Thermophysical Properties of Chlorine from Speed-of-Sound Measurements

The speed of sound was measured in gaseous chlorine using a highly precise acoustic resonance technique. The data span the temperature range 260 to 440 K and the pressure range 100 kPa to the lesser of 1500 kPa or 80% of the sample's vapor pressure. A small correction (0.003 to 0.06%) to the observed resonance frequencies was required to account for dispersion caused by the vibrational relaxation of chlorine. The speed-of-sound measurements have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. The reported values of C ^o _p are in agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound speed data to within 0.01% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less.     

Thermodynamic Properties of Gaseous Nitrous Oxide and Nitric Oxide from Speed-of-Sound Measurements

The speed of sound was measured in gaseous nitrous oxide (N₂O) and nitric oxide (NO) using an acoustic resonance technique with a relative standard uncertainty of less than 0.01%. The measurements span the temperature range 200 to 460 K at pressures up to the lesser of 1.6 MPa or 80% of the vapor pressure. The data were analyzed to obtain the constant-pressure ideal-gas heat capacity _p ⁰ as a function of temperature with a relative standard uncertainty of 0.1%. For N₂O, the values of _p ⁰ agree within 0.1% with those determined from spectroscopic data. For NO, the values of _p ⁰ differ from spectroscopic results by as much as 1.5%, which is slightly more than the combined uncertainties. The speed-of-sound data were fitted by virial equations of state to obtain temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials, and the second based on a hard-core Lennard-Jones intermolecular potential. The resulting virial equations reproduced nearly all the sound-speed data to within ±0.01% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less.     

Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements

The speed of sound in gaseous hydrogen bromide (HBr) and boron trichloride (BCl₃) was measured using a highly precise acoustic resonance technique. The HBr speed-of-sound measurements span the temperature range 230 to 440 K and the pressure range from 0.05 to 1.5 MPa. The BCl₃ speed-of-sound measurements span the temperature range 290 to 460 K and the pressure range from 0.05 MPa to 0.40 MPa. The pressure range in each fluid was limited to 80% of the sample vapor pressure at each temperature. The speed-of-sound data have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacities as a function of temperature with a relative standard uncertainty of 0.1%. The heat capacities agree with those calculated from spectroscopic data within their combined uncertainties. The speeds of sound were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on the hard-core square-well intermolecular potential model and the second based on the hard-core Lennard–Jones intermolecular potential model. The resulting virial equations of state reproduced the speed-of-sound measurements to 0.01% and can be expected to calculate vapor densities with a relative standard uncertainty of 0.1%. Transport properties calculated from the hard-core Lennard–Jones potential model should have a relative standard uncertainty of 10% or less.     

Thermophysical Properties of Gaseous Tungsten Hexafluoride from Speed-of-Sound Measurements

The speed of sound was measured in gaseous WF₆ using a highly precise acoustic resonance technique. The data span the temperature range from 290 to 420 K and the pressure range from 50 kPa to the lesser of 300 kPa or 80% of the sample's vapor pressure. At 360 K and higher temperatures, the data were corrected for a slow chemical reaction of the WF₆ within the apparatus. The speed-of-sound data have a relative standard uncertainty of 0.005%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. These heat capacities are in reasonable agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound-speed data to within ±0.005% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less. The hard-core Lennard–Jones potential was used to estimate the viscosity and the thermal conductivity of dilute WF₆. The predicted viscosities agree with published data to within 5% and can be extrapolated reliably to higher temperatures.     

Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements

A cylindrical resonator was employed to measure the sound speeds in gaseous CF₄ and C₂F₆. The CF₄ measurements span the temperature range 300 to 475 K, while the C₂F₆ measurements range from 210 to 475 K. For both gases, the pressure range was 0.1 MPa to the lesser of 1.5 MPa or 80% of the sample’s vapor pressure. Typically, the speeds of sound have a relative uncertainty of less than 0.01 % and the ideal-gas heat capacities derived from them have a relative uncertainty of less than 0.1%. The heat capacities agree with those determined from spectroscopic data. The sound speeds were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two models for the virial coefficients were employed, one based on square-well potentials and the second based on a Kihara spherical-core potential. The resulting virial equations reproduce the sound-speed measurements to within 0.005 % and yield densities with relative uncertainties of 0.1% or less. The viscosity calculated from the Kihara potential is 2 to 11% less than the measured viscosity.     

Determination of Second Virial Coefficients and Virial Equations of R-32 (Difluoromethane) and R-125 (Pentafluoroethane) Based on Speed-of-Sound Measurements

The second virial coefficients, B, for difluoromethane (R-32, CH₂F₂) and pentafluoroethane (R-125, CF₃CHF₂) are derived from speed-of-sound data measured at temperatures from 273 to 343 K with an experimental uncertainty of ±0.0072%. Equations for the second virial coefficients were established, which are valid in the extensive temperature ranges from 200 to 400 K and from 240 to 440 K for R-32 and R-125, respectively. The equations were compared with theoretically derived second virial coefficient values by Yokozeki. A truncated virial equation of state was developed using the determined equation for the virial coefficients. The virial equation of state represents our speed-of-sound data and most of the vapor PT data measured by deVries and Tillner-Roth within ±0.01 and ±0.1%, respectively.     

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%.     

Thermodynamic properties of seven gaseous halogenated hydrocarbons from acoustic measurements: CHClFCF3, CHF2 CF3, CF3 CH3, CHF2CH3, CF3CHFCHF2, CF3CH2CF3, and CHF2CF2CH2F

Measurements of the speed of sound in seven halogenated hydrocarbons are presented. The compounds in this study are 1-chloro-1,2,2,2-tetrafluoroethane (CHClFCF₃ or HCFC-124), pentafluoroethane (CHF₂ CF₃ or HFC-125), 1,1,1-trifluoroethane (CF₃CH₃ or HFC-143a), 1,1-difluoroethane (CHF₂CH₃ or HFC-152a), 1,1,1,2,3,3-hexafluoropropane (CF₃CHFCHF₂ or HFC-236ea), 1,1,1,3,3,3-hexafluoropropane (CF₃CH₂CF₃ or HFC-236fa), and 1,1,2,2,3-pentafluoropropane (CHF₂CF₂CH₂F or HFC-245ca). The measurements were performed with a cylindrical resonator at temperatures between 240 and 400 K and at pressures up to 1.0 MPa. Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the data. The ideal-gas heat capacity of HFC-125 from this work differs from spectroscopic calculations by less than 0.2% over the measurement range. The coefficients for virial equations of state were obtained from the acoustic data and hard-core square-well intermolecular potentials. Gas densities that were calculated from the virial equations of state for HCFC-124 and HFC-125 differ from independent density measurements by at most 0.15%, for the ranges of temperature and pressure over which both acoustic and Burnett data exist. The uncertainties in the derived properties for the other five compounds are comparable to those for HCFC-124 and HFC-125.     

Ideal-Gas Heat Capacity Values and Equations for Hydrofluorocarbon (HFC) Refrigerants Based on Speed-of-Sound Measurements

Final values of ideal-gas heat capacity c ⁰ _p derived from speed-of-sound measurements using an acoustic spherical resonator and equations of c ⁰ _p as a simple function of temperature are provided from an overall assessment of speed-of-sound measurements for five hydrofluorocarbon (HFC) refrigerants, difluoromethane (R32), pentafluoroethane (R125), 1,1,1,2-tetrafluoroethane (R134a), 1,1,1-trifluoroethane (R143a), and 1,1-difluoroethane (R152a). Some of the experimental results had systematic errors in comparison with theoretical calculations based on spectroscopic data, which seem to result from the impurity of the sample fluids. The agreement of the experimentally determined and theoretically calculated c ⁰ _p values was confirmed for HFC refrigerants. The uncertainty of c ⁰ _p values calculated from the proposed equations is estimated to be 0.1 or 0.2% corresponding to an ISO uncertainty with a coverage factor of k=1. An erratum for Table I in a previous report by Yokozeki et al. in 1999 is provided as an appendix.     

Determination of the compressibility factorZ(p,T) of three methane-ethane mixtures using the dielectric constant method

The compressibility behavior of three mixtures of the CH₄ C₂ H₆, system has been investigated experimentally by means of the dielectric constant method. Precise ( ± 1 ppm) measurements of the dielectric constant () as a function of the pressure (P) along one isotherm (T) are combined with the first three dielectric virial coefficients (A,B, andC) in order to obtain accurate values of the molar density (p). The compressibility factorZ=P/( _p RT) was obtained from the measured values ofp,P, andT. The coefficientA, is determined from the measurements of as a function ofP, while the higher-order coefficients (B, andC,) are obtained by an expansion technique. We report the measured values ofZ at 295.15 K up to 12 MPa for three mixtures of CH₄-C₂-H₆ containing, respectively. 9.54, 35.3, and 75.4% (molar) of ethane. Their exact composition was determined by weighing during the mixing process. The first three dielectric virial coefficients and the mixed second dielectric virial coefficient for the CH₄,-C₂, H₆ system agree with the calculated or the literature values within the limits of uncertainties. For the mixture containing 90.46% CH₄+C₂H₆, deviations in compressibility are of the order of 0.4% from GERG.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

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.     

A thermodynamic property formulation for ethylene from the freezing line to 450 K at pressures to 260 MPa

A new thermodynamic property formulation based upon a fundamental equation explicit in Helmholtz energy of the form A=A(, T) for ethylene from the freezing line to 450 K at pressures to 260 MPa is presented. A vapor pressure equation, equations for the saturated liquid and vapor densities as functions of temperature, and an equation for the ideal-gas heat capacity are also included. The fundamental equation was selected from a comprehensive function of 100 terms on the basis of a statistical analysis of the quality of the fit. The coefficients of the fundamental equation were determined by a weighted least-squares fit to selected P--T data, saturated liquid and saturated vapor density data to define the phase equilibrium criteria for coexistence, C _v data, velocity of sound data, and second virial coefficients. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (C _v), isobaric heat capacity (C _p), and velocity of sound are included. The fundamental equation reported here may be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ±3 %, and velocity of sound values within ±1 %, except in the region near the critical point. The fundamental equation is not intended for use near the critical point. This formulation is proposed as part of a new international standard for thermodynamic properties of ethylene.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Mean polarizabilities and second and third virial coefficients of the gases C2H4, C2H6, and SF6

Mean polarizabilities ₀(₀, T) as well as second and third virial coefficients B(T) and C(T) of the equation of state of the gases C₂H₄, C₂H₆, and SF₆ have been determined from refractive index measurements with a Michelson interferometer for wavelength ₀=632.99 nm in the overall ranges 250 KT 340 K and 0p3 MPa of temperature T and pressure p. Some negative C(T) values at low temperatures have been obtained. The C(T) data could be fitted satisfactorily to the simple three-parameter function C(T)= a(T–T ₀) exp[ –b(T–T ₀)], with the maximum near the critical temperature T _c. A possible correlation between C(T) and the vapor pressure p _v(T) is discussed.     

Thermodynamic Properties of Sulfur Hexafluoride

We present new vapor phase speed-of-sound data u(P, T), new Burnett density–pressure–temperature data (P, T), and a few vapor pressure measurements for sulfur hexafluoride (SF₆). The speed-of-sound data spanned the temperature range 230 KT460 K and reached maximum pressures that were the lesser of 1.5 MPa or 80% of the vapor pressure of SF₆. The Burnett (P, T) data were obtained on isochores spanning the density range 137 mol·m^–34380 mol·m^–3 and the temperature range 283 KT393 K. (The corresponding pressure range is 0.3 MPaP9.0 MPa.) The u(P, T) data below 1.5 MPa were correlated using a model hard-core, Lennard–Jones intermolecular potential for the second and third virial coefficients and a polynomial for the perfect gas heat capacity. The resulting equation of state has very high accuracy at low densities; it is useful for calibrating mass flow controllers and may be extrapolated to 1000 K. The new u(P, T) data and the new (P, T) data were simultaneously correlated with a virial equation of state containing four terms with the temperature dependences of model square-well potentials. This correlation extends nearly to the critical density and may help resolve contradictions among data sets from the literature.     

Isochoric p–ρ–T and Heat Capacity Cv Measurements for Ternary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), and 1,1,1,2-Tetrafluoroethane (R134a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships and constant volume heat capacity C _v 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––T and from 203 to 345 K for C _v, while for both data types pressures extended to 35 MPa. Measurements of p––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 C _v were carried out on liquid samples for the same two compositions. Published p––T data are in good agreement with this study. For the p––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<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%. For the C _v calorimeter, the uncertainty of the temperature rise is 0.002 K and for the change-of-volume work it is 0.2%; the latter is the principal source of uncertainty. When all components of experimental uncertainty are considered, the expanded relative uncertainty of the heat capacity measurements is estimated to be 0.7%.     

Ideal-Gas Heat Capacities and Virial Coefficients of HFC Refrigerants

Thermodynamic properties of HFC (hydrofluorocarbon) compounds have been extensively studied with worldwide interest as alternative refrigerants. Both quality and quantity in the experimental data far exceed those for the CFC and HCFC refrigerants. These data now provide a great opportunity to examine the validity of theoretical models, and vice versa. Among them, the ideal-gas heat capacity C _p ⁰ and virial coefficients derived from the experimental data are of particular interest, since they are directly related to the intramolecular and intermolecular potentials through the statistical mechanical procedure. There have been some discrepancies reported in the observed and theoretical C _p ⁰ for HFC compounds. We have performed new calculations of C _p ⁰ for several HFCs. The present results are consistent with the selected experimental values. The second (B) and third (C) virial coefficients have been reported for these HFC refrigerants from speed of sound data and Burnett PVT data. Often, a square well-type intermolecular potential is employed to correlate the data. However, the model potential cannot account consistently for both B and C coefficients with the same potential parameters. We have analyzed the data with the Stockmayer potential and obtained self-consistent results for various HFC (R-23, R-32, R-125, R-134a, R-143a, and R-152a) compounds with physically reasonable potential parameters.     

Virial Coefficients from Burnett Measurements for the R116 + CO<Subscript>2</Subscript> System

PVTx measurements for the R116 + CO₂ system for four isotherms (283, 304, 325 and 346 K) were performed. In total, 16 runs were performed in a pressure range from 5100 to 140 kPa. Seven runs along four isotherms in a pressure range from 3400 to 280 kPa were performed for pure hexafluoroethane (R116), and the second and third virial coefficients were derived. The values of the virial coefficients for CO₂ were adopted from our previous measurements. The second and third virial coefficients along with the second and third cross-virial coefficients were derived from the mixture results. The Burnett apparatus was calibrated using helium. The experimental uncertainty in second and third virial coefficients was estimated to be within ±2 cm³· mol^–1 and ±500 cm⁶ ·mol ^–2, respectively.     

Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13)

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, , 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, , 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(, 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%.     

C 1-stably ℒ p shadowable homoclinic classes

Let p be a hyperbolic saddle of diffeomorphism f on closed manifold M and H(p, f) be the homoclinic class associated with it. In this article, we introduce the notion of C ¹-stably ? _p shadowing and prove that if f is C ¹-stably ? _p shadowable on a homoclinic class H(p, f) then, H(p, f) has a dominated splitting. Moreover, we prove that if f is C ¹-stably Lipschitz ? _p shadowable on H(p, f) and H(p, f)-germ of f is expansive then the homoclinic class is hyperbolic.     

Preparation and Properties of Al2O3-doping LiNi1/3Co1/3Mn1/3O2 Cathode Materials

LiNi_1/3Co_1/3-xMn_1/3O₂ doped with Al₂O₃ (x = 0%, 2.5%, 5%, 10%) was synthesized by co-precipitation of Ni, Co, and Mn acetates. The influence of Al₂O₃ doping on structure and electrochemical performances of LiNi_1/3Co_1/3Mn_1/3O₂ was studied using X-ray diffraction (XRD) analysis, scanning electron microscopy, charge/discharge tester, and electrochemical workstation. It was found that the materials achieved the best electrochemical properties when x was 5%. The first discharge capacity was 156.3 mAh · g^?1(0.1 C, 2.0–4.8 V), which was close to the un-doped sample (156.8 mAh · g^?1). After 20 cycles, the capacity retention ratios at the C-ratios of 0.1C, 0.2C, and 0.5 C were 96.1%, 94.9%, and 89.4%, respectively, while the capacity retention ratios of the un-doped samples were only 92.6% (0.1 C), 91.8% (0.2 C), and 88.7% (0.5C). The alternating current impedance shows that the charge transfer in the electrode interface was the easiest when x was 5%.