A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

Electron transport properties of deformed potassium and a potassium-rubidium alloy from 0.08 to 4.2 K

Measurements have been performed of electrical resistivity and thermoelectric ratioG on deformed samples of potassium as well as of on a deformed 0.077 at %KRb alloy. A large anomaly in (T) forT<0.5 K is ascribed to electrons interacting with vibrating dislocations and it is shown that the data are consistent with a model of Gantmakher and Kulesko in which the scattering arises from local phonon modes associated with the dislocations. ForT>1 K, an increase in (T) is ascribed to the suppression of phonon drag by the dislocations. The latter is qualitatively confirmed by theG measurements. A maximum inG at 0.5 K is observed when dislocations are present. The two effects in (T) outlined above are so large that the change in the electron-electron scattering contribution to due to deformation cannot be precisely determined.     

Equation of state of a3He-4He mixture near its liquid-vapor critical point

Measurements of the pressure coefficient (P/T)_,x are reported for a ³ He- ⁴ He mixture with a mole fractionX=0.805 of ³ He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval–0.50.5 and over the temperature range–0.1 t0.1, where =(– _c )/ _c andt=(T-T _c )/T _c ,with _c andT _c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (P/T)_,x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT _c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT _c closer than1 mK, (P/T)_,x along the critical isochore appears to be discontinuous atT _c ,while for the isochore / _c 0.92, (P/T)_,x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (P/T)_,x from the scaling equation of state proposed by Leung and Griffiths for ³ He- ⁴ He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (P/T)_,x along the critical isochore show excellent agreement with theory.Work supported by a grant from the National Science Foundation. A report of this work has been presented at the Washington Meeting of the APS [Bull. Am. Phys. Soc. 20, 618 (1975)].     

Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures

Using superleak condenser transducers, the velocity of second soundU ₂ has been measured near the superfluid transition temperature T in³He-⁴He mixtures with molar concentrationsX of³He of 0.0, 0.038, 0.122, 0.297, and 0.440. We have obtained the superfluid density _s/ fromU ₂ on the basis of linearized two-fluid hydrodynamics. The results for _s/ are consistent with those obtained from the oscillating disk method, as expected from two-fluid hydrodynamics. The value of _s/ at eachX could be expressed by a single power law, _s/=k, where =1-T/R, with the experimental uncertainty. It is found that the exponent is independent of concentration forX0.44 within the experimental uncertainty. This concentration independence of is in agreement with the universality concept. From the conclusion that the values of are universal forX0.44, the concentration dependence of the superfluid component _s is expressed by an empirical equation _s(X, )=²_s(0, ). It is found that corresponds to the volume fraction of⁴He in the superfluid³He-⁴He mixture. The value of is in agreement with that obtained from the measurement of the molar volume by others.This paper is based on a thesis submitted to Tokyo University of Education in partial fulfillment of the requirements for the Ph.D. degree.     

A Viscosity Equation of State for R123 in the Form of a Multilayer Feedforward Neural Network

A multilayer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation =(T, ) for R123. The results obtained are very promising, with an average absolute deviation (AAD) of 1.02% for the currently available 169 primary data points, and are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high-accuracy equation of state for the fluid to be known to convert the experimental P, T into the independent variables , T, but such equation may not be available for the target fluid. With a view to overcoming this difficulty, a viscosity implicit equation of state in the form of T=T(P, ), avoiding the density variable, is obtained using the MLFN technique, starting from the same data sets as before. The prediction accuracy achieved is comparable with that of the former equation, =(T, ).     

The Viscosity Surfaces of Propane in the Form of Multilayer Feed Forward Neural Networks

The present work focuses on the development of a viscosity equation =(,T) for propane through a multilayer feedforward neural network (MLFN) technique. Having been successfully applied to a variety of fluids so far, the proposed technique can be regarded as a general approach to viscosity modeling. The MLFN viscosity equation has been based on the available experimental data for propane: validation on the 969 primary data shows an average absolute deviation (AAD) of 0.29% in the temperature, pressure, and density range of applicability, i.e., 90 to 630 K, 0 to 60 MPa, and 0 to 730 kgm^–3. This result is very promising, especially when compared with experimental data uncertainty. The minimum amount of required data for setting up the MLFN has been investigated, to explore the minimum cost of the model. Comparisons with other viscosity models are presented regarding amount of input data, claimed accuracy, and range of applicability, with the aim of providing a guideline when viscosity has to be calculated for engineering purposes. A high accuracy equation of state for the conversion of variables from experimental P,T to operative ,T has to be provided. To overcome this requirement, two viscosity explicit equations in the form =(P,T) are also developed, for the liquid and for the vapor phases. The respective AADs are 0.58 and 0.22%, comparable with those of the former =(,T) equation. Finally, the trend of the experimental viscosity second virial coefficient is reproduced and compared with that obtained from the MLFN.     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Dynamic Behavior of a Pure Fluid at and Near Its Critical Density Under Microgravity and 1g

A new sample cell allowing accurately measurable density quenches was developed for further and systematic investigation of dynamic temperature propagation, or the piston effect. Several experiments were performed under 1g and microgravity during and in preparation for the Perseus mission in 1999. The starting temperatures ranged in the one-phase state between 1 and 1000 mK above T _c, while the density varied between 0.7 _c<<1.3 _c. The method for the determination of the isentropic difference coefficients (/T)_S, (/p)_S, and (T/p)_S is explained. The coefficients are in reasonable agreement with the equation of state for SF₆, and the difference between the ground and the microgravity experiments is discussed. The advantage of the density quench method in contrast to the temperature quench method is demonstrated, particularly with regard to the influence of convection.     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

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.     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Superconductivity and structural disorder in ion-irradiated rhenium films

Single- and polycrystalline Re films were irradiated at room temperature and liquid nitrogen temperature with 350-keV N ions and 700-keV doubly charged Ar ions. With increasing ion fluence , the ion-induced residual resistivity ₀ and the superconducting transition temperatureT _c were observed to increase. The functional behavior of ₀() and the recovery spectra are found to depend on ion species and . Annealing stages II and III are seen after low-dose N- and Ne-ion irradiation, whereas at high ion fluences stages II, IV, and V are most pronounced. Thus the increase of ₀ at low fluences is attributed to vacancies mainly, and at high fluences to the formation of extended defects. TheT _c increase at low fluences is caused by inhomogeneously distributed vacancies, and at high fluences by vacancies pinned to dislocations. Extended defects alone do not seem to have any influence onT _c . Ion-induced recrystallization processes have also been observed.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Spin Gap and Hole Pairing of Sr14−x A x Cu24O41(A = Ca and La) Single Crystals Studied by the Electrical Resistivity and Thermal Conductivity

We have measured the electrical resistivity and the thermal conductivity of Sr _14–x A _x Cu ₂₄ O ₄₁(A = Ca and La) single crystals. The Arrhenius plot of ln vs T ^–1 gives two kinds of activation energy with a boundary temperature T . The activation energy at T < T is in approximate agreement with the spin gap in the ladder estimated from the NMR measurements, suggesting that holes in the ladder are paired and localized at T < T. The observed has been analyzed to be composed of _ph , _spin and _hole due to phonons, spins and holes, respectively. The _ph exhibits a small peak at 30 K in every direction of every single-crystal. The contribution of _spin is observed along the c-axis except for x(Ca) 6, and the spin gap, which corresponds to the spin excitation from spin-singlet to spin-triplet, has been estimated to be 420 K. For x(Ca) 6, the spin gap, which corresponds to the destruction of spin-singlet pairs i. e. the dissociation of hole pairs, has been estimated from along the c-axis at T > T to decrease with increasing x(Ca).     

Clear evidence for the spin-wave energy gap in terbium

Our electrical resistivity measurements on single-crystal terbium oriented along the c-axis clearly show the spin-wave energy gap at 21.5°K. The total resistivity fits the equation =₀+2.43×10^–7 T ⁵+2.544×10^–3 T ² exp(21.5/T) µ-cm in the temperature region below 21.5°K.This project was supported by a National Research Council of Canada grant.Killam Postdoctoral Fellow.     

Equation of State for Complex Liquid Mixtures from Surface Tension

The present work shows a successful extension of previous studies to molecular liquids for which the second virial coefficients are not known. Recent advances in the statistical mechanical theory of equilibrium fluids can be used to obtain an equation of state (EOS) for compressed normal liquids and molten alkali metals. Three temperature-dependent quantities are needed to use the EOS: the second virial coefficient, B(T), an effective van der Waals covolume, b(T), and a scaling factor, (T). The second virial coefficients are calculated from a correlation that uses the surface tension, _tr, and the liquid density at the triple point. Calculation of (T) and b(T) follows by scaling. Thus, thermodynamic consistency is achieved by use of two scaling parameters (_tr, _tr). The correlations embrace the temperature range T _tr<T<T _c and can be used in a predictive mode. The remaining constant parameter is best found empirically from _tr data for pure dense liquids. The equation of state is tested on 42 liquid mixtures The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T _tr to T _c.     

Explanation of Temperature-Dependent Resistivity of Sm-Doped Cuprates by Electron–Phonon Scattering

The resistivity of electron-doped cuprate Sm_1.85Ce_0.15CuO_{4 –} is theoretically analyzed within the framework of electron–phonon i.e., Bloch–Gruneisen (BG) model of resistivity. Characteristic temperatures as the Debye temperature and the Einstein temperature were first derived from an overlap repulsive potential. The optical phonons of the oxygen-breathing mode yield a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons above 220 K. While to that, below this temperature, acoustic phonon is a major cause of resistivity. Estimated contribution to resistivity by considering both phonons i.e., _ac (acoustic phonons) and _op (optical phonons), along with the zero limited resistivity, when subtracted from single crystal data, infers a quadratic temperature dependence over most of the temperature range (25 T 300). Power temperature dependence of _diff.{=[ _exp. – ( ₀ + _e-ph(= _ac + _op))]} points the contribution of electron–electron inelastic scattering. The present analysis allows us to infer that the single crystal experimental data is well approximated within the framework of BG electron–phonon model of resistivity. Further calculations of superconducting transition temperature and isotope effect exponent from Kresin's strong coupling theory indicates that the electron–phonon interaction plays an important role in the attractive pairing mechanism.