the critical composition.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

High-Pressure Measurements of the Viscosity and Density of Two Polyethers and Two Dialkyl Carbonates

The viscosity and density of four pure liquid compounds (dimethyl carbonate, diethyl carbonate, triethylene glycol dimethyl ether, and tetraethylene glycol dimethyl ether) were measured at several temperatures between 283.15 and 353.15 K. The density measurements were performed up to 60 MPa with an uncertainty of 1×10^–4g·cm^–3. The viscosity at atmospheric pressure was measured with an Ubbelohde-type glass capillary tube viscometer with an uncertainty of ±1%. At pressures up to 100 MPa the viscosity was determined with a falling ball viscometer with an uncertainty of ±2%. The density (410 experimental values) and viscosity data (184 experimental values) were fitted to several correlation equations.     

Effect of pressure on the solid-liquid phase equilibria of (carbon tetrachloride + p-xylene) and (carbon tetrachloride+benzene) systems

Solid-liquid phase equilibria of the carbon tetrachloride + p-xylene and the carbon tetrachloride+benzene systems have been investigated at temperatures from 278 to 323 K and pressures up to 500 MPa using a high-pressure optical vessel. The uncertainties in the measurements of temperature, pressure, and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. In the former system, which has an intermolecular compound with a congruent melting point, the freezing temperature at a constant composition increases monotonously with increasing pressure. The two eutectic points of this system shift to higher temperatures and richer compositions of the compound with increasing pressure. In the latter system, which has two intermolecular compounds with incongruent melting points, the one compound disappears under the present experimental conditions and the incongruent melting point of the other compound changes to the congruent melting point under high pressures. The solid-liquid coexistence curves of these systems can be correlated satisfactorily by the equation previously proposed.     

Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

Elementary excitations and sound speed in liquid 4He at negative pressures

No Heading We present neutron scattering measurements of the phonon-roton excitations of superfluid ⁴He at negative pressures in the porous medium MCM-41. The phonon and maxon energies decrease systematically below bulk values as the density is decreased below the bulk value due to stretching of the liquid. The negative internal pressures are estimated by comparison of the observed maxon energies with extrapolation of positive pressure values and from the sound speed. The maximum negative pressure realized, about –5.5 bar, is consistent with surface tension arguments and the MCM-41 pore diameter of 47 Å. Slight broadening of the intrinsic lineshape is observed, suggesting shorter lifetimes of the excitations.PACS numbers: 61.12.Ex; 61.25.Bi; 62.60.+v; 68.03.Cd; 68.03.Kn; 67.40.Mj     

An Analytical Equation of State for Alkaline Earth Metals

In this work, an analytical equation of state based on statistical mechanical perturbation theory, which was initially developed for normal fluids and can be applied to predict the P–V–T data for saturated liquid alkaline earth metals, is presented. The equation of state is that of Ihm, Song, and Mason, and the temperature-dependent parameters of the equation of state are calculated from a corresponding-states correlation as functions of the reduced temperature. Two scaling constants are sufficient for this purpose, the surface tension and the liquid density at the melting point. The equation of state is used to predict the saturated liquid density of molten alkaline earth metals from the melting point up to 2000 K, for which experimental data exist, within an accuracy of 5%.