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 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.     

Thermophysical Properties of Nitrogen Trifluoride, Ethylene Oxide, and Trimethyl Gallium from Speed-of-Sound Measurements

The speed of sound was measured in gaseous nitrogen trifluoride, ethylene oxide, and trimethyl gallium using a highly precise acoustic resonance technique. The measurements span the temperature range 200 to 425 K and reach pressures up to the lesser of 1500 kPa or 80% of the sample vapor pressure. The speed-of-sound measurements have a relative standard uncertainty of less than 0.01%. The data were analyzed to obtain the constant-pressure ideal-gas heat capacity C ⁰ _p as a function of temperature with a relative standard uncertainty of 0.1%. The values of C ⁰ _p are in agreement with those determined from spectro- scopic data. 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 the sound-speed data to within ±0.02%, 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 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.     

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.     

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.     

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%.     

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 Rational Fundamental Equation of State for Pentafluoroethane with Theoretical and Experimental Bases

A fundamental equation of state for pentafluoroethane was established on the basis of not only assessment of the experimental data but also by introducing parameters for virial coefficients having a theoretical background in statistical thermodynamics. The equation of state has a range of validity for temperatures from the triple point up to 500 K and pressures up to 70 MPa. The estimated uncertainties of the equation are 0.1% for the vapor pressure, 0.15% in density for the saturated-liquid phase, 0.5% in density for the saturated-vapor phase, 0.1% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.5% in density for the supercritical region, 0.01% in speed of sound for the gaseous phase, 0.9% in speed of sound for the liquid phase, 0.5% in isobaric specific heat for the liquid phase, and 1.2% in isochoric specific heat for the liquid phase. The derived specific heats in the gaseous phase are close to the values from the virial equation of state with the second and third virial coefficients derived from intermolecular potential models and precise speed-of-sound measurements.     

Viscosity and Speed of Sound of Gaseous Nitrous Oxide and Nitrogen Trifluoride Measured with a Greenspan Viscometer

The viscosity and speed of sound of gaseous nitrous oxide and nitrogen trifluoride were measured using a Greenspan acoustic viscometer. The data span the temperature range 225–375 K and extend up to 3.4 MPa. The average relative uncertainty of the viscosity is 0.68% for N₂O and 1.02% for NF₃. The largest relative uncertainties were 3.09 and 1.08%, respectively. These occurred at the highest densities (1702 mol · m^-3 for N₂O and 2770 mol · m^-3 for NF₃). The major contributor to these uncertainties was the uncertainty of the thermal conductivity. The speeds of sound measured up to 3.4 MPa are fitted by a virial equation of state that predicts gas densities within the uncertainties of the equations of states available in the literature. Accurate measurements of the speed of sound in both N₂O and NF₃ have been previously reported up to 1.5 MPa. The current measurements agree with these values with maximum relative standard deviations of 0.025% for N₂O and 0.04% for NF₃.     

Vapor-Phase Helmholtz Equation for HFC-227ea from Speed-of-Sound Measurements

This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of 900 cm³ at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.     

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.     

Practical determination of gas densities from the speed of sound using square-well potentials

The relationships between the first three density virial coefficients (B, C, and D) and the first four acoustic virial coefficients ( _a , _a , _a and _a are rederived and a published error relatingD to _a is corrected. We observe that even it thenth and higher-density virial coefficients of a hypothetical gas are identifically zero, thenth and higher acoustic virial coefficients are not zero; they depend on the temperature derivatives of the 1st through (n-1)th density virial coefficients. Thus, two density virial coefficients may suffice for a fit to acoustic data with a cubic pressure dependence. These results are exploited by extending the pressure range of fits to preciously published speed-of-sound data without either introducing additional parameters or degrading the fits. We deduce gas densities from fits to speed-of-sound data with acoustic virial coefficients having the temperature dependencies calculated from square-well potentials. The estimated densities differ from independent measurements be a few tenths of a percent in an important range of conditions, These estimates require nop p T data whatsoever.     

Acoustic determination of ideal-gas heat capacity and second virial coefficients of some refrigerants between 250 and 420 K

An apparatus for speed-of-sound measurements with a spherical resonator was adapted for temperatures up to 42(I K. This included new microphones with a special wiring, a pressure indicator which can be thermostatted to 420 K, and some installations to avoid temperature gradients. Calibration of the radius of the resonator with argon was extended to higher temperatures. Speed-of-sound measurements up to 420 K and 0.5 MPa were done onl,l-dilluoroethane (R152a). 1.l,l-trilluoroethane (R 143a ),l,l,l-chlorodifluoroethane (R 142b ), l,1,1,2-tetralluoroethane (R134a), and 2.2.2-trifluoroethanol. The ideal-gas heat capacities coincide with the statistical mechanical values, except for R134a, where our values as well as recent literature data are below the values calculated from spectroscopy. The reduced second virial coefficients can be interpreted in terms of the dipole moment and the angle between dipole moment and molecular axis. For the associated substance trifluoroethanol values of the third virial coefficient are given, which are appreciably negative at low temperatures.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994 Boulder, Colorado, U.S.A.     

CO2 + R23 Binary System: Virial Coefficients Derived from Burnett Measurements

Burnett PVT measurements were performed on trifluoromethane (R23) and mixtures of R23 with carbon dioxide (CO₂). The Burnett apparatus was calibrated using helium. Fourteen expansions were performed for 5 isotherms and in a pressure range from 130 kPa to 6 MPa for R23. Second and third virial coefficients were derived from the collected data and compared with literature values; good agreement was found between them. PVTx measurements for the binary CO₂+R23 system were carried out for five isotherms (303, 313, 323, 333, and 343 K). In all, 18 runs were performed in a pressure range from 150 kPa to 5.9 MPa. The composition of the mixtures was measured with a gas chromatograph after it had been calibrated using samples prepared gravimetrically. Second and third virial coefficients for the system were derived, together with the second and third cross virial coefficients, from experimental results using virial coefficients for CO₂ from previous measurements (for the same sample as used in the present study). Samples for composition measurements were collected during the first Burnett expansion. Second virial coefficients for the system showed positive deviations from ideal values, while the third virials were negative. No previous experimental results were found for the PVTx properties of this binary system.     

Joint Russian and Bulgarian Academies of Sciences Database of Intermolecular Potentials and Diffusion Coefficients for Components of the CVD Processes in Microelectronics

The goal of the database (DB) EPIDIF-JRB is to promote the modeling of gas-phase transport processes in CVD technologies in microelectronics. The transport properties (molecular diffusion coefficients, viscosity, and thermal conductivity) of pure gases and gas mixtures in the temperature range 250 to 2000K and at a pressure <0.1MPa are calculated using (1) the Chapman–Enskog method in binary collision approximation and (2) the three-parameter Lennard–Jones (m–6) intermolecular potentials (IP) with 8<m<100 for interactions of atoms and quasi-spherical molecules, and (3) the four-parameter m–6–3 Stockmayer IP for dipole molecules. In addition to the IP parameters a _ii , a _jj , and a _ij , the DB also supplies their variance–covariance matrix. For heavy globular molecules [such as CF₄, SiH₄, Si(CH₃)₄, and WF₆], the influence of the vibrational excitation on their effective size is considered. In this case, the isotropic Lennard–Jones (m–6) IP with temperature-dependent parameters was defined. At present, the DB EPIDIF-JRB contains 40 species of importance to Si gas-phase epitaxy processes and IP parameters for 820 pair interactions. It can be used to calculate the viscosity of pure gases and gas mixtures with any k components (k<11), and their binary diffusion coefficients, and to estimate their uncertainty as well.     

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.     

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.     

Second and third interaction virial coefficients of the (methane+propane) system determined from the speed of sound

The speed of sound has been measured in the binary gaseous mixture (0.85CH₄+0.15C₃H₈) along seven isotherms at temperatures between 225 and 375 K and at pressures up to 1.4 M Pa. From the measurements, second and third acoustic virial coefficients of the mixture were obtained. These results were analyzed together with values of the second and third acoustic virial coefficients of the two pure components to obtain a set of model intermolecular potential-energy functions for the methane-propane system. Nonpairwise additivity of the intermolecular forces was included in this analysis. Ordinary second and third interaction virial coefficients calculated from the model are reported, as are the second and third virial coefficients of the pure components. Gas densities calculated by means of these virial coefficients for the mixture (0.9298CH₄+0.0702C₃H₈) were found to agree with experimental values at temperatures between 280 and 330 K to within 0.02% at pressures up to 3 MPa and to within 0.08% at 4MPa.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.