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

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

Second virial coefficients in closed form for a Kihara (2m-m)-potential

In the literature second virial coefficients are calculated by series expansions or by direct numerical integration. For thermodynamic quantities such as thermodynamic functions, analytical expressions are wanted. This paper gives closed formulas for the second virial coefficient for a convex-body Kihara potential of the type U()= U ₀[( ₀/)_2m -2( ₀/) ^m ], where m can be a rational number n>3. Furthermore, a number of related problems such as dielectric virial coefficients and Buckingham-Pople integrals are reduced to the same Laplace-transformation-type technique.     

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.     

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.     

Measurements of PVTx Properties for Binary Mixtures of HFC-32 (CH2F2) and HFC-134a (CH2FCF3)

An experimental study of pressure–volume–temperature–composition (PVTx) properties for binary mixtures of HFC-32 and HFC-134a was conducted in the range of temperatures from 243 to 473 K, pressures up to 16.7 MPa, densities from 9.5 to 1065 kg·m^–3, and compositions from 0.39 to 0.89 mol fraction of HFC-32, with uncertainties of 8 mK, 1.7 kPa, 0.04%, and 0.001 mol fraction, respectively. A constant-volume method was used for the present measurements either with a spherical vessel approximately 270 cm³ in its inner volume or with a cylindrical vessel approximately 138cm³ in its inner volume. The present data were compared with the Piao equation of state for this substance.     

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

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.     

Benzene-methanol association. The excess molar enthalpy and second virial cross coefficients of (benzene+methanol)(g) and (cyclohexane+methanol)(g)

New measurements of the excess molar enthalpyH _m ¹ of (yCH₃OH+(1−y)C₆H₆)(g) and (yCH₃OH+(1−y)C₆H₁₂)(g) measured at standard atmospheric pressure over the temperature range 363.2 to 433.2 K are reported. these measurements supplement earlier measurements made over the range 454.2 to 523.0 K at pressures up to 4.0 MPa. The nonideality of the methanol vapor is described using a quasi chemical model model in which only dimer and tetramer association equilibria are considered. The values ofH _m ¹ for the (methanol+cyclohexane)(g) mixture were found to agree well with values calculated using the association model. For (methanol+benzene)(g) the experimental values ofH _m ¹ were found to be approximately 20% smaller than values calculated from the model and this was attributed to weak association between the unlike molecules. A quasi-chemical model used to describe the association between the unlike molecules yielded a value of the equilibrium constantK ₁₂(298.15 K)=0.22 MPa⁻¹, and a value for the enthalpy of the methanol-benzene association of ΔH ₁₂=−13 kJ·mol⁻¹. Second virial crosscoefficientsB ₁₂ for methanol-cyclohexane and methanol-benzene have been derived from theH _m ¹ measurements.     

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.     

Optimized parameters and exponents of Mie (n,m) intermolecular potential energy function based on the shape of molecules

Through the use of the second virial coefficient data, optimized parameters and exponents of the Mie (n,m) potential energy function are derived for a number of symmetric groups of molecules. In the optimizations performed, parameters of the potential function are varied for each molecule, but the exponents of the potential function are taken as functions of the shape of the groups of molecules considered. It is concluded that the attractive exponent, m = 7, is shared by all the symmetric groups considered. The repulsive exponent, n, is varied according to the shape of the molecules. Also, in this report, newly calculated parameters of the Lennard-Jones (12,6) and Mie (14,7) potential energy functions for 33 different symmetric and nonsymmetric molecules are reported. Results indicate that, generally, the Mie (14,7) pair-potential energy function is a better fit for the second virial coefficient data than the Lennard-Jones (12,6) function.     

Determination of the thermo-optic coefficient dn/dT of ytterbium doped ceramics (Sc2O3, Y2O3, Lu2O3, YAG), crystals (YAG, CaF2) and neodymium doped phosphate glass at cryogenic temperature

In this paper, we report the measurements of the thermal expansion coefficient and the thermo-optic coefficient dn/dT for the ytterbium doped cubic sesquioxides (Sc₂O₃, Y₂O₃, Lu₂O₃) at cryogenic temperature. These materials appear to have very interesting properties for setting up high average power laser chains useful for plasma physics and for inertial fusion energy drivers. Measurements have also been done on YAG ceramic and crystal, CaF₂ crystal, and neodymium phosphate glass (Hoya, LHG-8).     

Effects of Nd and B contents on the thermal stability of nanocomposite (Nd,Zr)2Fe14B/α-Fe magnets

The effects of Nd and B contents on the microstructure and thermal stability of nanocomposite (Nd,Zr)₂Fe₁₄B/α-Fe magnets have been investigated. It is shown that for Nd_xFe_93−xZr₁B₆ (x = 9–11) alloys, the volume fraction of Nd₂Fe₁₄B increases with increasing Nd content, and the sample with x = 10 exhibits the optimal microstructure and thermal stability. Though the room-temperature _iH_c of Nd₁₁Fe₈₂Zr₁B₆ sample is the highest, it decreases more rapidly than that of Nd₁₀Fe₈₃Zr₁B₆ as temperature increases, indicating the deterioration of the temperature coefficient β. For Nd₁₀Fe_89−yZr₁B_y (y = 5–8) alloys, the remanence and the temperature coefficient α deteriorate with increasing B content. The coercivity and the temperature coefficient β first improve with increasing B content, reaching the optimal values at y = 7, then deteriorate with further increasing B. Coarse grains and the Fe₃B phase are observed in the Nd₁₀Fe₈₁Zr₁B₈ alloy.