Virial equation of state and ideal-gas heat capacities of pentafluoro-dimethyl ether

A virial equation of state is presented for vapor-phase pentafluoro-dimethyl ether (CF₃−O−CF₂H), a candidate alternative refrigerant known as E125. The equation of state was determined from density measurements performed with a Burnett apparatus and from speed-of-sound measurements performed with an acoustical resonator. The speed-of-sound measurements spanned the ranges 260≤T≤400 K and 0.05≤P≤1.0 MPa. The Burnett measurements covered the ranges 283≤T≤373 K and 0.25≤P≤5.0 MPa. The speed-of-sound and Burnett measurements were first analyzed separately to produce two independent virial equations of state. The equation of state from the acoustical measurements reproduced the experimental sound speeds with a fractional RMS deviation of 0.0013%. The equation of state from the Burnett measurements reproduced the experimental pressures with a fractional RMS deviation of 0.012%. Finally, an equation of state was fit to both the speed-of-sound and the Burnett measurements simultaneously. The resulting equation of state reproduced the measured sound speeds with a fractional RMS deviation of 0.0018% and the measured Burnett densities with a fractional RMS deviation of 0.019%.     

An Equation of State for Fluoroethane (R161)

Fluoroethane (R161, C₂H₅F, 353-36-6) is a potential alternative refrigerant with excellent cycle performance, with zero ozone-depletion potential and low global warming potential. In this study, the thermodynamic property formulation for fluoroethane has been developed with the use of available experimental thermodynamic property data. In determining the equation of state, multiproperty fitting methods were used including single-phase pressure–density–temperature (pρT), vapor pressure, and saturated liquid-density data. The equation of state has been developed to conform to the Maxwell criterion for two-phase liquid–vapor equilibrium states, and is valid for temperatures from 130 K to 450 K, and pressures to 5 MPa. The extrapolation behavior of the equation of state at high temperatures and high pressures is reasonable. As there are very few compressed liquid-density experimental data published, the uncertainties in density of the equation of state are estimated to be 2.0 % in the compressed-liquid region and 0.5 % in the gas and supercritical regions. Uncertainties in vapor pressure are 0.5 % above 200 K and increase at lower temperatures. The uncertainties for all properties are higher in the critical region, except vapor pressure. Detailed comparisons between experimental and calculated data have been performed in this study.     

A general equation of state for dense fluids

A general equation of state, originally proposed for compressed solids by Parsafar and Mason, has been successfully applied to dense fluids. The equation was tested with experimental data for 13 fluids, including polar, nonpolar, saturated and unsaturated hydrocarbons, strongly hydrogen bonded, and quantum fluids. This equation works well for densities larger than the Boyle density ρ_B [1/ρ_B=T _B d B ₂(T _B)/T], where B₂(T_B) is the second virial coefficient at the Boyle temperature, at whichB ₂=0 and for a wide temperature range, specifically from the triple point to the highest temperature for which the experimental measurements have been reported. The equation is used to predict some important known regularities for dense fluids, like the common bulk modulus and the common compression points, and the Tait-Murnaghan equation. Regarding the common points, the equation of state predicts that such common points are only a low-temperature characteristic of dense fluids as verifed experimentally. It is also found that the temperature dependence of the parameters of the equation of state differs from those given for the compressed solids. Specifically they are given byA ₁ (T)=a ₁+b₁T+c₁T²-d₁ T ln (T).     

Subatmospheric vapor pressures evaluated from internal-energy measurements

Vapor pressures were evaluated from measured internal-energy changes in the vapor+liquid two-phase region, ΔU ⁽²⁾. The method employed a thermodynamic relationship between the derivative quantity (ϖU ⁽²⁾/ϖV) _T and the vapor pressure (p _σ) and its temperature derivative (ϖp/ϖT)_σ. This method was applied at temperatures between the triple point and the normal boiling point of three substances: 1,1,1,2-tetrafluoroethane (R134a), pentafluoroethane (R125), and difluoromethane (R32). Agreement with experimentally measured vapor pressures near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately ±0.04 kPa (±0.04%). The method was applied to R134a to test the thermodynamic consistency of a publishedp-p-T equation of state with an equation forp _σ for this substance. It was also applied to evaluate publishedp _σ data which are in disagreement by more than their claimed uncertainty.     

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     

An experimental study on the shear viscosity of liquid neon

By means of the torsional crystal method the coefficient of shear viscosity of liquid neon has been measured at temperatures from 27 K to 42 K and pressures up to 10 MN m^?2. Along the saturated vapour pressure line η shows an Arrhenius behaviour for temperatures T ? 0.8 T_c whereas its density dependence is very well described by the Batschinski equation.The experimental results are compared with the significant structure theory for rigid spheres and with the square-well theory based on statistical mechanics.     

A Multiparameter Viscosity Equation for 1,1-Difluoroethane (R152a) with an Optimized Functional Form

This paper presents a new formulation for the viscosity surface of 1,1-difluoroethane (R152a). The formulation is a multiparameter equation η = η(ρ, T) obtained from an optimization technique of the functional form based on available experimental data. The equation is valid for temperatures from 240 to 440 K and pressures up to 20 MPa. Two lines of viscosity minima have been observed, and they have been analytically defined. A high accuracy equation of state for R152a was used to convert the experimental variables (P,T) into the independent variables of the viscosity equation (ρ, T). Comparisons with data are given to establish the accuracy of the viscosity values calculated using this equation. The obtained results are very satisfactory with an average absolute deviation of 0.27% for the selected 264 primary data points, and this is a significant improvement with respect to other equations in the literature.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5-8, 2005, Bratislava, Slovak Republic.     

Thermal conductivity, heat capacity, and compressibility of atactic poly(propylene) under high pressure

The thermal conductivity λ and the heat capacity per unit volume of atactic poly(propylene) have been measured in the temperature range 90–420 K at pressures up to 1.5 GPa using the transient hot-wire method. The bulk modulus has been measured in the range 200–295 K and up to 0.7 GPa. These data were used to calculate the volume dependence of λ,g=−[∂λ/λ)/(∂V/V)] _T , which yielded the following values for the glassy state (T<256 K at atmospheric pressure): 3.80±0.19 at 200 K, 3.74±0.19 at 225 K, 3.90±0.20 at 250 K, 3.77±0.19 at 271 K, and 3.73±0.19 at 297 K. The resultant value forg of the liquid state was 3.61±0.15 at 297 K. Values forg which are calculated at 295 K, using theoretical models of λ(T), agree to within 12% with the experimental value for the glassy state.     

Electrical transport in light rare-earth vanadates

This paper reports electrical transport studies of rare-earth vanadates (RVO₄ with R = Ce, Pr, Nd, Sm, Eu and Gd), prepared by solid state reaction and characterized by X-ray diffraction studies. TGA study (300 to 1200 K) shows no weight loss; possible phase transitions in the range 1075 to 1300 K have been indicated by DTA studies. All these vanadates are typical semiconducting compounds with room temperature electrical conductivity (σ) lying between 10⁻⁴ and 10⁻²Ω⁻¹m⁻¹. Measurements of σ and the Seebeck coefficient (S) are reported in the temperature interval 400 to 1200 K. Two linear regions 400 to T ₁K and T ₁ to T ₂K have been obtained from the log σ against T ⁻¹ as well as the S against T ⁻¹ plots followed by a peak around T ₃ and minima around T ₄K. T ₄>T ₃>T ₂>T ₁, are different for different vanadates. It has been concluded that in the interval 400 to T ₁K, conduction is of the extrinsic hopping type with Ce⁴⁺ in CeVO₄, Pr⁴⁺ in PrVO₄ and V⁴⁺ in Nd to Gd vanadates as dominant defect centres. In the temperature interval T ₁, to T ₂K, the conduction has been shown to be of the intrinsic band type in all vanadates with polarons of intermediate coupling strength as the dominant charge carriers. Above T ₂ all vanadates tend to become metallic, but before this is achieved the phase change makes the conductivity smaller. T ₄ is close enough to the temperature corresponding to the DTA peak to be termed the phase transition temperature.     

Investigation of Volumetric Properties of Some Glycol Ethers Using a Simple Equation of State

In this work, a simple equation of state (EoS) has been used to predict the density and other thermodynamic properties such as the isobaric expansion coefficient, α _P , the isothermal compressibility, κ _T , and the internal pressure, P _i , of six glycol ethers including diethylene glycol monobutyl ether (DEGBE), propylene glycol propyl ether (PGPE), diethylene glycol monomethyl ether (DEGME), diethylene glycol monoethyl ether (DEGEE), triethylene glycol dimethyl ether (TriEGDME), and tetraethylene glycol dimethyl ether (TEGDME) at different temperatures and pressures. A comparison with literature experimental data has been made. Additionally, statistical parameters between experimental and calculated densities for the GMA EoS and four other EoSs (Soave–Redlich–Kwong, Peng–Robinson, Soave–Redlich–Kwong with volume translation, and Patel–Teja) indicate the superiority of the GMA EoS.     

Volumetric measurements under pressure for 2,2,4-trimethylpentane at temperatures up to 353.15 K and for benzene and three of their mixtures at temperatures up to 348.15 K

(p, V, T) data have been obtained in the form of volume ratios relative to 0.1 MPa for benzene (298.15 to 348.15 K), 2,2,4-trimethylpentane (TMP) (313.15 to 353.15 K), and their mixtures near 0.25, 0.5, and 0.75 mole fraction of benzene (313.15 to 348.15 K) for pressures up to near the freezing pressures for benzene and the mixtures, and up to 400 MPa for TMP. Isothermal compressibilitiesκ _T, isobaric expansivitie α, changes in heat capacity at constant pressureΔC _p, and excess molar volumesV ^E have been determined from the data. Literature data at atmospheric pressure have been used to convert theΔC _p toC _p at several temperatures. The isobars for α over the temperature range 278.15 to 353.15 K for TMP intersect near 47 MPa and reverse their order in temperature when plotted against pressure; normalization of the α's by dividing the values at each temperature by the α at 0.1 MPa prevents both the intersection and the reversal of the order. TheV ^E are positive and have an unusual dependence on pressure: they increase with temperature and pressure so that the order of the curves for 0.1, 50, and 100 MPa changes in going from 313.15 to 348.15 K.     

An Experimental Study of the <Emphasis Type="Italic">pVTx</Emphasis> Properties for Binary Mixtures of HFC-32 and HFC-125 from 258 to 354 K at Pressures up to 16.9 MPa

An experimental study of the pVTx properties for binary mixtures of HFC-32 (CH₂F₂) and HFC-125 (C₂HF₅) was conducted in the range of temperatures from 258 to 354 K, pressures up to 16.9 MPa, densities from 900 to 1400 kg·m⁻³, and compositions from 0 to 1 mole fraction of HFC-32, within the uncertainties of 4.8 mK of temperatures, 1.8 kPa of pressures, 0.022% of densities, and 0.0022 mole fraction of compositions. The present results were determined with the use of a constant-volume apparatus consisting of a cylindrical vessel of approximately 173 cm³ internal volume. The available data including the present measurements are critically compared with the equation of state developed by Tillner-Roth et al., and it is found that, in the liquid region for the range of compositions from 0.1 to 0.4 mole fraction of HFC-32, this equation of state is less reliable because of the lack of experimental data. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Thermal equation of state of natural chromium spinel up to 26.8 GPa and 628 K

A pressure–volume–temperature data set has been obtained for natural chromium spinel, using synchrotron X-ray diffraction with a resistance heated diamond-anvil cell (RHDAC). The unit cell parameter of the chromium spinel was measured by energy dispersive X-ray diffraction up to pressures of 26.8 GPa and temperatures of 628 K. No phase change has been observed. The observed P–V–T data were fit to the high-temperature Birch-Murnaghan equation of state, with V ₀ fixed at its experimental value, yields K ₀ = 209 ± 9 GPa, (∂K/∂T)_P = −0.056 ± 0.035 GPa K⁻¹, and α₀ = 7±1 × 10⁻⁵ K⁻¹. The temperature derivative of the bulk modulus (∂K/∂T)_P of chromium spinel is determined here for the first time. The obtained K ₀ is slightly higher than the previous results of synthetic spinel. We suggest that Fe²⁺–Mg²⁺ substitution is responsible for the high bulk modulus of chromium spinel.     

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid ³He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature T _c ^a is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/T _c ^a ) at 0.9T _c ^a as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.     

Virial equation of state of helium, xenon, and helium-xenon mixtures from speed-of-sound and burnettPρT measurements

The virial equation of state was determined for helium, xenon, and helium-xenon mixtures for the pressure and temperature ranges 0.5 to 5 MPa and 210 to 400 K. Two independent experimental techniques were employed: BurnettPρT measurements and speed-of-sound measurements. The temperature-dependent second and third density virial coefficients for pure xenon and the second and third interaction density virial coefficients for helium-xenon mixtures were determined. The present density virial equations of state for xenon and helium-xenon mixtures reproduce the speed-of-sound data within 0.01% and thePρT data within 0.02% of the pressures. All the results for helium are consistent, within experimental errors, with recent ab initio calculations, confirming the accuracy of the experimental techniques.     

Thermodynamic Properties of Methanol in the Critical and Supercritical Regions

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 (T_c = 512.78±0.02K) and the critical density (ρ_c = 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 C_VVT 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 0.98T_c≤ T ≤ 1.5T_c and in the density range 0.35ρ_c ≤ ρ leq 1.65 ρ_c, CREOS97-04 represents all available experimental thermodynamic data for pure methanol to within their experimental uncertainties.     

Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Thermoelectric properties of perovskite oxides La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CoO<Subscript>3</Subscript> prepared by polymerlized complex method

P-type perovskite oxides La_1−x Sr _x CoO₃ (0 ≤ x ≤ 0.2) have been prepared using a polymerlized complex method and sintering. The Seebeck coefficient, electrical conductivity, and thermal conductivity of the oxides were studied from room temperature to 773 K. The ln(σT)−1/T relationships revealed small-polaron hopping mechanism for the higher Sr contents. Large Seebeck coefficients were observed in lightly Sr-doped samples. Sr doping greatly reduced the Seebeck coefficient and enhanced the electrical and thermal conductivity of the samples. The temperature-induced spin-state transition of Co³⁺ ions strongly influenced the transport properties. The highest ZT value found in this series of oxides was 0.046 at 300 K for x = 0.1.     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

Equation of State for Molten Alkali Metals from Surface Tension. Part II

This work presents a new method for predicting the equation of state for molten alkali metals, based on statistical–mechanical perturbation theory from two scaling constants that are available from measurements at ordinary pressures and temperatures. The scaling constants are the surface tension and the liquid density at the boiling temperature (_b, _b). Also, a reference temperature, T _Ref, is presented at which the product (T _Ref T _b ^1/2 ) is an advantageous corresponding temperature for the second virial coefficient, B ₂(T). The virial coefficient of alkali metals cannot be expected to obey a law of corresponding states for normal fluids, because two singlet and triplet potentials are involved. The free parameter of the Ihm–Song–Mason equation of state compensates for the uncertainties in B ₂(T). The vapor pressure of molten alkali metals at low temperatures is very low and the experimental data for B ₂(T) of these metals are scarce. Therefore, an equation of state for alkali metals from the surface tension and liquid density at boiling temperature (_b, _b) is a suitable choice. The results, the density of Li through Cs from the melting point up to several hundred degrees above the boiling temperature, are within 5%.