Thermodynamic properties of titanium

This work reviews and discusses the data and information on the thermodynamic properties of titanium available through May 1984. These properties include heat capacity, enthalpy, enthalpy of transition and melting, vapor pressure, and enthalpy of vaporization. The recommended values for heat capacity cover the temperature range from 1 to 3800 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 3800 K.     

Thermodynamic properties of aluminum

This work reviews and discusses the data on the thermodynamic properties of aluminum available through May 1984. However, two papers dated 1985 which are useful to this work are also included. These properties include heat capacity, enthalpy, enthalpy of transition and melting, vapor pressure, and enthalpy of vaporization. The recommended values for heat capacity cover the temperature range from 0.1 to 2800 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 2800 K.     

Thermodynamic properties of vanadium

This work reviews and discusses the data and information on the various thermodynamic properties of vanadium available through March 1985. These include the heat capacity and enthalpy, enthalpy of melting, vapor pressure, and enthalpy of vaporization. The existing data have been critically evaluated and analyzed, and the recommended values for heat capacity, enthalpy, entropy, and Gibbs energy function covering the temperature range from 1 to 3800 K have been generated. These values are referred to temperatures based on IPTS-1968. The units used for various properties are joules per mole (J · mol^–1). The estimated uncertainties in the heat capacity are ±3% below 15 K, ±10% from 15 to 150 K, ±3% from 150 to 298.15 K, ±2% from 298.15 to 1000 K, ±3% from 1000 to the melting point (2202 K), and ±5% in the liquid region.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

The Caloric Properties of Liquid Bismuth

We investigated the enthalpy of liquid bismuth within the temperature range of 580–1325 K in a massive isothermal drop calorimeter using the mixture method. We obtained the approximation equations and determined the isobaric heat capacity. The estimated errors of the data on the enthalpy and the heat capacity are equal to 0.2% and 0.5%, respectively. The results are compared with the literature data. We confirmed the existence of a heat-capacity minimum of liquid bismuth of approximately 800 K. We show that above 940 K the heat capacity depends linearly on the temperature. We developed tables of the recommended values of the caloric properties within the range from the melting point to 1325 K.     

Measurement of the Specific Enthalpy of Vaporization on 1,1,1,2-Tetrafluoroethane in the Temperature Range from 180 to 240 K

An apparatus is described which is capable of measuring the enthalpy of vaporization in the temperature range from 100 to 250 K. The sample (R134a; purity, at least 99.999%) is located in the measuring cell at the saturated vapor pressure, p = p _s. A control circuit allows p to be kept constant by opening a motor-operated valve to a weighing cylinder after having switched on the electrical measuring cell heater. During the experiment, the temperature is kept constant within a 10mK. In the range 180 to 230 K, the data for R134a are compared with calculated values from the fundamental equation given by Tillner-Roth and Baehr, which is recommended by Annex 18 of the International Energy Agency (IEA) as an international standard. Good agreement within a standard uncertainty of 1.6×10^–3 is obtained. At temperatures of only 10 K above the triple-point temperature, the enthalpy of vaporization calculated from the Clausius–Clapeyron equation shows considerable uncertainty due to the determination of the small vapor pressure. It is chiefly in this range that it is advantageous to have the new apparatus.     

Combined DSC and Pulse-Heating Measurements of Electrical Resistivity and Enthalpy of Tungsten,Niobium, and Titanium

Measurements of thermophysical properties such as enthalpy, electrical resistivity, and specific heat capacity as a function of temperature starting from the solid state into the liquid phase for W, Nb, and Ti are presented in this work. An ohmic pulse-heating technique allows measurements of enthalpy and electrical resistivity from room temperature to the end of the stable liquid phase within 60 μ s. The simultaneous optical measurement of temperature is limited by the fast pyrometers with an onset temperature of T_min = 1200–1500 K; below these temperatures, the fast pyrometers are not sensitive. A differential scanning calorimeter (DSC) is used for determination of the specific heat capacity, and also to obtain enthalpy values in the temperature range of 600–1700 K. Combining the two methods entends the range of values of electrical resistivity and enthalpy versus temperature down to 600 K. Results on the metals W, Nb, and Ti are reported and compared to literature values. This paper is a continuation of earlier work. Paper presented at the Seventh International Workshop on Subsecond Thermophysics, October 6–8, 2004, Orléans, France.     

Numeric Databases in Chemical Thermodynamics at the National Institute of Standards and Technology

During the past year the activities of the Chemical Thermodynamics Data Center and the JANAF Thermochemical Tables project have been combined to obtain an extensive collection of thermodynamic information for many chemical species, including the elements. Currently available are extensive bibliographic collections and data files of heat capacity, enthalpy, vapor pressure, phase transitions, etc. Future plans related to materials science are to improve the metallic oxide temperature dependent tabulations, upgrade the recommended values periodically, and maintain the bibliographic citations and the thermochemical data current. The recommended thermochemical information is maintained on-line, and tied to the calculational routines within the data center. Recent thermodynamic evaluations on the elements and oxides will be discussed, as well as studies in related activities at NIST.     

Thermophysical properties of aqueous NaOH−H2O solutions at high concentrations

The working fluids, used in the majority of all mechanical heat pumps, are expected to be phased out within some few years due to their contribution to the stratospheric ozone depletion and global warming. Absorption heat pumps and transformers are receiving a new renaissance in the field of heating, refrigeration, air-conditioning, and heat recovery. Sodium hydroxide solutions are more propitious to the pulp and paper industry compared to other working pairs. Novel correlations have been developed to compute the vapor pressure, density, enthalpy, and viscosity of sodium hydroxide solutions. These correlations cover the most extensive range of validity ever proposed: 273–473 K for temperatures and 0.2–1 kg water per kg solution for concentrations.     

Thermodynamic Properties of 1,1,1,2,3,3,3-Heptafluoropropane

A vapor pressure equation has been developed for 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) based on previous measurements from 202 to 375K, from which the boiling point of HFC-227ea was determined. Based on the previous pressure–volume–temperature (PVT) measurements in the gaseous phase for HFC-227ea, virial coefficients, saturated vapor densities, and the enthalpy of vaporization for HFC-227ea were also determined. The vapor pressure equation and the virial equation of state for HFC-227ea were compared with the available data. Based on the previous measurements of speed of sound in the gaseous phase for HFC-227ea, the ideal-gas heat capacity at constant pressure and the second acoustic virial coefficient of HFC-227ea were calculated. A correlation of the second virial coefficient for HFC-227ea was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with results based on PVT measurements. A van der Waals-type surface tension correlation for HFC-227ea was proposed, based on our previous experimental data by the differential capillary rise method from 243 to 340K.     

A unified model for the cohesive enthalpy, critical temperature, surface tension and volume thermal expansion coefficient of liquid metals of bcc, fcc and hcp crystals

First the cohesive enthalpy of pure liquid metals is modeled, based on experimental critical temperatures of alkali metals. The cohesive enthalpies are scaled to the melting points of pure metals. The temperature coefficient of cohesive enthalpy is the heat capacity of the liquid metal. The surface tension and its temperature coefficient for pure liquid metals are modeled through the excess surface enthalpy, excess surface entropy and molar surface area supposing that the outer two surface layers of liquid metals are similar to the {1 1 1} plane of fcc crystals. The volumetric thermal expansion coefficient of liquid metals is scaled to the ratio of the heat capacity and cohesion enthalpy. From known values of melting point, heat capacity and molar volume the following calculated properties of liquid metals are tabulated: (i) cohesive enthalpy at melting point, (ii) cohesive energy of the solid metal at 0 K, (iii) critical temperature, (iv) surface tension at melting point, (v) volume thermal expansion coefficient, and (vi) temperature coefficient of surface tension. The present models are valid only for liquid metals of bcc, fcc or hcp crystals as only their structure and nature of bonding are similar enough to be treated together.     

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.     

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.     

Thermodynamic properties of multiwalled carbon nanotubes

The experimental study of the heat capacity of multiwalled carbon nanotubes has been conducted at a constant pressure and a temperature in the range from 60 to 300 K. The derived temperature dependence of the heat capacity has been shown to differ from that of graphite. The explanation of the fact has been given in terms of the special features of phonon spectra of the above materials. Based on the experimental results and reliable literature data standard values of the basic thermodynamic functions of multiwalled carbon nanotubes (enthalpy, entropy, and Gibbs reduced energy) have been calculated.     

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.     

Experimental Determination of Isobaric Heat Capacities of R227 (CF<Subscript>3</Subscript>CHFCF<Subscript>3</Subscript>) from 223 to 283 K at Pressures up to 20 MPa.

A new experimental method for measuring isobaric heat capacity c_p down to 223 K at pressures up to 30 MPa was developed with the aim to study alternative refrigerants at sub-ambient temperatures and elevated pressures. The experiments are carried out in a batch mode, using a differential fluxmetric calorimeter Setaram BT-215, equipped with a customized high-pressure unit. The measurements are performed at constant pressure with a continuous scan of temperature. First, the method was tested at atmospheric pressure with methanol in the temperature range 223–283 K. The relative deviation from recommended isobaric heat capacity data in the literature is about 0.5%. Second, the measurements were performed at pressure up to 18.2 MPa with an alternative refrigerant R134a (1,1,1,2-tetrafluoroethane) of well-known heat capacity. Our results agree with representative literature values within 0.4%. New original results were obtained for refrigerant R227 (1,1,1,2,3,3,3-heptafluoropropane) in the temperature range from 223 to 283 K and at pressures of 1.1, 5, 10, 15, and 20 MPa. The consistency of our isobaric heat capacities with calorimetric values above 273 K and with pVT data reported in the literature is discussed.     

Determination of thermophysical properties of 45% Pb‒55% Bi alloy. Thermodynamic simulation

The thermophysical properties of 45% Pb?55% Bi alloy were studied using thermodynamic simulation. Vapor pressure, partial pressures of the components of vapor, heat capacity, entropy, enthalpy, and the thermal conductivity of an alloy depending on temperature were determined. A comparison of the results from published data was made.     

Thermodynamic characteristics of vaporization of alkali metals

The saturation vapor of an alkali metal is treated as a monatomic particle real gas whose volumetric behavior is described by a truncated form of virial equation. The condensed state-vapor equilibrium constant, equal to the saturation fugacity for Li, Na, K, and Cs, is determined through evaluation of the second virial coefficient's temperature dependence. The third and the second law values of standard enthalpy of vaporization at the reference temperature 298 K for the same metals are determined. The applied procedure for evaluation of the second virial coefficient's temperature dependence produced small deviations for the resulting second law values and gave mean values in good agreement with literature data, especially with those of the JANAF Tables.     

Experimental Investigation of the Heat Capacity and Enthalpy of 12Kh18N9T and 12Kh18N10T (Chrome–Nickel–Titanium) Austenitic Steels in the Temperature Range from 300 to 1678 K

The results of experimental investigation of the enthalpy and of the true and mean heat capacity of 12Kh18N9T and 12Kh18N10T (chrome–nickel–titanium) austenitic stainless steels are given. The heat capacity is measured with an error of 1% in the temperature range from 300 to 900 K by the method of continuous adiabatic heating. The enthalpy and mean heat capacity are investigated by the method of mixtures in the temperature range from 1200 to 1678 K with an error of 1%. The experimental results are approximated by an unified equation for the temperature range from 298.15 to 1678 K using the least-squares method. The errors of calculated data are estimated.