A practical vapor pressure equation for helium-3 from 0.01 K to the critical point

A saturation vapor pressure equation, p(T), is an essential component in the ³He state equation currently under development. The state equation is valid over the range 0.01-20 K with pressures from 0 to the melting pressure or 15 MPa. The vapor pressure equation consequently must be valid from 0.01 K to the critical temperature. This paper surveys available ³He critical temperature and pressure measurements, leading to new recommended critical values of 3.3157 K and 114603.91 Pa. The ITS-90 temperature scale is defined by the ³He vapor pressure from 0.65 to 3.2 K. A new vapor pressure equation is developed for the interval from the upper end of the T₉₀ scale to this newly defined critical point, employing a mathematical form in which the second derivative d²p/dT² diverges in agreement with scaling laws at the critical point. Below 0.65 K, an empirical vapor pressure expression is adopted, consistent with a theoretical expression valid in the limit T → 0. These two new components are fitted to be piecewise continuous with the EPT-76 p(T) scale rather than the ITS-90 T(p) scale between 0.65 and 3.2 K. Probable deviations between this vapor pressure scale and PLTS-2000 melting pressure-temperature scale are recognized, but not reconciled.     

Thermophysical Properties of a Refrigerant Mixture of R365mfc (1,1,1,3,3-Pentafluorobutane) and Galden<Superscript>®</Superscript> HT 55 (Perfluoropolyether)

This work presents a comprehensive experimental study of various thermophysical properties of an azeotropic refrigerant mixture of 65 mass% R365mfc (1,1,1,3,3-pentafluorobutane) and 35 mass% Galden^? HT 55 (perfluoropolyether). Light scattering from bulk fluids has been applied for measuring both the thermal diffusivity and the speed of sound in the liquid and vapor phases under saturation conditions, between 293 K and the liquid–vapor critical point at 450.7 K. Furthermore, the speed of sound has been measured for the superheated-vapor phase along nine isotherms, between 393 and 523 K and up to a maximum pressure of about 2.5 MPa. For temperatures between 253 and 413 K, light scattering by surface waves on a horizontal liquid–vapor interface has been used for simultaneous determination of the surface tension and kinematic viscosity of the liquid phase. With light scattering techniques, uncertainties of less than ±2.0%, ±0.5%, ±1.5%, and ±1.5% have been achieved for the thermal diffusivity, sound speed, kinematic viscosity, and surface tension, respectively. In addition to vapor-pressure measurements between 304 and 448 K, the density was measured between 273 and 443 K using a vibrating-tube method. Here, measurements have been performed in the compressed- and saturated-liquid phases with uncertainties of ±0.3% and ±0.1%, respectively, as well as for the superheated vapor up to a maximum pressure of about 3 MPa with an uncertainty between ±0.3% and ±3%. Critical-point parameters were derived by combining the data obtained by different techniques.     

Quartz Tuning Fork in Helium

Use of a quartz tuning fork for precise measurements of density has been studied in normal ³He liquid and in ⁴He liquid and vapor, spanning a reasonably wide range of fluid densities. It is evident that the compressibility of the fluid must be accounted for in order to properly interpret the resonator response.      

Thermodynamic properties of 1-chloro-1,2,2,2-tetrafluoroethane (R124)

The critical temperature and pressure, vapor pressure, and PVT relations for gaseous and liquid 1-chloro-1,2,2,2-tetrafluoroethane (R124) were determined experimentally. The vapor pressure was measured in the temperature range from 278.15 K to the critical temperature. The PVT measurements were carried out using two types of volumeters in the temperature range from 278.15 to 423.15 K, at pressure up to 100 MPa. The numerical PVT data of gaseous state are fitted as a function of density to a modified Benedict-Webb-Rubin equation. The pressure-volume relations of the liquid at each temperature are correlated satisfactorily as a function of pressure by the Tait equation. The critical density and saturated vapor and liquid densities are also determined and some of the thermodynamic properties are derived from the experimental results.     

Thermodynamic properties of HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) at saturation conditions

The thermodynamic properties of HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) were determined. The critical point was ascertained by visual observation of the meniscus disappearance within an optical cell. The critical temperature, critical density, and critical pressure were determined to be 403.37 ± 0.03 K, 515.3 ± 5.0 kg m⁻³, and 2766.4 ± 4.5 kPa, respectively. Vapor pressures were also measured at temperatures ranging from 323 K (50 °C) to the critical temperature, and were correlated using the Wagner-type equation. The acentric factor and normal boiling point were determined to be 0.4053 and 280.58 K (7.43 °C), respectively, using the vapor pressure correlation. Based on the critical parameters and the acentric factor, saturated vapor densities and liquid densities were estimated using the Peng–Robinson equation and the Hankinson–Thomson equation, respectively. The heat of vaporization was also calculated from the Clausius–Clapeyron equation.     

Viscosity and Liquid Density of Asymmetric <Emphasis Type="Italic">n</Emphasis>-Alkane Mixtures: Measurement and Modeling

Viscosity and liquid density measurements were performed, at atmospheric pressure, in pure and mixed n-decane, n-eicosane, n-docosane, and n-tetracosane from 293.15 K (or above the melting point) up to 343.15 K. The viscosity was determined with a rolling ball viscometer and liquid densities with a vibrating U-tube densimeter. Pure component results agreed, on average, with literature values within 0.2% for liquid density and 3% for viscosity. The measured data were used to evaluate the performance of two models for their predictions: the friction theory coupled with the Peng–Robinson equation of state and a corresponding states model recently proposed for surface tension, viscosity, vapor pressure, and liquid densities of the series of n-alkanes. Advantages and shortcoming of these models are discussed.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A     

Thermodynamic Properties for R-404A

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.     

Mobility of 2D Electrons on Pure 4He and on 3He–4He Dilute Solution

The mobility of 2D electrons on pure ⁴He and on 0.5 % solution of ³He in ⁴He was investigated for different electron densities in the temperature range 0.12 to 1.3 K. The electrons in the same electron density show the same transition temperature from liquid state to Wigner crystal state in both pure ⁴He and in the solution. In the high temperature range where the gas-scattering is dominant, the electrons show a smaller mobility in the solution than in the pure ⁴He due to the electron collision with ³He gas atoms which have a higher vapor pressure. In the middle temperature range where the ripplon-scattering is dominant, the mobility in the solution is smaller than in ⁴He. This is explained by a smaller surface tension caused by ³He atoms collected at the surface. In the low temperature range where electrons are in the Wigner crystal state, the mobility gradually increases with decreasing temperature in the solution, while it stays almost constant in the pure ⁴He. The mobility increase is more pronounced in the low electron density. The results are qualitatively in agreement with the existing theory which includes the bulk ³He quasiparticle reflection from surface dimples and the effect of the surface layer of ³He atoms.     

Equation of State for the Thermodynamic Properties of <Emphasis Type="Italic">trans</Emphasis>-1,3,3,3-Tetrafluoropropene [R-1234ze(E)]

An equation of state for the calculation of the thermodynamic properties of the hydrofluoroolefin refrigerant R-1234ze(E) is presented. The equation of state (EOS) is expressed in terms of the Helmholtz energy as a function of temperature and density. The formulation can be used for the calculation of all thermodynamic properties through the use of derivatives of the Helmholtz energy. Comparisons to experimental data are given to establish the uncertainty of the EOS. The equation of state is valid from the triple point (169 K) to 420 K, with pressures to 100 MPa. The uncertainty in density in the liquid and vapor phases is 0.1 % from 200 K to 420 K at all pressures. The uncertainty increases outside of this temperature region and in the critical region. In the gaseous phase, speeds of sound can be calculated with an uncertainty of 0.05 %. In the liquid phase, the uncertainty in speed of sound increases to 0.1 %. The estimated uncertainty for liquid heat capacities is 5 %. The uncertainty in vapor pressure is 0.1 %.     

The orthobaric liquid and vapor densities of tetramethylsilane and of 2,2-dimethylpropane

The orthobaric densities of tetramethylsilane and 2,2-dimethylpropane have been measured by means of a hydrostatic density balance. For tetramethylsilane the liquid density has been determined from 289.73 K to the critical point 448.60 K and the vapor density from 353.55 K to the critical point, while for 2,2-dimethylpropane the liquid density has been measured from 290.88 K to the critical point 433.71 K and the vapor density from 349.01 K to the critical point. The results are represented well by the extended-scaling equation of Wegner with three correction terms and the critical indices α,β, andΔ ₁, obtained from renormalization-group theory. The fit is not improved by a term expressing an anomaly in the diameter using either of the exponents (1−α) or 2β. The critical density for tetramethylsilane is estimated as (0.2436±0.0001) g·cm⁻³ and that for 2,2-dimethylpropane as (0.2318±0.0001) g·cm⁻³.     

Thermal Response of a Two-Phase Near-Critical Fluid in Low Gravity: Strong Gas Overheating as Due to a Particular Phase Distribution

An experimental study of the thermal response to a stepwise rise of the wall temperature of two-phase near-critical SF₆ in low gravity for an initial temperature ranging from 0.1 to 10.1 K from the critical temperature is described. The change in the vapor temperature with time considerably exceeds the change in the wall temperature (overheating by up to 23% of the wall temperature rise). This strong vapor overheating phenomenon results from the inhomogeneous adiabatic heating process occurring in the two-phase near-critical fluid while the vapor bubble is thermally isolated from the thermostated walls by the liquid. One-dimensional numerical simulations of heat transfer in near-critical two-phase ³He confirm this explanation. The influence of heat and mass transfer between gas and liquid occurring at short time scales on the thermal behavior is analyzed. A model for adiabatic heat transfer, which neglects phase change but accounts for the difference between the thermophysical properties of the vapor and those of the liquid, is presented. A new characteristic time scale of adiabatic heat transfer is derived, which is found to be larger than that in a one-phase liquid and vapor.     

Measurements of the Superfluid Joule–Thomson Refrigerator Using High Concentration 3He–4He Mixtures

The superfluid Joule–Thomson refrigerator (SJTR) uses a liquid superfluid ³He–⁴He mixture to provide cooling below 1 K. Performance measurements of the SJTR using 5% and 11% ³He concentration mixtures are reported. High concentration operation shows higher cooling powers at high temperature. Ultimate temperatures are seen to increase with increasing concentration due to a pinching of the temperature defect in the recuperative heat exchanger. This pinching effect is due to the variation of the heat capacity of the ³He–⁴He mixture with temperature and concentration and is discussed in detail and design changes are suggested to mitigate it.     

New Fundamental Equations of State with a Common Functional Form for 2,3,3,3-Tetrafluoropropene (R-1234yf) and <Emphasis Type="Italic">trans</Emphasis>-1,3,3,3-Tetrafluoropropene (R-1234ze(E))

New fundamental equations of state explicit in the Helmholtz energy with a common functional form are presented for 2,3,3,3-tetrafluoropropene (R-1234yf) and trans-1,3,3,3-tetrafluoropropene (R-1234ze(E)). The independent variables of the equations of state are the temperature and density. The equations of state are based on reliable experimental data for the vapor pressure, density, heat capacities, and speed of sound. The equation for R-1234yf covers temperatures between 240 K and 400 K for pressures up to 40 MPa with uncertainties of 0.1 % in liquid density, 0.3 % in vapor density, 2 % in liquid heat capacities, 0.05 % in the vapor-phase speed of sound, and 0.1 % in vapor pressure. The equation for R-1234ze(E) is valid for temperatures from 240 K to 420 K and for pressures up to 15 MPa with uncertainties of 0.1 % in liquid density, 0.2 % in vapor density, 3 % in liquid heat capacities, 0.05 % in the vapor-phase speed of sound, and 0.1 % in vapor pressure. Both equations exhibit reasonable behavior in extrapolated regions outside the range of the experimental data.     

Density of <Emphasis Type="Italic">Jatropha curcas</Emphasis> Seed Oil and its Methyl Esters: Measurement and Estimations

Density data as a function of temperature have been measured for Jatropha curcas seed oil, as well as biodiesel jatropha methyl esters at temperatures from above their melting points to 90 ^° C. The data obtained were used to validate the method proposed by Spencer and Danner using a modified Rackett equation. The experimental and estimated density values using the modified Rackett equation gave almost identical values with average absolute percent deviations less than 0.03% for the jatropha oil and 0.04% for the jatropha methyl esters. The Janarthanan empirical equation was also employed to predict jatropha biodiesel densities. This equation performed equally well with average absolute percent deviations within 0.05%. Two simple linear equations for densities of jatropha oil and its methyl esters are also proposed in this study.     

Equation of State for Normal Liquid Helium-3 from 0.1 to 3.3157 K

An equation of state for normal liquid ³He has been constructed in the form of Helmholtz free energy as a function of independent parameters—temperature, and density. The equation was fitted simultaneously to the collected experimental p-ρ-T, specific heat, sound velocity, isobaric expansion coefficient and isothermal compressibility coefficient from the world’s literature to accuracies comparable with reasonable experimental errors in the measured quantities. Extensive comparisons between the equation of state and experimental data have been made by a set of deviation plots. The state equation is valid in the region for temperatures from 0.1 K to T _c = 3.3157 K, and for pressures from vapor pressures to melting pressures.     

A continuous He cryostat with pulse-tube pre-cooling and optical access

We have designed and constructed a continuously operating ³He cryostat with windows for laser ablation and spectroscopy. A two-stage pulse-tube refrigerator cools two platforms to base temperatures of approximately 40 K and 4 K respectively. The platforms are equipped with heat exchangers that cool separate streams of ⁴He and ³He. The ⁴He stream is used to run a thermally isolated evaporative refrigerator with a base temperature of approximately 1.5 K and a cooling power of 20 mW. The ⁴He refrigerator is used to condense ³He, which is used to run a ³He evaporative refrigerator on the experimental cell. The cryostat runs continuously at temperatures from 10 K to 0.4 K with a cooling power of 1.5 mW at 0.5 K.     

Thermodynamic properties of HFC-32 (difluoromethane)

An 18-coefficient modified Benedict–Webb–Rubin equation of state of HFC-32 (difluoromethane) has been developed, based on the updated available PVT measurements, heat capacity measurements and speed of sound measurements. Correlations of vapor pressure and saturated liquid density are also presented. The correlations have been developed based on the reported experimental saturation properties data. This equation of state is effective both in the superheated gaseous phase and compressed liquid phase at pressures up to 70 MPa, densities to 1450 kg/m³, and temperatures from 150 to 475 K, respectively.     

Compressed Liquid Densities and Helmholtz Energy Equation of State for Fluoroethane (R161)

In this study, compressed liquid densities of Fluoroethane (R161, CAS No. 353-36-6) were measured using a high-pressure vibrating-tube densimeter over the temperature range from (283 to 363) K with pressures up to 100 MPa. A Helmholtz energy equation of state for R161 was developed from these density measurements and other experimental thermodynamic property data from the literature. The formulation is valid for temperatures from the triple point temperature of 130 K to 420 K with pressures up to 100 MPa. The approximate uncertainties of properties calculated with the new equation of state are estimated to be 0.25 % in density, 0.2 % in saturated liquid density between 230 K and 320 K, and 0.2 % in vapor pressure below 350 K. Deviations in the critical region are higher for all properties. The extrapolation behavior of the new formulation at high temperatures and high pressures is reasonable.     

Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties

Quantized vortices in liquid ⁴ He are treated quantum mechanically with realistic many-body model wave functions in variational calculations for energy and core structure at T = 0 K. A rectilinear vortex and both small and large vortex rings are studied. Calculated results indicate that rotons are not just small-quantized vortex rings. We compare our results for quantized vortices with experimental data and with theoretical results calculated by others. Correlated basis functions and standard statistical mechanics are used in treating thermohydrodynamic properties of flowing liquid ⁴ He. The Helmholtz potential is evaluated for a model of the flowing liquid that includes phonons and interacting rotons. Characteristics of this potential are discussed. The physical nature of negative superfluid density is explained. Superfluid density, entropy, and specific heat for liquid He-II are evaluated using our theory and the results are compared with experimental data. Very good agreement is found, except in a small temperature range near the λ transition. We indicate that results obtained here can be used in extending the theory to include thermally excited vortices and to investigate the possible role of vortices in accounting for the λ transition in liquid ⁴ He.      

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.