A Rational Helmholtz Fundamental Equation of State for Difluoromethane with an Intermolecular Potential Background

A new fundamental thermodynamic equation of state for difluoromethane was developed by considering the intermolecular potential behavior for improving the reliability in the gaseous phase. Reliable second and third virial coefficients are introduced in accordance with the principle of a unified relation of the intermolecular potential energy and the fundamental equation of state. The fundamental equation of state is able to provide reliable thermodynamic properties even at low temperatures or in the region near saturation where precise and accurate experimental data are not available. The estimated uncertainties of calculated properties from the equation of state are 0.07% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.35% in pressure for the supercritical region, 0.07% in vapor pressure, 0.2% in saturated-liquid density, 0.7% in saturated-vapor density, 0.01% in speed of sound for the gaseous phase, 0.7% in speed of sound for the liquid phase, and 0.6% in isochoric specific heat for the liquid phase. The equation is valid for temperatures from the triple point to 450 K and pressures up to 72 MPa.     

A Rigorous Thermodynamic Property Model for Fluid-Phase 1,1-Difluoroethane (R-152a)

A new thermodynamic property model for the Helmholtz free energy with rational third virial coefficients for fluid-phase 1,1-difluoroethane (R-152a) was developed. The model was validated by existing experimental data for temperatures from the triple point to 450 K and pressures up to 60 MPa. Reasonable behavior of the second and third virial coefficients was confirmed from intermolecular potential models. The estimated uncertainties are 0.1% in density for the gaseous and liquid phases, 0.4% in density for the supercritical region, 0.05% in speed of sound for the gaseous phase, 2% in speed of sound for the liquid phase, and 1% in specific heat capacities for the liquid phase. From the reasonable behavior of the ideal curves and the third virial coefficients, the model can be assumed reliable in representing the thermodynamic properties not only at states with available experimental data but also at states for which no experimental data are available.     

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.     

Equation of state for gaseous propane determined from the speed of sound

An equation of state in the form of a truncated virial series has been developed for gaseous propane. Second, third, and fourth virial coefficients and their temperature derivatives were calculated from model two- and three-body intermolecular potentials, the parameters of which were fitted to experimental values of the speed of sound in the gas; no other data were used. The resulting model predicts accurately thermal and caloric properties of the gas over a wide range of temperatures at densities up to about one-quarter of the critical. The second and third (but not the fourth) virial coefficients are in very close agreement with directly measured values. To facilitate rapid calculation of thermodynamic properties, a look-up table for the virial coefficients and their temperature derivatives is provided together with a recommended means of interpolation.     

Equations of State for the Ozone-Safe Refrigerants R32 and R125

Equations of state for gaseous and liquid difluoromethane (R32) and pentafluoroethane (R125) were developed. The coefficients of the equations were determined using experimental density data and heat capacities c _v and c _s. The equations satisfy Maxwell's rule. The equations describe the thermodynamic properties of R32 and R125 at temperatures from 140 to 433 K and from 178 to 480 K, respectively, and at pressures up to 70 MPa within the experimental uncertainties. In particular, the root-mean-square deviations of the calculated values of density from the most reliable experimental data are equal to 0.10% for R32 and 0.12% for R125.     

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.     

Predicting the virial coefficients and thermodynamic properties of a multicomponent mixture with application to the ternary mixture of CH2F2+CF3CHF2+CF3CH2F

A model for estimating second and third virial coefficients, which has been used successfully to represent the behavior of pure gases and binary mixtures, was applied to a ternary mixture. An estimate for the ternary third virial coefficient.C ₁₂₃, was added to the model. Three experimentally determined binary interaction parameters were also used. The model has been applied to the ternary mixture CH₂F₂+CF₃CHF₂+CF₃CH₂F (R32+R125+R134a). The results are useful for calculating gas-phase densities, thermodynamic properties, and fugacities for phase equilibrium calculations. The use of such models leads to a considerable economy of effort in the case of multicomponent mixtures. Examples of the thermodynamic properties are given for the equimolar ternary mixture in the range from the dew-point temperature to 400 K at pressures of 0.5, 1, and 2 MPa. Calculated densities and speeds of sound are compared with new experimental values for a near-equimolar composition.     

An equation of state for oxygen vapour—second and third virial coefficients

Based on a selected p, ρ, T data set of oxygen for the range from low to moderate densities an equation of state for oxygen vapour has been established. From this evaluation, new values for the second and third virial coefficients were derived. In addition, correlation equations for the temperature dependence of these virial coefficients are given. Estimations for the fourth virial coefficient were compared with the one predicted by the Lennard-Jones potential.     

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.     

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.     

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.     

Sound-velocity measurements for HFC-134a and HFC-152a with a spherical resonator

A spherical acoustic resonator was developed for measuring sound velocities in the gaseous phase and ideal-gas specific heats for new refrigerants. The radius of the spherical resonator, being about 5 cm, was determined by measuring sound velocities in gaseous argon at temperatures from 273 to 348 K and pressures up to 240 kPa. The measurements of 23 sound velocities in gaseous HFC-134a (1,1,1,2-tetrafluoroethane) at temperatures of 273 and 298 K and pressures from 10 to 250 kPa agree well with the measurements of Goodwin and Moldover. In addition, 92 sound velocities in gaseous HFC-152a (1,1-difluoroethane) with an accuracy of ±0.01% were measured at temperatures from 273 to 348 K and pressures up to 250 kPa. The ideal-gas specific heats as well as the second acoustic virial coefficients have been obtained for both these important alternative refrigerants. The second virial coefficients for HFC-152a derived from the present sound velocity measurements agree extremely well with the reported second virial coefficient values obtained with a Burnett apparatus.Paper dedicated to Professor Joseph Kestin.     

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 investigation of metastable states of binary mixtures in the neighborhood of spinodal using the integral equation method

A generating functional is suggested for the purpose of producing a set of integral equations for radial distribution functions of binary mixtures in the neighborhood of stability limit, i.e., spinodal. This set of integral equations is used to derive an equation of state from which it follows that the terms which are non-analytical by the total density of mixture start to play an important part in the region of thermodynamic variables where the third virial coefficient must be included.     

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.     

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.     

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.     

Mixture equations of state: Composition dependence

This paper discusses theoretical models for the composition dependence of equations of state and compares the quality of predictions against experimental thermodynamic property data. The mean density approximation (MDA) and the van der Waals one-fluid (VDW1) model are compared with hybrid mixing rules (HMR), in which rigorous composition dependence is used for the second and third virial coefficients and the conformai solution model is used for equation-of-state density terms beyond the third virial term. It is found that when values of unity are used for all binary and three-body unlike interaction parameters, calculated densities for methane-normal heptane mixtures have average absolute deviations of 3.54% for MDA, 4.04% for VDW1, and 2.59% for HMR. When vapor-liquid equilibrium calculations were performed for the methane-normal heptane system, average absolute deviations of calculatedK values from experimental values were 16.7% for methane and 36.4% for normal heptane using HMR, whereas when conformal solution model (CSM) mixing rules were used, the results were 34.8% for methane and 66.7% for normal heptane. When the binary interaction parameter for the characterization of interaction energies is determined, it is found to be less sensitive to state conditions in the case of HMR than either MDA or VDW1. These preliminary results suggest the potential of mixture equation-of-state methods which utilize rigorous composition dependence for the lower-order virial coefficients.Paper presented at the Second U.S.-Japan Joint Seminar on Thermophysical Properties, June 23, 1988, Gaithersburg, Maryland, U.S.A.     

Equations of state for the thermodynamic properties of R32 (difluoromethane) and R125 (pentafluoroethane)

Thermodynamic properties of difluoromethane (R32) and pentafluoroethane (R125) are expressed in terms of 32-term modified Benedict-Webb-Rubin (MBWR) equations of state. For each refrigerant, coefficients are reported for the MBWR equation and for ancillary equations used to fit the ideal-gas heat capacity and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined with a multiproperty fit that used the following types of experimental data: PVT: isochoric, isobaric, and saturated-liquid heal capacities; second virial coefficients; and properties at coexistence. The respective equations of stale accurately represent experimental data from 160 to 393 K and pressures to 35 MPa for R32 and from 174 to 448 K and pressures to 68 MPa for R125 with the exception of the critical regions. Both equations give reasonable results upon extrapolation to 500 K and 60 MPa. Comparisons between predicted and experimental values are presented.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado. U.S.A.