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 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.     

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.     

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.     

An analytical equation of state for molten alkali metals

This paper brings the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range. As for normal fluids, the latent heat of vaporization and density at freezing temperature are the only inputs (scaling factors). The correspondingstates correlation of normal fluids is used to calculate the second virial coefficient,B ₂(T), of alkali metals, which is scarce experimentally and its calculation is complicated by dimer formation. Calculations of the other two temperature-dependent constants,(T) andb(T), follow by scaling. The virial coefficients of alkali metals cannot be expected to obey a law of corresponding states for normal fluids. The fact that two potentials are involved may be the reason for this. Thus, alkali metals have the characteristics of interacting through singlet and triple potentials so that the treatment by a single potential here is fortuitous. The adjustable parameter of the equation of state,, compensates for the uncertainties inB ₂(T). The procedure used to calculate the density of liquids Li through Cs from the freezing line up to several hundred degrees above the boiling temperatures. The results are within 5 %.     

Equation of state for fluid alkali metals: Binodal

The three-parameter generalized van der Waals equation of state for liquids and gases is analyzed. This equation contains the generalized expressiona/V" for the molecular pressure: here the parametern takes into account the specificity of intermolecular attractive forces for various substances. The equation is presented in the reduced form, from which follows the single-parameter law of corresponding states with the thermodynamic similarity parametern. 11 is established that for alkali metals the value of the parameter it is the same and does not depend on temperature substantially. From the given generalized equation, the expressions for the binodal (equilibrium curve of the liquid and vapor phases) are obtained. For cesium. rubidium, and potassium, the temperature dependence of density is calculated over the temperature range from their melting point to the critical point: the results of the calculations agree with experimental data. It is established that for alkali metals, the law of rectilinear diameter breaks down in the vicinity of the critical point.Paper presented al the Twelfth Symposium on Thermophysical Properties. June 19 –24, 1994, Boulder, Colorado, U.S.A.     

Shock-induced vaporization in metals

Results of well-controlled experiments on shock-induced vaporization studies in zinc, indium, and aluminum are presented. A titanium alloy impact at a velocity of 10.4 km/s will melt these materials totally. The expansion products upon release will consist of liquid–vapor mixtures. The ratio of liquid to vapor in the mixture depends on the material and also on the degree of expansion upon release. The impact generated debris propagates a gap dimension up to 125 mm before it stagnates against a stationary witness plate. The non-uniform spatial loading on the witness plate is determined using multiple velocity interferometers. Radiographic measurements of the debris cloud are also taken before it stagnates against the witness plate. Both radiographic and the velocity interferometer measurements suggest lateral and axial expansion. We have identified that the kinetics of the vaporization process can be related to the energy of the material shocked to the high-pressure state. In particular, the energy E of the material in the shocked state is expressed in units of the energy E_v required to vaporize a gram of material from room temperature. Results of these experiments indicate that the rate of vaporization is strongly dependent on E/E_v as it is increased by an order of magnitude from 1 to 10.     

Simulation of shock-induced fragmentation and vaporization in metals

Simulations of experiments on shock-induced melting, fragmentation and vaporization in aluminum and zinc targets are presented. A titanium impactor moves at a velocity of 10.4 km/s and causes melting of these materials in a shock wave. Under rarefaction the thermodynamic path crosses the liquid–vapor coexistence boundary and enters into a metastable liquid region. Liquid in a metastable state may undergo either liquid–vapor phase separation or mechanical fragmentation. Homogeneous nucleation theory and the mechanical fragmentation criterion of Grady are taken into account to control the kinetics of these processes in our model. The first effect dominates in the vicinity of the critical point, the second one – at lower temperatures. Analysis of phase transitions and kinetics of phase separations is performed using a thermodynamically complete equation of state with stable and metastable states for all materials under consideration.     

The critical constants of long-chain normal paraffins

Because of the recent availability of the critical constants of normal alkanes up to octadecane, some modifications in the estimation procedures for the critical constants have become necessary. It has been shown that the equation of Ambrose for the critical temperature of normal alkanes leads to the result that as n , the limiting value for the critical temperature is equal to the limiting value for the normal boiling point and the limiting value for the critical pressure is 1 atm. Currently, the CH₂ increment for the critical volume is considered constant. The recent data of Teja have shown that the CH₂ increment increases indefinitely in a homologous series until the critical volume reaches its limiting value. This has made the current procedure for estimating the critical volume obsolete. Taking into account the new measurements of Teja, we have now developed new equations for estimating the critical constants. The limiting values for an infinitely long alkyl chain for T _b, T _c, P _c, and V _c have been found to be 1021 K, 1021 K, 1.01325 bar, and 18618 cm³ · mol^–1, respectively. These new concepts have been applied to the estimation of various properties other than the critical constants.Nomenclature M Molar mass, kg·mol ^–1 - V _c Critical volume, cm³·mol^–1 - V ₁ Saturated liquid volume, cm³·mol^–1 - P _c Critical Pressure, bar - T _c Critical temperature, K - T _b Normal boiling point, K - T _B Boyle temperature, K - T _A Temperature at which the third virial coefficient is zero, K - V _c Limiting value of critical volume = 18,618 cm³ · mol^–1 - P _c Limiting value of critical pressure=1.01325 bar - T _c Limiting value of critical temperature = 1021 K - T _b Limiting value of normal boiling point = 1021 K - P _b Pressure at the normal boiling point, 1 atm - Z _c Critical compressibility factor - Z _c Limiting value for the critical compressibility factor = 0.22222 - R Gas constant, 83.1448×10^–6m³ · bar · K^–1 · mol^–1 - Acentric factor - X (T _c–T _b)/T _c - X ₁ (T _c–T)/T _c - X ₂ 1–(T _B/T)^5/4 - X ₃ 1–(T _A/T)^5/2 - Y P _c/RT _c - Surface tension, mN · m^–1 - B Second virial coefficient, cm³ · mol^–1 - B Limiting value for the second virial coefficient = –30,463 cm³ · mol^–1 - C Third virial coefficient, cm⁶ · mol^–2 - C _b Third virial coefficient at the normal boiling point, cm⁶ · mol^–2 - C _c Third virial coefficient at the critical temperature, cm⁶ · mol^–2 - C _B Third virial coefficient at the Boyle temperature, cm⁶ · mol^–2 - H _vb Enthalpy of vaporization at the normal boiling point, kJ · mol^–1 - n Number of carbon atoms in a homologous series - p Platt number, number of C-C-C-C structural elements - a, b, c, d, e, etc Constants associated with the specific equation - T _c ^* , T _b ^* , P _c ^* , V _c ^* , etc. Dimensionless variables     

Phonon dispersion in alkali metals and their equiatomic sodium-based binary alloys

In the present article, the theoretical calculations of the phonon dispersion curves (PDCs) of five alkali metals viz. Li, Na, K, Rb, Cs and their four equiatomic sodium-based binary alloys viz. Na_0.5Li_0.5, Na_0.5K_0.5, Na_0.5Rb_0.5 and Na_0.5Cs_0.5 to second order in a local model potential is discussed in terms of the realspace sum of the Born von Karman central force constants. Instead of the concentration average of the force constants of pure alkali metals, the pseudo-alloy-atom (PAA) is adopted to directly compute the force constants of the four equiatomic sodium based binary alloys and was successfully applied. The exchange and correlation functions due to the Hartree (H) and Ichimaru-Utsumi (IU) are used to investigate the influence of the screening effects. The phonon frequencies of alkali metals and their four equiatomic sodium-based binary alloys in the longitudinal branch are more sensitive to the exchange and correlation effects in comparison with the transverse branches. The PDCs of pure alkali metals are found in qualitative agreement with the available experimental data. The frequencies in the longitudinal branch are suppressed rather due to IU-screening function than those due to static H-screening function.     

First-Principles Calculation of the Air–Water Second Virial Coefficient

Recent theoretical work has produced quantitatively accurate potential-energy surfaces for water with common gases. These pair potentials have been used to calculate second interaction virial coefficients with an accuracy superior to that obtained by most experiments. In this work, results for water–nitrogen, water–oxygen, and water–argon are combined to calculate an effective second virial coefficient for water with air. The results are in agreement with the existing experimental data, but they cover a wide range of temperatures while the experimental data extend only from 253 to 348 K. These results will be useful for humidity standards and other applications requiring thermodynamic properties of moist air.     

Error in the Second Mixed Virial Coefficient for Moist Nitrogen

Calculations are presented on the random and systematic components of the error in the second mixed virial coefficient for moist nitrogen B_aw. In the temperature range 9–50°C, the total error for the mean value of B_aw is not more than ±14% (three standard deviations). __________ Translated from Izmeritel'naya Tekhnika, No. 8, pp. 68–71, August, 2005.     

Viscosity and thermal conductivity of binary eutectics of alkali metals in the vapor phase

Values calculated for the dynamic viscosity and thermal conductivity are presented for vapors of binary eutectics of the alkali metals at temperatures from 800 to 1500 K and at pressures from 100 to 8×10⁵ Pa. Data are presented for the vapors of the systems Li + Na, Na + Rb, Na + Cs, K + Rb, K + Cs, Na + K, and Rb + Cs. The values of the concentrations of the five components in the vapor phase of each binary eutectic are also presented. The accuracy of the calculated viscosities is estimated to be within 4–5% and the accuracy of the calculated thermal conductivities is estimated to be within 8–10%.     

超流氦蒸发焓计算方法的对比分析

为准确计算超流氦蒸发焓,比较了Watson方程、WVK方程、FL方程、TS方程、H.W.Xiang方程以及Somayajulu方程的适用性,并对系统参数作了回归分析.结果表明,Watson方程、FL方程、6参数TS方程、H.W.Xiang方程和Somayajulu方程具有较高的计算精度.     

Compression factor and vapor pressure of bromotrifluoromethane in the temperature range 245–393 K at pressures up to 12 MPa

The compression factors and vapor pressures have been measured on bromotrifluoromethane using a Burnett apparatus. The results on the compression factor cover the range of temperatures 263 to 393 K and of pressures 0.14 to 11.6 MPa, corresponding to a density variation from 7 to 1367 kg· m^–3. The experimental uncertainty of these 176 measurements of compression factor was estimated to be 0.2%. Thirty measurements of vapor pressure were made for temperatures 245 to 339 K, with an experimental uncertainty of 0.1%. Based on these results, the second virial coefficients were determined for temperatures 293 to 393 K.     

The infrared absorption coefficient of alkali halides

Available data on the absorption coefficient of six alkali halides, LiF, NaF, NaCl, KCl, KBr, and KI, were surveyed, evaluated, and analyzed. For the multiphonon absorption region, an equation was formulated to describe the absorption coefficient as a function of both frequency and temperature. Constants in the equation were determined based on data fitting calculations and empirical correlations. The Urbach Rule is applied to the uv absorption edge of the transparent region, and our equation is considered as its counterpart in the IR absorption edge. Comparing with Deutsch's exponential equation, the present expression includes the temperature as an additional independent variable. The calculated values are in concordance with the experimental data.     

A nonlinear regression analysis for estimating low-temperature vapor pressures and enthalpies of vaporization applied to refrigerants

A new method is presented to extrapolate experimental vapor pressures down to the triple Point. The method involves a nonlinear regression analysis based on the Clausius Clapeyron equation and a simple relation for the enthalpy of vaporization Triple-point pressures and vapor pressures up to 0.1 0.2 MPa are estimated for R125, R32, R143a, R134a, R152a, R123, R124, and ammonia; they generally agree with available experimental data within their uncertainty, Equations for the enthalpy of vaporization which describe this property fairly well at low temperatures are obtained as a byproduct.