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.     

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 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.     

Measurements of PρT properties,vapor pressures,saturated densities,and critical parameters for R 1234ze(Z) and R 245fa

Pressure-density-temperature (PρT) properties, vapor pressures, and saturated liquid and vapor densities for refrigerants R 1234ze(Z) (cis-1,3,3,3-tetrafluoroprop-1-ene; CF₃CHCHF) and R 245fa (1,1,1,3,3-pentafluoropropane; C₃H₃F₅) were measured with two types of isochoric methods. Pressure was measured with a digital quartz pressure transducer. Temperature was measured with 25 Ω standard platinum resistance thermometer on the ITS-90 temperature scale. Density was calculated from the mass of sample and the inner volume of pressure vessel. By using the present vapor pressure data, new vapor pressure correlations for R 1234ze(Z) and R 245fa have been formulated. In addition, the critical temperature T_c, critical density ρ_c, and critical pressure P_c were directly determined on the basis of direct observation of the meniscus disappearance.     

An equation of state for 1,1-difluroethane (HFC 152a)

An equation of state for 1,1-difluoroethane (HFC 152a, CH₃CHF₂) has been developed on the basis of reliable experimental data including PVT, liquid C_p, and saturated-liquid-density data measured by our group. It is a non-dimensionalized virial equation whose functional form is the same as that originally developed for 1,1,1,2-tetrafluoroethane (HFC 134a) in our group. The effective range is for pressures up to 15 MPa, temperatures from 230 to 450 K, and densities to 1000 kg m⁻³. The equation represents reliable PVT measurements within ± 1% in pressure for the superheated vapour and supercritical fluid, while within ±0.5% in density for the compressed liquid. In addition, it should be noted that the equation represents the other essential thermodynamic properties including vapour pressures, saturated-liquid/ vapour densities, isobaric/isochoric specific heats and sound velocity in both the liquid and gaseous phase of HFC 152a.     

Equation of State for Nonpolar Fluids: Prediction from Boiling Point Constants

A new corresponding states correlation for the second virial coefficient of nonpolar fluids in terms of the boiling point constants is presented. The scaling constants are the normal boiling point temperature, T _bp, which is used to form a dimensionless temperature and the liquid density at the normal boiling point, _bp, which is used to form a dimensionless second virial coefficient. The procedure has been examined for a large number of substances including noble gases, diatomic molecules, saturated hydrocarbons up to C₈, and a number of aliphatic, aromatic, and cyclic hydrocarbons. The resulting correlation has been applied to predict the equation of state of fluids over the range from the vapor-pressure curve to the freezing curve at various temperatures from the triple point up to the nonanalytical critical region. The equation of state has been applied to reproduce the liquid density of a great number of compounds both in the saturation and compressed states, at temperatures up to 2000 K and pressures up to 10000 bar, within an accuracy of a few percent. In particular we have shown that knowledge of two readily measurable constants is sufficient to determine the pvT surface of pure normal fluids having a variety of structural complexities.     

Thermodynamic properties of two gaseous halogenated ethers from speed-of-sound measurements: Difluoromethoxy-difluoromethane and 2-difluoromethoxy-1,1,1-trifluoroethane

We present measurements of the speed of sound in gaseous difluoromethoxy-difluoromethane (CHF₂-O-CHF₂) and 2-difluoromethoxy-1,1,1-trifluoroethane (CF₃-CH₂-O-CHF₂). These measurements were performed in an all-metal apparatus between 255 and 384 K. We have obtained ideal-gas heat capacities and second acoustic virial coefficients from analysis of these measurements. Two methods of correlating the second acoustic virial coefficients, a square well model of the intermolecular interaction and a function due to Pitzer and Curl, are presented.     

Thermodynamic properties of HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) at saturation conditions

The thermodynamic properties of HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) were determined. The critical point was ascertained by visual observation of the meniscus disappearance within an optical cell. The critical temperature, critical density, and critical pressure were determined to be 403.37 ± 0.03 K, 515.3 ± 5.0 kg m⁻³, and 2766.4 ± 4.5 kPa, respectively. Vapor pressures were also measured at temperatures ranging from 323 K (50 °C) to the critical temperature, and were correlated using the Wagner-type equation. The acentric factor and normal boiling point were determined to be 0.4053 and 280.58 K (7.43 °C), respectively, using the vapor pressure correlation. Based on the critical parameters and the acentric factor, saturated vapor densities and liquid densities were estimated using the Peng–Robinson equation and the Hankinson–Thomson equation, respectively. The heat of vaporization was also calculated from the Clausius–Clapeyron equation.     

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 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 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 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.     

Saturated Liquid Densities for 33 Binary Refrigerant Mixtures Based on the ISM Equation of State

In this work, the ISM equation of state based on statistical-mechanical perturbation theory has been extended to liquid refrigerant mixtures by using correlations of Boushehri and Mason. Three temperature-dependent parameters are needed to use the equation of state: the second virial coefficient, B₂(T), an effective van der Waals covolume, b(T), and a scaling factor, α (T). The second virial coefficients are calculated from a correlation based on the heat of vaporization, ΔH_vap, and the liquid density at the normal boiling point, ρ_nb. α(T) and b(T) can also be calculated from second virial coefficients by a scaling rule. The theory has considerable predictive power, since it permits the construction of the PVT surface from the heat of vaporization and the liquid density at the normal boiling point. The equation of state was tested on 33 liquid mixtures from 12 refrigerants. The results indicate that the liquid densities can be predicted to at most 2.8% over a wide range of temperatures, 170–369 K.     

The critical constants of long-chain normal paraffins

Because of the recent availability of the critical constants of normal alkanes up to octadecane, some modifications in the estimation procedures for the critical constants have become necessary. It has been shown that the equation of Ambrose for the critical temperature of normal alkanes leads to the result that as n , the limiting value for the critical temperature is equal to the limiting value for the normal boiling point and the limiting value for the critical pressure is 1 atm. Currently, the CH₂ increment for the critical volume is considered constant. The recent data of Teja have shown that the CH₂ increment increases indefinitely in a homologous series until the critical volume reaches its limiting value. This has made the current procedure for estimating the critical volume obsolete. Taking into account the new measurements of Teja, we have now developed new equations for estimating the critical constants. The limiting values for an infinitely long alkyl chain for T _b, T _c, P _c, and V _c have been found to be 1021 K, 1021 K, 1.01325 bar, and 18618 cm³ · mol^–1, respectively. These new concepts have been applied to the estimation of various properties other than the critical constants.Nomenclature M Molar mass, kg·mol ^–1 - V _c Critical volume, cm³·mol^–1 - V ₁ Saturated liquid volume, cm³·mol^–1 - P _c Critical Pressure, bar - T _c Critical temperature, K - T _b Normal boiling point, K - T _B Boyle temperature, K - T _A Temperature at which the third virial coefficient is zero, K - V _c Limiting value of critical volume = 18,618 cm³ · mol^–1 - P _c Limiting value of critical pressure=1.01325 bar - T _c Limiting value of critical temperature = 1021 K - T _b Limiting value of normal boiling point = 1021 K - P _b Pressure at the normal boiling point, 1 atm - Z _c Critical compressibility factor - Z _c Limiting value for the critical compressibility factor = 0.22222 - R Gas constant, 83.1448×10^–6m³ · bar · K^–1 · mol^–1 - Acentric factor - X (T _c–T _b)/T _c - X ₁ (T _c–T)/T _c - X ₂ 1–(T _B/T)^5/4 - X ₃ 1–(T _A/T)^5/2 - Y P _c/RT _c - Surface tension, mN · m^–1 - B Second virial coefficient, cm³ · mol^–1 - B Limiting value for the second virial coefficient = –30,463 cm³ · mol^–1 - C Third virial coefficient, cm⁶ · mol^–2 - C _b Third virial coefficient at the normal boiling point, cm⁶ · mol^–2 - C _c Third virial coefficient at the critical temperature, cm⁶ · mol^–2 - C _B Third virial coefficient at the Boyle temperature, cm⁶ · mol^–2 - H _vb Enthalpy of vaporization at the normal boiling point, kJ · mol^–1 - n Number of carbon atoms in a homologous series - p Platt number, number of C-C-C-C structural elements - a, b, c, d, e, etc Constants associated with the specific equation - T _c ^* , T _b ^* , P _c ^* , V _c ^* , etc. Dimensionless variables     

Vapor pressure determination for solid and liquid La<Subscript>2</Subscript>S<Subscript>3</Subscript> using boiling points

A high-temperature technique was developed for vapor pressure determination of solid and liquid γ-La₂S₃ (we called it the boiling point technique). Melting temperatures and total vapor pressures were measured for incongruently vaporizing γ-La₂S₃ at 1853–2210 K and 0.3–3.0 atm pressures. Having compared the slopes of the log p(S₂) versus 1/T plots measured by various techniques, we recommend the equation log p(S₂) [atm] = (6.31 ± 0.15) ? (12720±310)T ^?1 for T = 1021–2013 K as the most reliable for practical use.     

Calculation of second virial coefficients and gaseous viscosities of the refrigerants HFC-32 (CH2 F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2)

The second virial coefficients of refrigerants HFC-32 (CH₂F₂), HFC-23 (CHF₃), and HCFC-22 (CHC1F₂) have been correlated on the bisis of site site model potential and have been compared with experimental results. The molecular interactions consisted of repulsion dispersion and electrostatic parts. From the site site potentials adjusted to the experimental second virial coefficients, spherically averaged potentials have been determined and a subsequent calculation of gaseous viscosity has been carried out. Agreement between measured and calculated values of second virial coellicients and gaseous viscosity is satisfactory. Calculated values of second virial coefficients and gaseous viscosity beyond available experimental data, therefore. can be assumed as a reliable extrapolation to lower and higher temperatures.     

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.     

Ideal-gas specific heat and second virial coefficient of HFC-125 based on sound-velocity measurements

The sound velocity in gaseous pentafluoroethane (HFC-125, CF₃CHF₂) has been measured by means of a spherical acoustic resonator, Seventy-two sound-velocity values were measured with an uncertainty of ±0.01% at temperatures from 273 to 343 K and pressures from 101 to 250 kPa. The ideal-gas specific heats and the second acoustic-virial coefficients have been determined on the basis of the Sound-velocity measurements. The second virial coefficients calculated from the present sound-velocity measurements agree with literature values which were determined fromPVT measurements by means of a Burnett method.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24 1994, Boulder, Colorado, U.S.A.     

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

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

A Thermodynamic Equation of State for Pentafluoroethane (R-125)

We developed a fundamental equation of state for pentafluoroethane (R-125, CHF₂CF₃) which is represented in terms of a non-dimensional Helmholtz free energy. The equation has been established on the basis of selected measurements of the pressure-density-temperature relation, speed of sound, heat capacities, and saturation properties. Linear and non-linear regression analysis was employed to determine the functional form and the numerical parameters. The equation represents all the thermodynamic properties of R-125 in the liquid and gaseous phases for temperatures between the triple point and 470 K, and pressures up to 35 MPa. The uncertainties are estimated to be about ±0.05% or 0.1 kPa for the vapor pressure, ± 0.05 % for the liquid and vapor densities, about ± 1 % for the isobaric and isochoric heat capacities in the liquid, and ± 0.5 % or ± 0.02 % for the speed of sound in the liquid and vapor, respectively.