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.     

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.     

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.     

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 nickel

This work reviews and discusses the data and information on the thermodynamic properties of nickel 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 3200 K. The recommended values for enthalpy, entropy, Gibbs energy function, and vapor pressure cover the temperature range from 298.15 to 3200 K.     

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.     

Caloric Properties of Hydrocarbons in Liquid,Gaseous, and Supercritical States: <Emphasis Type="Italic">n</Emphasis>-Heptane

Detailed experimental data are presented on the n-heptane isobaric heat capacity obtained by a modernized adiabatic running calorimeter with the calorimetric measurement of the flow rate in the liquid, gaseous, and supercritical domains, within a temperature range of 300–620 K and a pressure range of 0.5–60 MPa. A thorough consideration of errors made it possible to obtain an error of 0.4% within a wide range of the state parameters. According to the experimental data on the heat capacity, using the known thermodynamics relations, the tables of the n-heptane enthalpy, entropy, and Gibbs energy were calculated (estimated against the accuracy) on the basis of the reliable state equations and the available literature data. The obtained results can be applied directly in the design of chemical processes and the processes in the bedded systems of the hydrocarbon deposits and for development and testing of the equations of state and the methods of the thermodynamic similarity.     

Calorific properties of liquid copper

The enthalpy of liquid copper up to a temperature of 2000 K is investigated by the drop method with an error from 1 to 1.5%. The measurement results are compared with the literature data. It is shown that the spectral emissivity of copper melt depends on temperature. The obtained data on enthalpy are approximated by an equation. The true heat capacity of liquid copperc _p = 36.33 J/(mol K), the melting heat ΔH = 13.59 kJ/mol, and the melting entropy ΔS = 10.0 J/(mol K) of copper are calculated.     

An experimental investigation of the enthalpy of erbium trifluoride in the solid and liquid states

A high-temperature massive isothermal calorimeter is used for measuring the enthalpy of high-purity ErF₃ in the temperature range from 396 to 1596 K. The temperature dependences of enthalpy and heat capacity in single-phase regions are obtained, as well as the jumps of enthalpy and heat capacity under conditions of polymorphous transformation and melting. Initial experimental data are given.     

Combined DSC and Pulse-Heating Measurements of Electrical Resistivity and Enthalpy of Platinum,Iron, and Nickel

Measurements of the enthalpy, electrical resistivity, and specific heat capacity as a function of temperature starting from the solid state up into the liquid phase for Fe, Ni, and Pt are presented. Two different measurement approaches have been used within this work: an ohmic pulse-heating technique, which allows – among others – the measurement of enthalpy, specific heat capacity, and electrical resistivity up to the end of the stable liquid phase, and a differential–scanning–calorimetry technique (DSC) which enables determination of specific heat capacity from near room temperature up to 1500 K. The microsecond ohmic pulse-heating technique uses heating rates up to 10⁸ K·s^–1 and thus is a dynamic measurement, whereas the differential–scanning–calorimetry technique uses heating rates of typically 20 K·min^–1 and can be considered as a quasi-static process. Despite the different heating rates both methods give good agreement of the thermophysical data within the stated uncertainties of each experiment. Results on the metals Fe, Ni, and Pt are reported. The enthalpy and resistivity data are presented as a function of temperature and compared to literature values.     

Specific Heat Capacity of Liquid Zirconium up to 4100 K

The temperature dependence of the specific heat capacity of liquid zirconium is investigated experimentally at atmospheric pressure and at temperatures from 2128 to 4100 K. Measured under conditions of pulsed (microseconds) electric heating of foil samples are the electric resistance, the specific energy input (equal to specific enthalpy E), and the temperature (with the aid of a high-speed pyrometer and solid-state light guide). Use is made of the specific enthalpy dependence of temperature, previously obtained [1] for two options of blackbody model, developed for investigation of liquid carbon. The first one of those models is a square tube made up of four zirconium strips, with the light guide introduced at the tube end. The second model is made up of two strips of zirconium, with the light guide introduced on the side into the gap between the two strips (two-strip blackbody model). The temperature dependence of the heat capacity of liquid zirconium up to 4100 K is given for both blackbody models. The random and systematic errors of the measured quantities are given. The values of specific heat capacity are compared with the available experimental data for the near melting stage of the liquid zirconium, obtained using a steady-state technique.     

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.     

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.     

Investigation of thermal conductivity and thermal diffusivity of liquid bismuth within the temperature range of 545–970 K

Thermal conductivity and thermal diffusivity of liquid bismuth within the temperature range from 545 K up to 970 K are investigated by the laser flash method. The measurement errors are equal to (3.5–4.5)%. Approximating equations are obtained, and the reference tables are presented for the temperature dependencies of the properties. The measurement results are compared to the published data available. The temperature dependence of the Lorentz number is calculated up to 970 K.     

The thermophysical properties of hafnium in the temperature range from 293 to 2000 K

The temperature dependences are given of enthalpy, heat capacity, mean temperature coefficient of linear expansion, density, thermal conductivity, thermal diffusivity, and emissive properties of hafnium in the temperature range from 293 to 2000 K, which are obtained as a result of analysis and simultaneous processing of literature data.     

Microsecond Laser Polarimetry for Emissivity Measurements on Liquid Metals at High Temperatures—Application to Tantalum

The aim of this work was to determine accurate and reliable thermophysical properties of liquid tantalum from melting up to temperatures of 5000 K. Temperature measurements on pulse-heated liquid metal samples reported by different authors have always been performed under the assumption of a constant emissivity over the whole liquid range because of the lack of data for liquid metals. The uncertainty in temperature measurement is reduced in this work by the direct measurement of emissivity during the experiments. The emissivity measurements are performed by linking a laser polarimetry technique with the established method for performing high speed measurements on liquid tantalum samples at high temperatures during microsecond pulse-heating experiments. A set of improved thermophysical properties for liquid tantalum, such as temperature dependences of normal spectral emissivity at 684.5 nm, heat capacity, enthalpy, electrical resistivity, thermal diffusivity, and thermal conductivity, was obtained.     

Heat capacity and thermodynamic functions of GaSe from 300 to 700 K

The heat capacity of ?-GaSe has been determined by differential scanning calorimetry in the temperature range 300–700 K. Smoothed heat capacity data have been used to evaluate the thermodynamic functions of gallium monoselenide (entropy, enthalpy increment, and reduced Gibbs energy).     

High-temperature thermodynamic properties of LuPO<Subscript>4</Subscript>

The high-temperature enthalpy of lutetium orthophosphate has been determined as a function of temperature in the range 432.92–1744.58 K using drop calorimetry. The present and earlier experimental data have been used to calculate temperature-dependent heat capacity of LuPO₄ in the range 1–1750 K.     

Graphite Melting and Properties of Liquid Carbon

The results of fast heating (by electrical pulse current) of highly oriented pyrolytic graphite specimens are presented. Experimental data are obtained for graphite melting: the enthalpy of solid and liquid phases under melting, the heat of melting, and the heat capacity of solid and liquid phases near melting. Liquid carbon resistivity is measured under fast heating of cylindrical graphite specimens in thick-walled sapphire capillary tubes. Preliminary data for the isobaric heat capacity C _p for liquid carbon up to 10,000 K and for the isochoric heat capacity C _v up to 8000 K are presented.     

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.