A thermodynamic property formulation for 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. A new vapor pressure equation and equations for the saturated liquid and vapor densities as functions of temperature are also included. The techniques used for development of the fundamental equation are those reported in a companion paper for ethylene. 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 also included in that paper. The property formulation using the fundamental equation reported here may generally be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ± 2%, and velocity of sound values within ±2%. The fundamental equation is not intended for use near the critical point.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

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.     

Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa

A thermodynamic property formulation for standard dry air based upon experimental P––T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.     

A thermodynamic property formulation for cyclohexane

A formulation for the thermodynamic properties of cyclohexane is presented. The equation is valid for single-phase and saturation states from the melting line to 700 K at pressures up to 80 MPa. It includes a fundamental equation explicit in reduced Helmholtz energy with independent variables of reduced density and temperature. The functional form and coefficients of the ancillary equations were determined by weighted linear regression analyses of evaluated experimental data. An adaptive regression algorithm was used to determine the final equation. To ensure correct thermodynamic behavior of the Helmholtz energy surface the coefficients of the fundamental equation were determined with multiproperty fitting, Pressure-density-temperature (P-p-T) and isobaric heat capacity (C _p -P-T) data were used to develop the fundamental equation, SaturationP-p-T values, calculated from the estimating functions, were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Separate functions were used for the vapor pressure, saturated liquid density, saturated vapor density. ideal-gas heat capacity. and pressure on the melting curve, Comparisons between experimental data and values calculated using the fundamental equation are given to verify the accuracy of the formulation. The formulation given here may be used to calculate densities within ±0.1 %, heat capacities to within ±2 %. and speed of sound to within ± 1 %, except near the critical point.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Molar heat capacity at constant volume for air from 67 to 300 K at pressures to 35 MPa

Measurements of the molar heat capacity at constant volumeC _v for air were conducted with an adiabatic calorimeter. Temperatures ranged from 67 to 300 K, and pressures ranged up to 35 MPa. Measurements were conducted at 17 densities which ranged from gas to highly compressed liquid states. In total, 227C _v values were obtained. The air sample was prepared gravimetrically from research purity gases resulting in a mole fraction composition of 0.78112 N₂ + 0.20966 O₂ + 0.00922 Ar. The primary sources of uncertainty are the estimated temperature rise and the estimated quantity of substance in the calorimeter. Overall, the uncertainty (± 2) of theC _v values is estimated to be less than ± 2% for the gas and ±0.5% for the liquid.Nomenclature C _v Molar heat capacity at constant volume, J · mol^–1 K^–1 - C _v ⁰ Molar heat capacity in the ideal-gas state, J · mol^–1 · K^–1 - V _bomb Volume of the calorimeter containing sample, cm³ - P Pressure, MPa - P Pressure rise during a heating interval, MPa - T Temperature, K - T ₁,T ₂ Temperature at start and end of heating interval, K - T Temperature rise during a heating interval, K - Q Calorimetric heat energy input to bomb and sample, J - Q ₀ Calorimetric heat energy input to empty bomb, J - N Moles of substance in the calorimeter, mol - Fluid density, mol · dm^–3     

A new equation of state for chlorodifluoromethane (R22) covering the entire fluid region from 116 K to 550 K at pressures up to 200 MPa

A new equation of state in the form of a fundamental equation explicit in the dimensionless Helmholtz free energy has been developed for chlorodifluoromethane (R 22). This equation, which contains 22 fitted coefficients, covers the entire fluid region from 116 K (triple point temperature) to 550 K at pressures up to 200 MPa. The mathematical form of the equation was determined with the help of a new method to optimize its structure. New pressure-density-temperature data in the liquid region and especially new vapour pressures and saturated liquid densities, as well as speed of sound data have been incorporated to extend the range of validity and to improve the accuracy of properties calculated with this equation beyond that of previous formulations. Independent equations are also included for the vapour pressure as well as for the saturated liquid and vapour densities. The uncertainty of the new wide-range equation of state can roughly be given as follows: ± 0.1% in density (with the exception of the critical region), ± 1% in heat capacity, ± 0.5% in speed of sound in the liquid and 0.1% in speed of sound in the gas phase. The new equation of state corresponds to the International Temperature Scale of 1990 (ITS-90).     

Determination of thermodynamic properties from the speed of sound

We describe methods by which all of the observable thermodynamic properties of a compressed gas, including the compressibility factor and the isochoric heat capacity, may be determined from sound speed data by numerical integration of a pair of partial differential equations. The technique may be employed over a wide range of conditions. Initial values are required. but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of analytic and numerical results. The results indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24. 1994, Boulder, Colorado. U.S.A.     

A thermodynamic property formulation for air. II. Pressure and density estimation functions for the dew and bubble lines

As a companion to a new correlation for the thermodynamic properties of air in single-phase states, new values for the properties on the dew and bubble lines have been calculated. Phase equilibrium properties for air at low and moderate pressures were predicted from accurate equations of state for argon, nitrogen, and oxygen using extended corresponding-states (ECS) methods. For pressures near the critical pressure, property values were calculated using a modified Leung-Griffiths model for mixtures of argon, nitrogen, and oxygen. Available experimental data and newly predicted values have been used in developing new correlating functions for estimating density and pressure on the dew and bubble lines of air. Estimates of the accuracies of these correlations based upon comparisons of calculated properties to data from other sources are also included.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Improvements of the Patel-Teja equation of state

The Patel Teja equation of state has been improved by modifying the temperature dependence of the attractive term to give simultaneous representation of vapor pressure, liquid density, and liquid heat capacity data for polar and nonpolar compounds, For many high-boiling industrially important compounds, the combination of available heat capacity and vapor pressure data provides a thermodynamically sound method of establishing the temperature dependence of the attractive term in the most practical range of 273-523 K, The performance of the equation of state is greatly improved if the critical pressure is used as the adjustable parameter to correlate the thermodynamic properties under the conditions of interest.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

An improved parametric crossover model for the thermodynamic properties of fluids in the critical region

An improved parametric equation for the thermodynamic properties of fluids is presented that incorporates the crossover from singular thermodynamic behavior in the immediate vicinity of the critical point to regular thermodynamic behavior far away from the critical point. Based on a comparison with experimental data for ethane and methane, it is demonstrated that the crossover model is capable of representing the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point.     

An interim analytic equation of state for sulfurhexafluoride

An interim analytic equation of state for Sulfurhexafluoride is given in the form of a reduced Helmholtz energy function. It represents the thermodynamic properties over the temperature range 222.38 to 525 K for pressures up to 55 MPa. The data selected for determining the linear coefficients of the equation are given, which includes some values predicted using the principle of corresponding states. The method used for the multiproperty fitting is given and, in particular, the functions used for fitting isobaric heat capacities as primary data. Comparisons with values predicted by the equation of state are given for saturation properties, second virial coefficients, densities, and isobaric and isochoric heat capacities. The accuracy of the representation of the equation of state is discussed and, also, the problems arising from inconsistencies between the different data sets. The interim status of this equation of state is due to these inconsistencies.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

An equation of state for the thermodynamic properties of R143a (1,1,1-trifluoroethane)

Thermodynamic properties of 1,1,1-trifluoroethane (R143a) are expresed in terms of a 32-term modified Benedict-Webb-Rubin (MBWR) equation of state. Coefficients are reported for the MBWR equation and for ancillary equations used to lit the ideal-gas heat capacity, and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined from a multiproperty fit that used the following types of experimental data:PVT: isochoric, isobaric, and saturated-liquid heat capacities: second virial coefficients: speed of sound and properties at coexistence. The equation of state was optimized to the experimental data from 162 to 346 K and pressures to 35 MPa with the exception of the critical region. Upon extrapolation to 500 K and 60 MPa, the equation gives thermodynamically reasonable results. Comparisons between calculated and experimental values are presented.     

Experimental study of the ultrasonic velocity in liquid cesium at high temperatures and pressures

The sound velocity in liquid cesium under pressures up to 60 MPa and temperatures to 1500 K is measured using a modified-pulses phase-sensitive technique. The sound velocity (at frequency 10 MHz) is determined by means of the pulse propagation time measurement through the cesium sample. The experimental error is 0.2%. The results obtained are discussed.Paper submitted to the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region

We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.     

Ideal-gas thermodynamic properties for natural-gas applications

Calculating caloric properties from a thermal equation of state requires information such as isobaric heat capacities in the ideal-gas state as a function of temperature. In this work, values for the parameters of thec _p ⁰ correlation proposed by Aly and Lee were newly determined for 21 pure gases which are compounds of natural gas mixtures. The values of the parameters were adjusted to selectedc _p ⁰ data calculated from spectroscopic data for temperatures ranging from 10 to 1000 K. The data sources used are discussed and compared with literature data deduced from theoretic models and caloric measurements. The parameters presented will be applied in a current GERG project for evaluating equations of state (e.g., the AGA 8 equation) for their suitability for calculating caloric properties.     

An equation of state formulation of the thermodynamic properties of R134a (1,1,1,2-tetrafluoroethane)

New correlations for the thermodynamics properties of R134a are presented. A classical equation for the molar Helmholtz energy is used with temperature and density as the independent variables. The equation is accurate for both the liquid and vapour phases at pressures up to 70 Pa, and for a temperature range from the triple point to 450 K. Temperatures are given on the new International Temperature Scale of 1990 (ITS 90). The equation was developed by using experimental data for pressure-volume-temperature (PVT) properties, isochoric heat capacity, second virial coefficients, speed of sound and coexistence properties. Comparisons with experimental data and with two other equations of state are given. Ancillary equations representing the saturated liquid and vapour densities and the vapour pressure are also presented.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

A Thermodynamic Equation of State For the Critical Region of Ethylene

A fundamental equation of state that describes the behavior of the thermodynamic properties of ethylene in the vicinity of the critical point is formulated. Specifically, a crossover equation of state that takes into account not only the scaling laws at the critical point but also the analytical behavior far away from the critical point is presented. Analysis of different sets of data for the thermodynamic properties is made.     

Aluminum. I. Measurement of the relative enthalpy from 273 to 929 K and derivation of thermodynamic functions for Al(s) from 0 K to Its melting point

The relative enthalpy of pure, polycrystalline aluminum (NBS Standard Reference Material 44f, for the freezing point of aluminum on IPTS-68) has been measured over the temperature range 273 to 929 K. The enthalpy measurements were made in a precision isothermal phase-change calorimeter and are believed to have an inaccuracy not exceeding 0.2%. Pt-10Rh alloy and quartz glass were used as the encapsulating materials. The enthalpy data for Al(s) and SiO₂(l) have been fitted by the method of least squares with cubic polynomial functions of temperature. Heat capacity data for Al(s), derived from these polynomials, have been smoothly merged using a spline technique to the most reliable low-temperature heat capacity data for Al(s) below 273 K. The merged data are compared with corresponding data from the literature as well as with published critical compilations of heat capacity data for Al(s). A new table of thermodynamic functions for Al(s) has been derived. A theoretical interpretation of the results apears in the following paper.