PVT Measurements on tetrafluoroethane (R134a) along the vapor-liquid equilibrium boundary between 288 and 373 K and in the liquid state from the triple point to 265 K

For the investigations of the gas-liquid phase equilibria, a new apparatus has been developed capable of simultaneously determining the pressure and the liquid and vapor densities using Archimedes' principle. The relative measurement uncertainties of the liquid and vapor densities of R134a (purity, 99.999%) at 313 K are 2×10^–4 and 7×10^–4, respectively (95% confidence level). For the measurements in the liquid region along nine quasi-isochores at pressures up to 5 MPa, an isochoric apparatus was used. The relative measurement uncertainty ofpv/(RT) is less than 1×10^–3. In addition to the investigation of the (p, v, T) properties, the temperature and pressure at the triple point and the vapor pressure between the triple point and 265 K were measured. On the basis of these data, a vapor pressure correlation has been developed that reproduces the measured vapor pressures within the uncertainty of measurement. The results of our measurements are compared with a fundamental equation for R134a, which is based on the measurements of other research groups.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A Small-Volume Apparatus for the Measurement of Phase Equilibria

An apparatus has been designed and constructed for the measurement of vapor-liquid equilibrium properties. The main components of the apparatus consist of an equilibrium cell and a vapor circulation pump. The cell and all of the system valves are housed inside a temperature controlled, insulated aluminum block. The temperature range of the apparatus is 260 K to 380 K to pressures of 6 MPa. The uncertainty of the temperature measurement is 0.03 K, and the uncertainty in the pressure measurement is 9.8 × 10⁻⁴ MPa. An automated data acquisition system is used to measure temperature and pressure at equilibrium. The apparatus has been performance tested by measuring the vapor pressures of propane, butane, and a standard mixture of propane + butane.     

A nonlinear regression analysis for estimating low-temperature vapor pressures and enthalpies of vaporization applied to refrigerants

A new method is presented to extrapolate experimental vapor pressures down to the triple Point. The method involves a nonlinear regression analysis based on the Clausius Clapeyron equation and a simple relation for the enthalpy of vaporization Triple-point pressures and vapor pressures up to 0.1 0.2 MPa are estimated for R125, R32, R143a, R134a, R152a, R123, R124, and ammonia; they generally agree with available experimental data within their uncertainty, Equations for the enthalpy of vaporization which describe this property fairly well at low temperatures are obtained as a byproduct.     

Vapor pressures of new fluorocarbons

The vapor pressures of four fluorocarbons have been measured at the following temperature ranges: R123 (2,2-dichloro-l,l,l-trifluoroethane), 273–457 K; R123a (1,2-dichloro-1,1,2-trifluoroethane), 303–458 K; R134a (1,1,1,2-tetrafluoroethane), 253–373 K; and R132b (l,2-dichloro-l,l-difluoroethane), 273–398 K. Determinations of the vapor pressure were carried out by a constant-volume apparatus with an uncertainty of less than 1.0%. The vapor pressures of R123 and R123a are very similar to those of R11 over the whole experimental temperature range, but the vapor pressures of R134a and R132b differ somewhat from those of R12 and R113, respectively, as the temperature increases. The numerical vapor pressure data can be fitted by an empirical equation using the Chebyshev polynomial with a mean deviation of less than 0.3 %.     

Subatmospheric vapor pressures evaluated from internal-energy measurements

Vapor pressures were evaluated from measured internal-energy changes in the vapor+liquid two-phase region, ΔU ⁽²⁾. The method employed a thermodynamic relationship between the derivative quantity (ϖU ⁽²⁾/ϖV) _T and the vapor pressure (p _σ) and its temperature derivative (ϖp/ϖT)_σ. This method was applied at temperatures between the triple point and the normal boiling point of three substances: 1,1,1,2-tetrafluoroethane (R134a), pentafluoroethane (R125), and difluoromethane (R32). Agreement with experimentally measured vapor pressures near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately ±0.04 kPa (±0.04%). The method was applied to R134a to test the thermodynamic consistency of a publishedp-p-T equation of state with an equation forp _σ for this substance. It was also applied to evaluate publishedp _σ data which are in disagreement by more than their claimed uncertainty.     

Thermal conductivity andPVT measurements of pentafluoroethane (refrigerant HFC-125)

By means of the transient and steady-state coaxial cylinder methods, the thermal conductivity of pentafluoroethane was investigated at temperatures from 187 to 419 K and pressures from atmospheric to 6.0 MPa. The estimated uncertainty of the measured results is ±(2–3)%. The operation of the experimental apparatus was validated by measuring the thermal conductivity of R22 and R12. Determinations of the vapor pressure andPVT properties were carried out by a constant-volume apparatus for the temperature range 263 to 443 K, pressures up to 6 MPa, and densities from 36 to 516 kg m^–3. The uncertainties in temperature, pressure, and density are less than ±10 mK, ±0.08%, and ±0.1%, respectively.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Thermodynamic properties of nickel

This work reviews and discusses the data and information on the thermodynamic properties of nickel available through May 1984. These properties include heat capacity, enthalpy, enthalpy of transition and melting, vapor pressure, and enthalpy of vaporization. The recommended values for heat capacity cover the temperature range from 1 to 3200 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 3200 K.     

Thermodynamic properties of titanium

This work reviews and discusses the data and information on the thermodynamic properties of titanium available through May 1984. These properties include heat capacity, enthalpy, enthalpy of transition and melting, vapor pressure, and enthalpy of vaporization. The recommended values for heat capacity cover the temperature range from 1 to 3800 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 3800 K.     

Precise Measurements of the Vapor-Liquid Equilibria (VLE) of HFC-32/134a Mixtures Using a New Apparatus

A new apparatus for precise measurements of the vapor-liquid equilibria of mixtures by the circulation method has been developed. This apparatus has two special components: a high-stability temperature control system and a helium pressurization system. The temperature in the liquid bath surrounding the sample cell is kept constant within ±0.5mK. The helium pressurization system increases the pressure of the sampled mixture when measuring the compositions at low temperatures by gas chromatography. With these components, the uncertainty in measuring the vapor-liquid equilibria has been reduced. Using this apparatus, the vapor-liquid equilibria of HFC-32/134a mixtures were measured in a temperature range of 263.15 to 293.15K. These results are in good agreement with the calculated results from REFPROP (Ver. 6.01) with a relative pressure difference of about 2%.     

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.     

Thermodynamic properties of aluminum

This work reviews and discusses the data on the thermodynamic properties of aluminum available through May 1984. However, two papers dated 1985 which are useful to this work are also included. These properties include heat capacity, enthalpy, enthalpy of transition and melting, vapor pressure, and enthalpy of vaporization. The recommended values for heat capacity cover the temperature range from 0.1 to 2800 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 2800 K.     

The vapor pressure of 1,1,1,2-tetrafluoroethane (R134a) and chlorodifluoromethane (R22)

We measured the vapor pressure of chlorodifluoromethane (commonly known as R22) at temperatures between 217.1 and 248.5 K and of 1,1,1,2-tetrafluoroethane (commonly known as R134a) in the temperature range 214.4 to 264.7 K using a comparative ebulliometer. For 1,1,1,2-tetrafluoroethane at pressures between 220.8 and 1017.7kPa (corresponding to temperatures in the range 265.6 to 313.2K), additional measurements were made with a Burnett apparatus. We have combined our results for 1,1,1,2-tetrafluoroethane with those already published from this laboratory at higher pressures to obtain a smoothing equation for the vapor pressure from 215 K to the critical temperature. For chlorodifluoromethane our results have been combined with certain published results to provide an equation for the vapor pressure at temperatures from 217 K to the critical temperature.     

Quasi-isochoricpπT measurements and second virial coefficient ofn-heptane

Quasi-isochoricpT measurements onn-heptane vapor were carried out in the low density region using an improved apparatus that was originally proposed by Opel and Schaffenger (Wiss. Z. Univ. Rostock N18:871, 1969). The experimental results extend over the temperature range between 350 and 600 K and the density range between 11.5 and 52.2 mol · m^–3. Above 473 K a small but significant influence of decomposition was found. Accordingly, a correction scheme assuming a trace of decomposition products was applied to these data. Second virial coefficients were derived with an assumed maximum uncertainty of ±3%.. The results are compared with others in the literature and used to develop an improved correlation function for the temperature dependence ofB(T).     

New Equation for Vapor Pressures of Difluoromethane (HFC-32)

Critically evaluated experimental vapor-pressure data sets supplemented with calculated data for low-temperature region were used in the development of vapor-pressure equations. The optimum number of terms, coefficients, and exponents of the Wagner-type equation were derived by means of the Setzmann–Wagner program OPTIM based on the combination of the stepwise regression analysis and evolutionary optimization method. Equations were checked by the reduced enthalpy of vaporization criterion derived from the Clausius–Clapeyron equation and specific volume of ideal gas. An equation developed using 261 experimental data points and low-temperature data calculated by Lüddecke and Magee gives an RMS deviation of 0.102%; a second equation based on the same experimental data and low-temperature data calculated by Tillner-Roth gives an RMS deviation of 0.101% from experimental points. The triple-point pressure extrapolated to the measured temperature T _tp = 136.34 K is discussed. Comparisons with vapor pressure equations by Outcalt and McLinden, Duarte-Garza and Magee. and Kubota et al. are also given.     

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.     

Isochoricp-ϱ-T measurements on Difluoromethane (R32) from 142 to 396 K and pentafluoroethane (R125) from 178 to 398 K at pressures to 35 MPa

Thep--T-relationships were measured for difluoromethane (R32) and pentafluoroethane (R125) by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 142 to 396 K for R32 and from 178 to 398 K for R125, while pressures were up to 35 MPa. Measurements were conducted on compressed liquid samples. Determinations of vapor pressures were made for each substance. I have used vapor pressure data and thep--T data to estimate saturated liquid densities by extrapolating each isochore to the vapor pressure, and determining the temperature and density at the intersection. Publishedp--T data are in good agreement with this study. For thep T apparatus. the uncertainty of the temperature is ±0.03 K. and for pressure it is ±0.01%, atp > 3 MPa and ±0.05% atp < 3 MPa. The principal source of uncertainty is the cell volume (28.5193 cm³ at 0 K and 0 M Pa), which has a standard uncertainty of ±0.003 cm³. When all components of experimental uncertainty are considered. the expanded uncertainty (at the two-sigma level) of the density measurements is estimated to be 0.05%.     

Isochoric p–ρ–T and Heat Capacity Cv Measurements for Ternary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), and 1,1,1,2-Tetrafluoroethane (R134a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships and constant volume heat capacity C _v were measured for ternary refrigerant mixtures by isochoric methods with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K for p––T and from 203 to 345 K for C _v, while for both data types pressures extended to 35 MPa. Measurements of p––T were carried out on compressed gas and liquid samples with the following mole fraction compositions: 0.3337 R32+0.3333 R125+0.3330 R134a and 0.3808 R32+0.1798 R125+0.4394 R134a. Measurements of C _v were carried out on liquid samples for the same two compositions. Published p––T data are in good agreement with this study. For the p––T apparatus, the uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%. For the C _v calorimeter, the uncertainty of the temperature rise is 0.002 K and for the change-of-volume work it is 0.2%; the latter is the principal source of uncertainty. When all components of experimental uncertainty are considered, the expanded relative uncertainty of the heat capacity measurements is estimated to be 0.7%.     

A practical vapor pressure equation for helium-3 from 0.01 K to the critical point

A saturation vapor pressure equation, p(T), is an essential component in the ³He state equation currently under development. The state equation is valid over the range 0.01-20 K with pressures from 0 to the melting pressure or 15 MPa. The vapor pressure equation consequently must be valid from 0.01 K to the critical temperature. This paper surveys available ³He critical temperature and pressure measurements, leading to new recommended critical values of 3.3157 K and 114603.91 Pa. The ITS-90 temperature scale is defined by the ³He vapor pressure from 0.65 to 3.2 K. A new vapor pressure equation is developed for the interval from the upper end of the T₉₀ scale to this newly defined critical point, employing a mathematical form in which the second derivative d²p/dT² diverges in agreement with scaling laws at the critical point. Below 0.65 K, an empirical vapor pressure expression is adopted, consistent with a theoretical expression valid in the limit T → 0. These two new components are fitted to be piecewise continuous with the EPT-76 p(T) scale rather than the ITS-90 T(p) scale between 0.65 and 3.2 K. Probable deviations between this vapor pressure scale and PLTS-2000 melting pressure-temperature scale are recognized, but not reconciled.     

Calorific properties of liquid copper

The enthalpy of liquid copper up to a temperature of 2000 K is investigated by the drop method with an error from 1 to 1.5%. The measurement results are compared with the literature data. It is shown that the spectral emissivity of copper melt depends on temperature. The obtained data on enthalpy are approximated by an equation. The true heat capacity of liquid copperc _p = 36.33 J/(mol K), the melting heat ΔH = 13.59 kJ/mol, and the melting entropy ΔS = 10.0 J/(mol K) of copper are calculated.     

Measurement of the enthalpy and specific heat of a Be2C-graphite-UC2 reactor fuel material to 1980 K

The enthalpy and specific heat of a Be₂C-Graphite-UC₂ composite nuclear fuel material have been measured over the temperature range 298–1980 K using both differential scanning calorimetry and liquid argon vaporization calorimetry. The fuel material measured was developed at Sandia National Laboratories for use in pulsed test reactors. The material is a hot-pressed composite consisting of 40 vol% Be₂C, 49.5 vol% graphite, 3.5 vol% UC₂, and 7.0 vol% void. The specific heat was measured with the differential scanning calorimeter over the temperature range 298–950 K, while the enthalpy was measured over the range 1185–1980 K with the liquid argon vaporization calorimeter. The normal spectral emittance at a wavelength of 6.5×10^–5 cm was also measured over the experimental temperature range. The combined experimental enthalpy data were fit using a spline routine and differentiated to give the specific heat. Comparison of the measured specific heat of the composite to the specific heat calculated by summing the contributions of the individual components indicates that the specific heat of the Be₂C component differs significantly from literature values and is approximately 0.56 cal · g^–1 · K ^–1 (2.3×10³J · kg^–1 · K ^–1) for temperatures above 1000 K.