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.     

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 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.     

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.     

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.     

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.     

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.     

An Equation of State for 1,1,1-Trifluoroethane (R-143a)

A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P––T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.     

Thermodynamic Properties of 1,1,1,2,3,3,3-Heptafluoropropane

A vapor pressure equation has been developed for 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) based on previous measurements from 202 to 375K, from which the boiling point of HFC-227ea was determined. Based on the previous pressure–volume–temperature (PVT) measurements in the gaseous phase for HFC-227ea, virial coefficients, saturated vapor densities, and the enthalpy of vaporization for HFC-227ea were also determined. The vapor pressure equation and the virial equation of state for HFC-227ea were compared with the available data. Based on the previous measurements of speed of sound in the gaseous phase for HFC-227ea, the ideal-gas heat capacity at constant pressure and the second acoustic virial coefficient of HFC-227ea were calculated. A correlation of the second virial coefficient for HFC-227ea was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with results based on PVT measurements. A van der Waals-type surface tension correlation for HFC-227ea was proposed, based on our previous experimental data by the differential capillary rise method from 243 to 340K.     

An interim analytic equation of state for sulfurhexafluoride

An interim analytic equation of state for Sulfurhexafluoride is given in the form of a reduced Helmholtz energy function. It represents the thermodynamic properties over the temperature range 222.38 to 525 K for pressures up to 55 MPa. The data selected for determining the linear coefficients of the equation are given, which includes some values predicted using the principle of corresponding states. The method used for the multiproperty fitting is given and, in particular, the functions used for fitting isobaric heat capacities as primary data. Comparisons with values predicted by the equation of state are given for saturation properties, second virial coefficients, densities, and isobaric and isochoric heat capacities. The accuracy of the representation of the equation of state is discussed and, also, the problems arising from inconsistencies between the different data sets. The interim status of this equation of state is due to these inconsistencies.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

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.     

A Thermodynamic Property Model for Fluid Phase Hydrogen Sulfide

A Helmholtz free energy equation of state for the fluid phase of hydrogen sulfide has been developed as a function of reduced temperature and density with 23 terms on the basis of selected measurements of pressure–density–temperature (P, , T), isobaric heat capacity, and saturation properties. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from the triple point temperature (187.67 K) to 760 K at pressures up to 170 MPa. The uncertainty in density calculation of the present equation of state is 0.7% in the liquid phase, and that in pressure calculation is 0.3% in the vapor phase. The uncertainty in saturated vapor pressure calculation is 0.2%, and that in isobaric heat capacity calculation is 1% in the liquid phase. The behavior of the isobaric heat capacity, isochoric heat capacity, speed of sound, and Joule–Thomson coefficients calculated by the present model shows physically reasonable behavior and those of the calculated ideal curves also illustrate the capability of extending the range of validity. Graphical and statistical comparisons between experimental data and the available thermodynamic models are also discussed.     

Dielectric-Constant Gas Thermometry and the Relation to the Virial Coefficients

At PTB new dielectric-constant gas thermometry (DCGT) measurements were performed at the temperature of the triple point of water. As discussed recently in an accompanying paper, the main goal was the determination of the Boltzmann constant \(k\) as a contribution to the international efforts directed to a new definition of the base unit kelvin via fixing the value of  \(k\) . Besides the linear term in the series expansion used for fitting the results of measurements of DCGT isotherms that reveals \(k\) , in this paper the higher-order terms are analyzed. For retrieving highly accurate virial coefficients of helium from the data obtained at gas pressures up to 7 MPa, an extended DCGT working equation is developed. Applying this equation, information is deduced on the viral coefficients up to the fourth density virial coefficient. Finally, comparisons with the latest ab initio calculations for the second and third density virial coefficients as well as the second dielectric virial coefficient are performed.     

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%.     

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.     

Importance of Third Virial Coefficients for Representing the Gaseous Phase Based on Measuring PVT-Properties of 1,1,1-Trifluoroethane (R143a)

For a reliable derivation of the thermodynamic properties in the gaseous phase from thermodynamic equations of state, it has been pointed out that third virial coefficients significantly affect calculations of heat capacities. Among existing equations of state including internationally accepted equations, there is a large discrepancy, sometimes more than 5%, in calculated heat-capacity values near saturation. Two different approaches have been conducted in addressing this problem. One is for providing the third virial coefficient from intermolecular-potential models based on speed-of-sound measurements with a spherical resonator, and another is for confirming the effect of the third virial coefficient on density values near saturation by measuring the density precisely with a magnetic suspension densimeter. This report is focused on the latter case, i.e., precise measurements of density for 1,1,1-trifluoroethane, R143a, near saturation and some important evidence for the necessity of considering third virial coefficients for calculating reliable thermodynamic properties in the gaseous phase.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

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.     

A thermodynamic property formulation for cyclohexane

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

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.