Eric W. Lemmon

A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa

A new formulation for the thermodynamic properties of nitrogen has been developed. Many new data sets have become available, including high accuracy data from single and dual-sinker apparatuses which improve the accuracy of the representation of the pρT surface of gaseous, liquid, and supercritical nitrogen, including the saturation states. New measurements of the speed of sound from spherical resonators yield accurate information on caloric properties in gaseous and supercritical nitrogen. Isochoric heat capacity and enthalpy data have also been published. Sophisticated procedures for the optimization of the mathematical structure of equations of state and special functional forms for an improved representation of data in the critical region were used. Constraints regarding the structure of the equation ensure reasonable results up to extreme conditions of temperature and pressure. For calibration applications, the new reference equation is supplemented by a simple but also accurate formulation, valid on...

Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa

A thermodynamic property formulation for standard dry air based upon available experimental p–ρ–T, heat capacity, speed of sound, and vapor–liquid equilibrium data is presented. This formulation is valid for liquid, vapor, and supercritical air at temperatures from the solidification point on the bubble-point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of reliable experimental data for air above 873 K and 70 MPa, air properties were predicted from nitrogen data in this region. These values were included in the determination of the formulation to extend the range of validity. Experimental shock tube measurements on air give an indication of the extrapolation behavior of the equation of state up to temperatures and pressures of 5000 K and 28 GPa. The available measurements of thermodynamic properties of air are summarized and analyzed. Separate ancillary equations for the calculation of dew and bubble-point pressures and densities of air are presented. In the range from the solidif...

A Formulation for the Static Permittivity of Water and Steam at Temperatures from 238 K to 873 K at Pressures up to 1200 MPa, Including Derivatives and Debye–Hückel Coefficients

A new formulation is presented of the static relative permittivity or dielectric constant of water and steam, including supercooled and supercritical states. The range is from 238 K to 873 K, at pressures up to 1200 MPa. The formulation is based on the ITS-90 temperature scale. It correlates a selected set of data from a recently published collection of all experimental data. The set includes new data in the liquid water and the steam regions that have not been part of earlier correlations. The physical basis for the formulation is the so-called g-factor in the form proposed by Harris and Alder. An empirical 12-parameter form for the g-factor as a function of the independent variables temperature and density is used. For the conversion of experimental pressures to densities, the newest formulation of the equation of state of water on the ITS-90, prepared by Wagner and Pruss, has been used. All experimental data are compared with the formulation. The reliability of the new formulation is assessed in all su...

Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and Orthohydrogen

If the potential for a boom in the global hydrogen economy is realized, there will be an increase in the need for accurate hydrogen thermodynamic property standards. Based on current and anticipated needs, new fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen were developed to replace the existing property models. To accurately predict thermophysical properties near the critical region and in liquid states, the quantum law of corresponding states was applied to improve the normal hydrogen and orthohydrogen formulations in the absence of available experimental data. All three equations of state have the same maximum pressure of 2000MPa and upper temperature limit of 1000K. Uncertainty estimates in this paper can be considered to be estimates of a combined expanded uncertainty with a coverage factor of 2 for primary data sets. The uncertainty in density is 0.04% in the region between 250 and 450K and at pressures up to 300MPa. The uncertainties of vapor pressures and satura...

A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125)

A widely used form of an equation of state explicit in Helmholtz energy has been modified with new terms to eliminate certain undesirable characteristics in the two phase region. Modern multiparameter equations of state exhibit behavior in the two phase that is inconsistent with the physical behavior of fluids. The new functional form overcomes this dilemma and results in equations of state for pure fluids that are more fundamentally consistent. With the addition of certain nonlinear fitting constraints, the new equation now achieves proper phase stability, i.e., only one solution exists for phase equilibrium at a given state. New fitting techniques have been implemented to ensure proper extrapolation of the equation at low temperatures, in the vapor phase at low densities, and at very high temperatures and pressures. A formulation is presented for the thermodynamic properties of refrigerant 125 (pentafluoroethane, CHF2–CF3) using the new terms and fitting techniques. The equation of state is valid for te...

Correlation for the Second Virial Coefficient of Water

A new correlation has been developed to represent the second virial coefficient of water (H2O) as a function of temperature. The formulation was fitted to experimental data, both for the second virial coefficient itself and for a quantity related to its first temperature derivative, at temperatures between approximately 310 and 1170 K. The high-temperature extrapolation behavior was guided by results calculated from a high-quality intermolecular pair potential. The new correlation agrees well with the experimental data deemed to be reliable, and at high temperatures is a significant improvement over the best previous formulation.

A generalized model for the thermodynamic properties of mixtures

A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.

Critical Properties and Vapor Pressure Equation for Alkanes CnH2n+2: Normal Alkanes With n⩽36 and Isomers for n=4 Through n=9

A correlation for estimating the vapor pressure of normal alkanes from methane through n-hexatriacontane and isomers of butane to nonane is reported. This work extends the correlation for normal alkanes (CnH2n+2), with n⩽20, reported by Ambrose, to both normal alkanes with n⩽36 and their isomers with n⩽9. This vapor pressure equation was based on the Wagner equation and is similar to that used by Ambrose. Literature vapor pressure measurements have been reviewed. Tables are given that list the type of apparatus, measurement range and precision, and chemical purity. These criteria were initially used to select measurements for inclusion in the regression analyses to determine the coefficients of the correlation. Vapor pressures estimated from the correlation were compared with all vapor pressure (p1+g) measurements reviewed in this work. At pressures greater than 1 kPa, the vapor pressure equation presented here has the following accuracies: 0.0001⋅p1+g for methane, 0.001⋅p1+g for ethane, propane, and n-bu...

Equations of State for Mixtures of R-32, R-125, R-134a, R-143a, and R-152a

Mixture models explicit in Helmholtz energy have been developed to calculate the thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, R143a, and R-152a. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real fluid) contribution, and the contribution from mixing. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures, including dew and bubble point properties, within the experimental uncertainties of the available measured properties. It incorporates the most accurate equations of state available for each pure fluid. The estimated uncertainties of calculated properties are 0.1% in density and 0.5% in heat capacities and in the speed of sound. Calculated bubble point pressures have typical uncertainties of 0.5%.

A Reference Quality Equation of State for Nitrogen

A new formulation describing the thermodynamic properties of nitrogen has been developed. New data sets which have been used to improve the representation of the p–ρ–T surface of gaseous, liquid and supercritical nitrogen, including the saturated states are now available. New measurements on the speed of sound from spherical resonators have been used to improve the accuracy of caloric properties in gaseous and supercritical nitrogen. State-of-the-art algorithms for the optimization of the mathematical structure of the equation and special functional forms for an improved description of the critical region were used to represent even the most accurate data within their experimental uncertainty. The uncertainty in density of the new reference equation of state ranges from ±0.01% between 270 and 350 K at pressures less than 12MPa, within ±0.02% over all other temperatures less than 550 K and pressures less than 12 MPa, and up to a maximum of ±0.6% at the highest pressures. The equation is valid from the triple point to temperatures of 1000 K and pressures up to 2200 MPa. The new formulation yields a reasonable extrapolation up to the limits of chemical stability of nitrogen as indicated by comparison to experimental shock tube data. Constraints regarding the structure of the equation ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 25 GPa. For typical calibration applications, the new reference equation is supplemented by a simple but also highly accurate formulation, valid only for supercritical nitrogen between 270 and 350 K at pressures up to 30 MPa.