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 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%.     

A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol

A formulation for the thermodynamic properties of ethanol (C₂H₅OH) in the liquid, vapor, and saturation states is presented. The formulation is valid for single-phase and saturation states from 250 to 650K at pressures up to 280MPa. The formulation includes a fundamental equation and ancillary functions for the estimation of saturation properties. The experimental data used to determine the fundamental equation include pressure-density-temperature, ideal gas heat capacity, speed of sound, and vapor pressure. Saturation values computed from the ancillary functions were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Comparisons between experimental data and values computed using the fundamental equation are given to verify the uncertainties in the calculated properties. The formulation presented may be used to compute densities to within ±0.2%, heat capacities to within ±3%, and speed of sound to within ±1%. Saturation values of the vapor pressure and saturation densities are represented to within ±0.5%, except near the critical point.     

Compressed Liquid Densities and Helmholtz Energy Equation of State for Fluoroethane (R161)

In this study, compressed liquid densities of Fluoroethane (R161, CAS No. 353-36-6) were measured using a high-pressure vibrating-tube densimeter over the temperature range from (283 to 363) K with pressures up to 100 MPa. A Helmholtz energy equation of state for R161 was developed from these density measurements and other experimental thermodynamic property data from the literature. The formulation is valid for temperatures from the triple point temperature of 130 K to 420 K with pressures up to 100 MPa. The approximate uncertainties of properties calculated with the new equation of state are estimated to be 0.25 % in density, 0.2 % in saturated liquid density between 230 K and 320 K, and 0.2 % in vapor pressure below 350 K. Deviations in the critical region are higher for all properties. The extrapolation behavior of the new formulation at high temperatures and high pressures is reasonable.     

Viscosity Measurements on Gaseous Argon, Krypton, and Propane1

A new vibrating-wire viscometer was designed to perform quasi-absolute measurements of very high precision on gases. It was applied to determine the viscosity of argon at temperatures of 298.15, 348.15, and 423.15 K and pressures up to 20 MPa, and the viscosity of krypton at 298.15 and 348.15 ,K and pressures up to 16 MPa. Furthermore, several isothermal series of viscosity measurements on gaseous propane were carried out. The subcritical isotherms at 298.15, 323.15, 348.15, and 366.15 K were restricted to 95% of the saturated vapor pressure, the supercritical isotherms at 373.15, 398.15, and 423.15 K to 20 MPa. In general, the measurements are characterized by a reproducibility of ±0.05% and an accuracy of ±0.2%. However, close to the critical point an accuracy of ±3% has to be accepted, mainly due to the uncertainty of the density. In this context the influence of the equation of state used for propane is discussed.     

Application of nonlinear regression in the development of a wide range formulation for HCFC-22

An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based onP--T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

An Equation of State for 1,1,1-Trifluoroethane (R-143a)

A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P––T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.     

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.     

The transport properties of ethane. I. Viscosity

A new representation of the viscosity of ethane is presented. The representative equations are based upon a body of experimental data that have been critically assessed for internal consistency and for agreement with theory in the zero-density limit, vapor phase, and critical region. The representation extends over the temperature range from 100 K to the critical temperature in the liquid phase and from 200 K to the critical temperature in the vapor phase. In the supercritical region, the temperature range extends to 1000 K for pressures up to 2 MPa and to 500 K for pressures up to 60 MPa. The ascribed accuracy of the representation varies according to the thermodynamic state from ±0.5 % for the viscosity of the dilute gas near room temperature to ±3.0% for the viscosity at high pressures and temperatures. Tables of the viscosity, generated by the relevant equations, at selected temperatures and pressures and along the saturation line, are also provided.     

The transport properties of ethane. II. Thermal conductivity

A new representation of the thermal conductivity of ethane is presented. The representative equations are based upon a body of experimental data that have been critically assessed for internal consistency and for agreement with theory in the zero-density limit and in the critical region. The representation extends over the temperature range from 100 K to the critical temperature in the liquid phase and from 225 K to the critical temperature in the vapor phase. In the supercritical region the temperature range extends to 1000 K for pressures up to 1 MPa and to 625 K for pressures up to 70 MPa. The ascribed accuracy of the representation varies according to the thermodynamic state from ±2% for the thermal conductivity of the dilute gas near room temperature to ±5% for the thermal conductivity at high pressures and temperatures. Tables of the thermal conductivity, generated by the relevant equations, at selected temperatures and pressures and along the saturation line are also provided.     

A Rational Helmholtz Fundamental Equation of State for Difluoromethane with an Intermolecular Potential Background

A new fundamental thermodynamic equation of state for difluoromethane was developed by considering the intermolecular potential behavior for improving the reliability in the gaseous phase. Reliable second and third virial coefficients are introduced in accordance with the principle of a unified relation of the intermolecular potential energy and the fundamental equation of state. The fundamental equation of state is able to provide reliable thermodynamic properties even at low temperatures or in the region near saturation where precise and accurate experimental data are not available. The estimated uncertainties of calculated properties from the equation of state are 0.07% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.35% in pressure for the supercritical region, 0.07% in vapor pressure, 0.2% in saturated-liquid density, 0.7% in saturated-vapor density, 0.01% in speed of sound for the gaseous phase, 0.7% in speed of sound for the liquid phase, and 0.6% in isochoric specific heat for the liquid phase. The equation is valid for temperatures from the triple point to 450 K and pressures up to 72 MPa.     

Equation of state and critical point of cesium

Equation-of-state measurements for cesium at temperatures from 350 to 2200 K and pressures from 1 to 60 MPa by means of a hermetically sealed two-zone dilatometer are presented. The experimental range includes the liquid and gaseous phases together with the coexistence curve up to critical point and supercritical region. The critical parameters are 1938 K, 9.4 MPa, 0.39 g · cm^–3. The data were used for the calculation of tables of the density and its derivatives for cesium. The results are discussed.     

Speed of Sound of n-Hexane and n-Hexadecane at Temperatures Between 298 and 373 K and Pressures up to 100 MPa

Measurements of the speed of sound u for n-hexane and n-hexadecane at temperatures of 298.3, 323.15, 348.15, and 373.15 K and at pressures up to 100 MPa are reported. The speeds of sound, the temperatures, and the pressures are subject to an uncertainty of ±0.1%, ±0.01 K, and ±0.2 MPa, respectively. These measurements were undertaken using a new apparatus which has been constructed for measurement of the speed of sound in liquids and supercritical fluids at pressures up to 200 MPa and at temperatures between 248 and 473 K. The technique is based on a pulse-echo method with a single transducer placed between two plane parallel reflectors. The speed of sound is obtained from the difference between the round-trip transit times in the two paths. It is expected that both the precision and the accuracy of the method can be further improved.     

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.     

Equation of State for the Thermodynamic Properties of 1,1,2,2,3-Pentafluoropropane (R-245ca)

An equation of state for the calculation of the thermodynamic properties of 1,1,2,2,3-pentafluoropropane (R-245ca), which is a hydrofluorocarbon refrigerant, is presented. The equation of state (EOS) is expressed in terms of the Helmholtz energy as a function of temperature and density, and can calculate all thermodynamic properties through the use of derivatives of the Helmholtz energy. The equation is valid for all liquid, vapor, and supercritical states of the fluid, and is valid from the triple point to 450 K, with pressures up to 10 MPa. Comparisons to experimental data are given to verify the stated uncertainties in the EOS. The estimated uncertainty for density is 0.1 % in the liquid phase between 243 K and 373 K with pressures up to 6.5 MPa; the uncertainties increase outside this range, and are unknown. The uncertainty in vapor-phase speed of sound is 0.1 %. The uncertainty in vapor pressure is 0.2 % between 270 K and 393 K. The uncertainties in other regions and properties are unknown due to a lack of experimental data.     

A New Apparatus for Combined Measurements of the Viscosity and Density of Fluids for Temperatures from 233 To 523 K at Pressures up to 30 Mpa

A new apparatus for measuring the viscosity and density of fluids is presented. The main element of the instrument is an electronically controlled magnetic suspension coupling. For the density measurement (buoyancy principle according to the single-sinker method), this coupling is used for the contactless transfer of the forces acting on a sinker in the measuring cell to an analytical balance. The coupling also serves as a frictionless bearing for a slender rotating cylindrical body which is slowed down due to the viscous drag of the fluid surrounding the cylinder. The viscosity of the fluid can be directly determined from the decay rate of the rotational frequency. The new combined viscometer-densimeter covers a viscosity range of 5 to 150 Pa·s and a density range from 20 to 2000 kg·m^–3 at temperatures from 233 to 523 K and pressures up to 30 MPa. Test measurements on the viscosities and densities of nitrogen and carbon dioxide at 253, 293, and 523 K at pressures up to 30 MPa show an estimated total uncertainty of ±0.6 to ±1.0% in viscosity and of ±0.02 to ±0.05% in density.     

Viscosity of Gaseous HFC-125 (Pentafluoroethane) Under High Pressures

This paper reports experimental results lor the viscosity of gaseous HFC-125 (pentafluoroethane) under high pressures. The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K and at pressures up to the saturated vapor pressures at each temperature at subcritical conditions or up to 9 MPa at supercritical temperatures. Intermolecular scaling parameters of HFC-125 for the extended corresponding states were determined from the viscosity data at 0.1 MPa. An empirical viscosity equation is proposed to interpolate the present experimental results as a function of temperature and density.     

Solid-liquid phase equilibria of (α-methylnaphthalene + β-methylnaphthalene) and (chlorobenzene + bromobenzene) systems under high Pressures

Solid-liquid phase equilibria of the (-methylnaphthalene + -methylnaphthalene) and the (chlorobenzene + bromobenzene) systems have been investigated at temperatures from 278 to 343 K and pressures up to 500 MPa using a high-pressure optical vessel. The uncertainties of the measurements of temperature, pressure, and composition were within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. In both systems, the freezing and melting pressures at a constant composition increase almost linearly with increasing temperatures. In the former system, where the two components can form a solid solution with one another to a limit extent, the eutectic point shifts to a higher temperature and to a -methylnaphthalene-rich composition with increasing pressures. In the latter system, where the two components are completely soluble in each other in the solid phase, the freezing points of all mixtures lie between those of the pure components at each pressure. It is found that the coexistence curves obtained can be expressed by a quadratic equation in pressure.     

Compressed Liquid and Supercritical Densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea)

Densities of 1,1,1,2,3,3,3-heptafluoropropane (R227ea) have been measured with a computer-controlled high-temperature high-pressure vibrating-tube densimeter system (DMA-HDT) in the sub- and supercritical states. The densities were measured at temperatures from 278 to 473 K and pressures up to 30 MPa (overall 257 data points), whereby a density range between 285 and 1588 kgm^–3 was covered. The uncertainty in the density measurement was estimated to be better than ±0.2 kgm^–3. The experimental data of R227ea were correlated with a virial-type equation of state (EoS) and compared with published data. A comparison is also made with a recent wide-range dedicated equation of state for R227ea.     

Solid-liquid phase equilibria of benzene + 2-methyl-2-propanol system under high pressures

Solid-liquid phase equilibria of the benzene + 2-methyl-2-propanol system have been investigated at temperatures from 278 to 323 K and pressures up to 300 MPa using a high-pressure optical vessel. The uncertainties of the measurements of temperature, pressure and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. The freezing pressure at a constant composition increases monotonously with pressure. The eutectic point shifts to a higher temperature and benzene-rich composition with increasing pressure. In order to describe the pressure-temperature-composition relation of high-pressure solid-liquid phase equilibria, a new simple equation has been proposed as follows: