Density Virial Coefficients Research Articles

Helium virial coefficients—a comparison between new highly accurate theoretical and experimental data

Critical tests of the accuracy of ab initio theoretical values of the helium virial coefficients have been made based on experiments with a new dielectric-constant gas thermometry (DCGT) setup established at PTB. As the main starting point, most accurate experimental results for the thermodynamic temperature and the dielectric polarizability of 3He and 4He have been deduced recently. This paper now concentrates on the results for the two- and three-particle interaction described by the second and third density virial coefficients of helium. A comparison between experimental DCGT results and new highly accurate theoretical ab initio results shows an impressive agreement. The experimental uncertainties have been estimated via Monte-Carlo simulations and are comparable to the uncertainty of the latest theory.

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 p0 as a function of temperature with a relative standard uncertainty of 0.1%. For N2O, the values of p0 agree within 0.1% with those determined from spectroscopic data. For NO, the values of p0 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.

Second caloric virial coefficients for real gases and combined spherical symmetric potential for simple molecular interactions

The second heat capacity virial coefficients for argon, carbon dioxide, water, n-pentane, n-octane, and 1-propanol were determined from precise isochoric heat capacity measurements from our previous publications in the temperature ranges: argon, between 148 K and 201 K; carbon dioxide, 348 K and 453 K; water, 578 K and 1024 K; n-alkanes, 473 K and 693 K; and 1-propanol, 520 K and 690 K. The results were compared with values calculated from recommended density virial coefficients equations and and improved combined spherical symmetric potential function. Values of the second temperature derivatives T 2d 2 B/d T 2 derived from C V,m measurements for argon, n-pentane, and n-octane were compared with values reported by other authors from C p,m measurements. A new method was developed to calculate second density virial coefficients from caloric (heat capacity) measurements. This method provided the conversion of heat capacity to density second virial coefficients. This paper also describes a new improved combined spherical symmetric model intermolecular potential and a second density virial coefficient equation. The new potential function consists of a repulsive barrier and an attractive square well. Over large distances, it is proportional to r −6. The parameters of the interaction potential for noble gases (Ar, Ne, Kr, Xe), carbon dioxide, water, n-alkanes ( n-C 5H 12 and n-C 8H 18), ammonia, and 1-propanol were determined from experimental second density virial coefficients. This potential describes second density virial coefficients B( T) within their experimental uncertainties over a wide temperature range.

Determination of a vapour phase Helmholtz equation for 1,1,1-trifluoroethane (HFC-143a) from speed of sound measurements

The speed of sound in gaseous 1,1,1-trifluoroethane has been obtained at temperatures between (270 and 370) K from measurements of the resonance frequency of the radial modes of a spherical resonator. Ideal gas heat capacities and acoustic virial coefficients have been calculated from the results. The acoustic data have been used to determine density virial coefficients with a hard-core square-well intermolecular potential equation of state. A Helmholtz energy equation of state is proposed, whose parameters are directly fitted to the present speed of sound data and uses the acoustically determined temperature dependence of the perfect gas heat capacity. The Helmholtz equation so obtained compares favourably with other conventional methods and provides a high accuracy equation specific for the vapour phase of the fluid. The performance of the equation, in terms of the accuracy of the thermodynamic properties derived from it, has been determined by comparison of predicted densities with available experimental data. The equation of state shows very good extrapolation behaviour beyond the range of temperatures and pressures of the experimental data to which it was fitted.

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 C0p as a function of temperature with a relative standard uncertainty of 0.1%. The values of C0p 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.

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.

A direct reduction procedure for gas density determination of R143a from acoustic measurements

Measurements of the speed of sound in the vapour phase of 1,1,1-trifluoroethane (HFC-143a) are presented. The measurements were performed in a stainless-steel spherical resonator of ∼900 cm 3 at temperatures (T) between 270 K and 350 K and at pressures (p) up to 500 kPa. The experimental apparatus is described. Ideal-gas heat capacities and acoustic virial coefficients are directly deduced from the data. The results of these measurements are utilised to develop a virial equation of state with high accuracy, which represents the (p, p, T) surface of the vapour phase in the same temperature and pressure ranges, with density p. The temperature dependences of the three density virial coefficients are obtained directly from speed of sound data regression with virial expansions truncated after the third or fourth coefficient. The deduced vapour densities are compared with those obtained from a dedicated equation of state in the Schmidt--Wagner form. A validation is also presented against experimental density data.

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.

Thermophysical properties of difluoromethane (HFC-32)

The research work on thermophysical properties of difluoromethane (HFC-32) is summarized. Experimental data of critical parameters, vapor pressure, PVT, speed of sound, ideal-gas heat capacity, surface tension, viscosity, thermal conductivity are given and corresponding correlations are developed. The cross equation of state, the correlations of saturated liquid density and second virial coefficient for HFC-32 are also developed.

An automated apparatus for measuring sound speeds in hazardous gases

Our laboratory has developed an automated apparatus for measuring the sound speed in hazardous gases such as those used in processing semiconductors. The sound speed is deduced from measurements of the acoustic resonance frequencies of a gas-filled, cylindrical cavity. After the cavity is calibrated with argon, the uncertainty in the sound speed is less than 0.01%. The u(P,T) data span the temperature and pressure ranges 200–475 K and 100–1500 kPa. From the measured sound speeds we derive the ideal gas heat capacities from the zero-pressure intercepts with a typical uncertainty of only 0.1%. The virial equation of state is also deduced from u(P,T) providing the temperature-dependent density virial coefficients. In comparisons with Burnett measurements, we find that the densities calculated with the derived virial equation of state have uncertainties of less than 0.1% in density. Some recent measurements in SF6, CF6, and C2F6 will be used to illustrate the systems capabilities. Work in progress on BCl3 will also be discussed.

Density and Virial Coefficients of Gaseous Butane from 265 to 450 K at Pressures to 3.3 MPa

The Burnett-isochoric (B-I) method has been used to measure gas densities and virial coefficients for butane from 265 to 450 K (IPTS, 1990; Preston-Thomas, 1990). Two independent B-I runs were performed but both with a base isotherm of 450 K, which is well above the critical temperature of 425 K. Significant physical adsorption of butane molecules onto the highly-polished, stainless steel cell walls was found below 375 K in agreement with conclusions reached by Ewing and associates in comparing their sonic-velocity-based density virial coefficients with those from the P−V−T literature. Our data below 375 K were then corrected for adsorption errors by previously published procedures developed by our laboratory for highly polar gases. Using statistical weighting of our two B-I runs, recommended density second virial coefficients B(T) are reported from 265 to 450 K whereas third virial coefficients C(T) are reported only from 325 to 450 K as values below 325 K are too uncertain due to the vapor pressure dropping under 300 kPa. However, then the virial equation of state truncated after B(T) is sufficient to represent the gas densities. At the lower temperatures of this investigation, our B(T) values lie between those from sonic velocities and the more negative values from the P−V−T literature, which are uncorrected for adsorption errors; we are closer to the values from sonic velocities and about 1/4 of the way between the two sets. At the higher temperatures, we agree very closely with the better P−V−T measurements whereas the sonic-velocity-based values become increasingly more negative.

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.

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 (β a ,γ a ,δ a ande a are rederived and a published error relatingD toδ 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.

Vapor Pressures, Gas-Phase PVT Properties, and Second Virial Coefficients for 1,1,1-Trifluoroethane

The PVT properties of 1,1,1-trifluoroethane (R-143a) in the gas phase have been measured by a Burnett apparatus in the range of temperatures from 320 to 380 K and at pressures up to 6 MPa. The vapor pressures in the range of temperatures from 295 to 342 K have also been measured, and a vapor-pressure correlation has been developed. The critical pressure was determined to be (3.776 {+-} 0.005) MPa on the basis of the present measurements. The second virial coefficients have been determined along seven isotherms, and a truncated virial equation of state has also been developed to represent the temperature dependence of the second virial coefficients and the present Burnett PVT measurements. The experimental uncertainties of temperature, pressure, density, and second virial coefficient throughout the present study were estimated to be no more than {+-} 8 mK, {+-} 0.8 kPa, {+-} 0.12%, and {+-} 5%, respectively. The purity of the R-143a sample used was better than 99.95 mol %.

Temperature Dependence of the Second Dielectric Virial Coefficients of Rare Gases

Second dielectric virial coefficients Bε (T) of the rare gases Ne, Ar, Kr, and Xe are calculated in a broad range of temperature using accurate HFD-type interatomic interaction potentials and available information on the trace of the pair polarizability Δα. It is shown that the experimentally determined temperature-variation of Bε(T) cannot be reproduced by existing theories. However, it is observed that the reduced dimensionless form of Bε(T) follows a remarkably regular pattern, strongly resembling the sign-inverted temperature variation of the second density virial coefficient Bϱ(T) with the same Boyle-temperature.

Dispersion of mean molecular dipole polarizability and second density virial coefficients of 1,3‐butadiene

AbstractFor the first time, measurements of the gas‐phase refractive index of 1,3‐butadiene are performed in the ranges of temperature 295 K < T < 365 K, pressure 0 < p < 1.7 · 105 Pa, and wavelength 325 nm < λ < 633 nm, respectively. Precise values of the dispersion of the mean dipole polarizability α0(λ, T) with an uncertainty of Δα0/α0 < 0.25% are obtained. Moreover, second density virial coefficients B(T) are estimated with error bounds of 10cm3mol−1 from the interferometric measurements.

Direct Measurements of the Dielectric Virial Coefficients of 4He between 3 K and 18 K

The second and third dielectric virial coefficients of 4He have been measured by the symmetrical gas-expansion technique of Buckingham, Cole and Sutter for six isotherms between 3,00 K and 17,68 K. The effects of helium adsorption are important, and are considered in detail. No temperature dependence of the second coefficient is seen at a level of δb=±0,008 cm3 mol-1, and average values of the second and third coefficients are b = 0,006 (10) cm3 mol-1 and c = -5 (4) cm6 mol-2, respectively. The uncertainty for b is relatively large because it has a systematic dependence on c: reanalysis of all the existing data shows that a more probable value of the third coefficient is c = -2 (1) cm6 mol-2, which when combined with our data gives b (3 K - 18 K) = -0,001 (4) cm-3 mol-1. The very small value suggests that theoretical calculations of the excess polarizability of the helium diatom need to be reconsidered. The small value and the small uncertainty of b indicate that future work to improve experimental values of the second density virial coefficient of 4He for this temperature range may without ambiguity make use of the methods of dielectric constant gas thermometry.

Thermophysical properties of gaseous refrigerants from speed-of-sound measurements. II. Results for 1,1-dichloro-1-fluoroethane (CCl2FCH3)

The speed of sound in gaseous 1,1-dichloro-1-fluoroethane (CCl2FCH3, commonly known as R141b) has been measured between 260 and 315 K. Perfect-gas heat capacities and second acoustic virial coefficients have been calculated from the results. The second acoustic virial coefficients are used to estimate the density virial coefficients B(T) and an effective square-well potential. Our estimates of B(T) are consistent with B(T) deduced from high-quality p(Vm, T) results. We provided estimates of the vibrational relaxation time for R141b.