Richard B. Stewart

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.

Thermodynamic Properties of Oxygen from the Triple Point to 300 K with Pressures to 80 MPa

A joint project by the authors has resulted in two new thermodynamic property formulations for oxygen. The fundamental equation explicit in Helmholtz energy by Schmidt and Wagner has been used for the calculation of the property tables presented here, and for comparisons of calculated properties to the experimental data. The formulation of Stewart and Jacobsen is used in this paper in comparisons of properties calculated by the two formulations. These comparisons provide the basis for independent assessment of the accuracy of the available data and calculated properties. The procedures used in determining the formulations by Wagner and Schmidt, and by Stewart and Jacobsen were published earlier. The fundamental equation is valid for thermodynamic properties of oxygen from the freezing line to 300 K at pressures to 80 MPa. A separate vapor pressure equation and equations for the saturated liquid and saturated vapor densities and the ideal gas heat capacity are included. Functions for calculating internal e...

Thermodynamic Properties of Ethylene from the Freezing Line to 450 K at Pressures to 260 MPa

A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of ethylene from the freezing line to 450 K at pressures to 260 MPa is presented. Independent equations for the vapor pressure for the saturated liquid and vapor densities as functions of temperature, and 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‐ρ‐T data, saturated liquid, and saturated vapor density data to define the phase equilibrium criteria for coexistence, Cv data, velocity of sound data, and second virial coefficient 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 o...

Thermodynamic Properties of Neon for Temperatures from the Triple Point to 700 K at Pressures to 700 MPa

The published experimental data on the thermodynamic properties of neon have been used as the basis for a new thermodynamic property formulation for neon. The new correlation uses a fundamental equation (equation of state) explicit in Helmholtz energy, which provides for the calculation of derived thermodynamic properties by differentiation. The fundamental equation for neon is a subset of a larger comprehensive function which has also been used in developing thermodynamic property formulations for other fluids of cryogenic interest including oxygen, nitrogen, argon, and ethylene. In addition, new equations for the vapor pressure, saturated liquid density, and saturated vapor density are presented. The formulation presented here may be used to calculate pressure, density, temperature, enthalpy, entropy, internal energy, isochoric and isobaric heat capacities, and velocity of sound for neon. Summary comparisons of properties calculated with the new formulation for neon with selected experimental data are included to verify the accuracy of the fundamental equation for calculation of thermodynamic properties.

A New Fundamental Equation for Thermodynamic Property Correlations

A new fundamental equation for correlation of thermodynamic property data for fluids is presented. The fundamental equation (equation of state) is explicit in Helmholtz energy and is readily adapted to system analysis applications. All thermodynamic properties are derived by differentiation of the fundamental equation. A comprehensive function containing up to 100 terms provides the basis for the correlation. The fundamental equation for a specific fluid is a subset of this comprehensive function. The individual terms of the comprehensive function may be easily changed by varying exponents of the functions of the independent variables. Functions for the calculation of derivative properties are given, and the incorporation of calorimetric information via ideal gas heat capacity equations is discussed. Applications to fluids of cryogenic interest include oxygen, nitrogen, argon, ethylene and neon. Coefficients for calculation of thermodynamic properties of these fluids taken from formulations published elsewhere are 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(ρ, 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-ρ-T data, saturated liquid and saturated vapor density data to define the phase equilibrium criteria for coexistence, Cv 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 (Cv), isobaric heat capacity (Cp), 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.

Thermodynamic Properties of Ethylene at Saturation

In the development of an equation of state for a fluid, accurate values of vapor pressure, saturated vapor density and saturated liquid density are used to define the phase equilibrium conditions for temperatures between the triple point and critical point. The vapor pressure equation and equations for the density of the saturated liquid and the saturated vapor as functions of temperature include the critical region. The equations for the saturation states are given here with comparisons to data. These equations were determined using a stepwise regression procedure1 for the selection of an optimum group of terms from the various comprehensive functions.

An interim thermodynamic property formulation for air

Abstract A new interim formulation for the thermodynamic properties of air which includes estimated properties for the liquid is reported. The range of the formulation is for temperatures from 85 K to 873 K at pressures to 70 MPa. Separate equations for the calculation of bubble point and dew point properties are included. The need for further measurements of liquid air properties and of properties on and near the dew point curve and bubble point curve to provide the basis for a new accurate correlation is summarized. Vapor properties are believed to be sufficiently accurate for design and analysis work, except near the dew point curve, but no substantiated claim for the accuracy of the calculated liquid properties can be made.