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.     

Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13)

Measurements of the molar heat capacity at constant volume C _v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, , T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, , T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C _v predictions with measurements was found. Published C _v(, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C _v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.     

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 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.     

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.     

Calorimetric study of the molecular mobility in a filled plasticized epoxide resin

Results are presented on the observed dependence of the thermophysical parameters C_p, , anda on temperature, filler content, and plasticizer concentration for ÉD-5 epoxide resin.Notation C_p specific heat capacity at constant pressure - thermal conductivity - a thermal diffusivity - C_p specific heat discontinuity - T_v vitrification point - density - u_so velocity of sound - l phonon mean free path - f frequency Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 853–858, May, 1971.     

Isochoric Heat Capacity Measurements for Heavy Water Near the Critical Point

Isochoric heat capacity measurements of D₂O are presented as a function of temperature at fixed densities of 319.60, 398.90, 431.09, and 506.95 kg·m^–3. The measurements cover a range of temperatures from 551 to 671 K and pressures up to 32 MPa. The coverage includes one- and two-phase states and the coexistence curve near the critical point of D₂O. A high-temperature, high-pressure, adiabatic, and nearly constant-volume calorimeter was used for the measurements. Uncertainties of the heat capacity measurements are estimated to be 2 to 3%. Temperatures at saturation T _S () were measured isochorically using a quasi-static thermogram method. The uncertainty of the phase transition temperature measurements is about ±0.02 K. The measured C _V data for D₂O were compared with values predicted from a parametric crossover equation of state and six-term Landau expansion crossover model. The critical behavior of second temperature derivatives of the vapor pressure and chemical potential were studied using measured two-phase isochoric heat capacities. From measured isochoric heat capacities and saturated densities for heavy water, the values of asymptotic critical amplitudes were estimated. It is shown that the critical parameters (critical temperature and critical density) adopted by IAPWS are consistent with the T _S – _S measurements for D₂O near the critical point.     

Isochoric p–ρ–T and Heat Capacity Cv Measurements for Ternary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), and 1,1,1,2-Tetrafluoroethane (R134a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships and constant volume heat capacity C _v were measured for ternary refrigerant mixtures by isochoric methods with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K for p––T and from 203 to 345 K for C _v, while for both data types pressures extended to 35 MPa. Measurements of p––T were carried out on compressed gas and liquid samples with the following mole fraction compositions: 0.3337 R32+0.3333 R125+0.3330 R134a and 0.3808 R32+0.1798 R125+0.4394 R134a. Measurements of C _v were carried out on liquid samples for the same two compositions. Published p––T data are in good agreement with this study. For the p––T apparatus, the uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%. For the C _v calorimeter, the uncertainty of the temperature rise is 0.002 K and for the change-of-volume work it is 0.2%; the latter is the principal source of uncertainty. When all components of experimental uncertainty are considered, the expanded relative uncertainty of the heat capacity measurements is estimated to be 0.7%.     

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 Model for Fluid Phase Hydrogen Sulfide

A Helmholtz free energy equation of state for the fluid phase of hydrogen sulfide has been developed as a function of reduced temperature and density with 23 terms on the basis of selected measurements of pressure–density–temperature (P, , T), isobaric heat capacity, and saturation properties. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from the triple point temperature (187.67 K) to 760 K at pressures up to 170 MPa. The uncertainty in density calculation of the present equation of state is 0.7% in the liquid phase, and that in pressure calculation is 0.3% in the vapor phase. The uncertainty in saturated vapor pressure calculation is 0.2%, and that in isobaric heat capacity calculation is 1% in the liquid phase. The behavior of the isobaric heat capacity, isochoric heat capacity, speed of sound, and Joule–Thomson coefficients calculated by the present model shows physically reasonable behavior and those of the calculated ideal curves also illustrate the capability of extending the range of validity. Graphical and statistical comparisons between experimental data and the available thermodynamic models are also discussed.     

Persistent currents and critical velocities in3He-4He mixtures

Using the method of Doppler-shifted fourth sound, we have investigated the angular velocity _c1 for the onset of vorticity, the saturated critical velocity, and the dependence of _s/ onv _n –v _s for⁴He in three different pore sizes and for three different mixtures of ³ He- ⁴ Hein one of the powders used. These are the first measurements of critical velocities in ³ He- ⁴ He mixtures. We observe only a weak dependence of _c1on the pore size and within the limits of the experiment no dependence on concentrationX up toX=0.11. We find, however, that the maximumv _n –v _s attainable increases as the concentration of ³ He increases forX0.17. The observed dependence of the superfluid density onv _n –v _s is approximately two orders of magnitude stronger than predicted.     

Molar heat capacity at constant volume of difluoromethane (R32) and pentafluoroethane (R125) from the triple-point temperature to 345 K at pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of dill uoromethane (R32) and pentalluoroethane (R125) were measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C _v ⁽²⁾ ), saturated liquid (C orC _x ), and singlephase (C _v) molar heat capacities. TheC data were used to estimate vapor pressures for values less than 0.3 MPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature (T _tr) and the enthalpy of fusion (_fus H) were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-ofvolume work adjustment. The expanded uncertainty (at the two-sigma level) forC _v is estimated to be 0.7%, forC _v ⁽²⁾ it is 0.5%, and forC it is 0.7%.     

Temperature similarity of heat transfer processes

New relationships are presented which describe the temperature and humidity of the medium at the edges of the boundary layer in heat and mass transfer processes.Notation A thermal equivalent of mechanical work - g acceleration due to gravity - c_p specific heat of medium - T_f and T_w arithmetic mean temperatures of medium in flow core and at heat transfer surface - w_x and w_y, u_v and v_v projections of mixture and vapor velocities on the X and Y axes - and _T molecular and turbulent thermal conducitvities of medium - andT molecular and turbulent diffusion coefficients - P pressure - r latent heat of condensation - l characteristic geometrical dimension (tube diameter) - l ₀ arbitrary characteristic dimension taken as zero reading - x humidity of mixture - I heat content of mixture - and _v density of mixture and vapor - specific weight - a thermal diffusivity - k diffusion conductivity - Gr Grashof number - Pr Prandtl number     

Thermal diffusivity measurement by the transient hot-wire technique: A reappraisal

The theory of the transient hot-wire technique for thermal conductivity measurements is reassessed in the special context of thermal diffusivity measurements. A careful examination of the working equation and an error analysis are employed to identify the principal sources of error. Notwithstanding earlier claims to the contrary, the best precision that can be attained in thermal diffusivity measurements is of the order of ±3%, while the accuracy is inevitably poorer. Experimental evidence is adduced from two different instruments that supports the analysis given here. Although the technique cannot yield values of the thermal diffusivity, k, as accurate as can be achieved by the use of the best possible individual values of ,, and C _p in the relation k=/C _p, the simplicity of the technique makes it attractive for many purposes. It is even possible to derive values of the isobaric heat capacity C _p for many fluids not available from other methods.     

Isochoric Heat Capacity of Heavy Water at Subcritical and Supercritical Conditions

The heat capacity of heavy water was measured in the temperature range from 294 to 746 K and at densities between 52 and 1105 kg·m^–3 using a high-temperature, high-pressure adiabatic calorimeter. The measurements were performed at 14 liquid and 9 vapor densities between 52 and 1105 kg·m^–3. Uncertainties of the measurements are estimated to be within 3% for vapor isochores and 1.5% for the liquid isochores. In the region of the immediate vicinity of the critical point (0.97T/T _c1.03 and 0.75/_c1.25), the uncertainty is 4.5%. The original C _V data were corrected and converted to the new ITS-90 temperature scale. A parametric crossover equation of state was used to represent the isochoric heat capacity measurements of heavy water in the extended critical region, 0.8T/T _c1.5 and 0.35/_c1.65. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and saturation densities were extracted from experimental data for each measured isochore. Most of the experimental data are compared with the Hill equation of state, and the overall statistics of deviations between experimental data and the equation of state are given.     

Isochoric Heat Capacity Measurements for 2,2-Dichloro-1,1,1-Trifluoroethane (R123) at Temperatures from 167 to 341 K and 1-Chloro-1,2,2,2-Tetrafluoroethane (R124) from 94 to 341 K at Pressures to 35 MPa

Molar heat capacities at a constant volume (C _v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C ⁽²⁾ _v), saturated liquid (C or C _x ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T _tr) and the enthalpy of fusion ( _fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2 level) for C _v is estimated to be 0.7%, for C ⁽²⁾ _v it is 0.5%, and for C it is 0.7%.     

Relationship between thermal conductivity,speed of sound,and isobaric heat capacity of liquids

Using two liquids-water and toluene — as an example, the author determines the dependence of the coefficient of thermal conductivity on the speed of sound and isobaric molar heat capacity for high state parameters.Notation coefficient of thermal conductivity - u speed of sound - _S same for a saturated liquid - c isobaric molar heat capacity - density - p_s same, for a saturated liquid - p pressure - p_s same, for a saturated liquid - R gas constant - T absolute temperature - x coefficient of thermal activity - x _s same, for a saturated liquid - L, constants in Eqs. (1) and (2) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 311–314, August, 1980.     

Modeling turbulent flow at a permeable plate with strong injection

It is shown that available experimental data on the thickness of the turbulent-boundary layer and the filling of the velocity profile under strong injection are satisfactorily generalized using the parameter _wv²w/ ₀u ₀ ² .Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 1, pp. 94–98, January, 1978.     

Molar Heat Capacity at Constant Volume of 1,1-Difluoroethane (R152a) and 1,1,1-Trifluoroethane (R143a) from the Triple-Point Temperature to 345 K at Pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of 1,1-difluoroethane (R152a) and 1,1,1-trifluoroethane (R143a) have been measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase ((C _v ⁽²⁾ ), saturated-liquid (C or C _x ^' ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 105 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) for C _v is estimated to be 0.7%, for C _v ⁽²⁾ it is 0.5%, and for C it is 0.7%.