R. T. Jacobsen

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...

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...

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000 K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity (Cv), isobaric heat capacity (Cp), velocity of sound, the isotherm derivative (∂P/∂ρ)τ, and the isochor derivative (∂P/∂T)ρ. The thermodynamic property tables are based on an equation of state, P=P (ρ,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P‐ρ‐T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P‐ρ‐T data and, simultaneously, to Cv data ...

Thermodynamic Properties of Nitrogen from the Freezing Line to 2000 K at Pressures to 1000 MPa

A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of nitrogen from the freezing line to 2000 K at pressures to 1000 MPa is presented. New independent equations for the vapor pressure and for the saturated liquid and vapor densities as functions of temperature 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‐ρ‐T data, saturated liquid, and saturated vapor density data to define the phase equilibrium criteria for coexistence, and velocity of sound data. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (Cv), isobaric heat capacity (Cp), and velocity of sound are included. Tables of thermodynamic properties of nitrogen are given for liquid and vapor states within the range of...

Thermodynamic properties of argon from the triple point to 1200 K with pressures to 1000 MPa

A new thermodynamic property formulation for argon is presented. The formulation includes a fundamental equation explicit in Helmholtz energy, a vapor pressureequation, and estimating functions for the densities of saturated liquid and vapor states. The coefficients of the fundamental equation and ancillary functions were determined by a weighted least‐squares fit of selected experimental data using a statistical procedure to select the terms for the equation most appropriate for the representation of the data. In determining the coefficients of the fundamental equation, multi‐property fitting methods were used to represent pressure‐density‐temperature data, saturated liquid and saturated vapor densities, and velocity of sound measurements. The fundamental equation is valid for liquid and vapor phases except near the critical point. The equation has been developed to conform to the Maxwell criterion for two‐phase liquid–vapor equilibrium states. Comparisons between the data used to determine the fundamental equation and values calculated from the formulation are given to verify the accuracy of the fundamental equation. The formulation given here may be used to calculate pressures and densities generally with an accuracy of ±0.1%, heat capacities within ±3%, and velocity of sound within ±2% except near the critical point. Tables of thermodynamic properties of argon calculated with the formulation presented here are given for fluid states within the range of validity of the correlation.

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...

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.

18 Multiparameter equations of state

Publisher Summary Accurate thermophysical properties of fluids are needed for the development of reliable mathematical models of energy systems. Although significant improvements are being made in predicting thermodynamic properties of pure fluids and mixtures using theory-based methods, there is a need for more accurate equations of state both for applications in engineering system design and analysis and to satisfy scientific data needs. Current practice in the development of computer programs, property tables, and charts involves the correlation of selected experimental data for a particular fluid or mixture using a model, which is accurate for calculating properties over a wide range of pressures and temperatures. A typical thermodynamic property formulation is based on an equation of state, which allows the correlation and computation of all thermodynamic properties of the fluid, including properties such as entropy that cannot be measured directly. The term “fundamental equation” is often used in the literature to refer to empirical descriptions of one of four fundamental relations: internal energy as a function of volume and entropy, enthalpy as a function of pressure and entropy, Gibbs energy as a function of pressure and temperature, and Helmholtz energy as a function of density and temperature. Modern equations of state for pure fluid properties are usually fundamental equations explicit in the Helmholtz energy as a function of density and temperature.