Freezing Line Research Articles

Thermodynamic Properties of Ethylene from the Freezing Line to 450 K at Pressures to 260 MPa

A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of ethylene from the freezing line to 450 K at pressures to 260 MPa is presented. Independent equations for the vapor pressure for the saturated liquid and vapor densities as functions of temperature, and for the ideal gas heat capacity are also included. The fundamental equation was selected from a comprehensive function of 100 terms on the basis of a statistical analysis of the quality of the fit. The coefficients of the fundamental equation were determined by a weighted least-squares fit to selected P-ρ-T data, saturated liquid, and saturated vapor density data to define the phase equilibrium criteria for coexistence, Cv data, velocity of sound data, and second virial coefficient data. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (Cv), isobaric heat capacity (Cp), and velocity of sound are included. Tables of thermodynamic properties of ethylene are given for liquid and vapor states within the range of validity of the fundamental equation. The fundamental equation reported here may generally be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ±3%, and velocity of sound values within ±1%. Comparisons of calculated properties to experimental data are included to verify the accuracy of the formulation.

Thermodynamics using effective spherical potentials for CO2 anisotropies

We examine the fluid thermodynamics of a model homonuclear diatomic system with anisotropies characteristic of CO2. The density (CO2 densities) and temperature regime is 1.6 g/cm3≲ρ≲2.6 g/cm3 and 1000 K≲T≲7000 K. Extensive molecular dynamics data for the model equation of state are presented. Comparisons are then made to the thermodynamics from three effective spherical potentials; the potential median, the radial median, and an exponential-six with parameters adjusted to best fit the true thermodynamics. The two median potentials typically give 3% agreement for the higher temperature fluid with a 5%–10% comparison nearer the freezing line for both pressure and internal energy while the fit is good to 3% or better. Thus there exists an effective spherical potential that very accurately models the thermodynamics of dense fluid CO2, a system whose potential energy in the repulsive region varies by three to four orders of magnitude as a function of angles with fixed center of mass separation. The median averages give an excellent representation of this effective spherical potential.

Shock temperatures and melting in CsI.

Shock-temperature measurements have been made on CsI up to 10 800 K and 0.9 Mbar. Melting has been observed to occur at 0.25 Mbar and 3500 K. A simple model for melting based on the packing of soft spheres is shown to adequately describe the data. The results suggest that in the liquid along the freezing line there is a gradual pressure-induced change from an open NaCl-like structure to one in which atoms are arranged as in a close-packed monatomic fluid. Above 5000 K, electronic excitation is observed to occur due to the high shock temperatures generated and the narrowing of the CsI band gap under pressure.

Ultrasonic speeds and thermodynamics for binary solutions of n-alkanes under high pressures

Ultrasonic speeds and densities for binary solutions of n-alkanes: [ n-hexane+ n-decane] , [ n-octane+ n-dodecane] and [ n-decane+ n-tetradecane] were measured at 298.15 K under pressures up to the freezing line or 100 MPa. These results are used to calculate the thermodynamic properties. An examination of these quantities offers powerful clues to the understanding of the character of binary solutions under high pressure.

A perturbation theory of classical equilibrium fluids

A new perturbation theory which is reliable over a wide fluid region is presented. The new theory reduces to the theory of Weeks, Chandler, and Anderson at densities near or below the triple point density of a simple fluid but it can also accurately predict thermodynamic properties at higher densities near the freezing line of the fluid. This is done by employing an optimized reference potential whose repulsive range decreases with increase in density. Thermodynamic properties for Lennard-Jones, exponential-6, and inverse nth-power (n=12, 9, 6, and 4) potentials have been calculated from the new theory. Comparison of the calculated data with available Monte Carlo simulations and additional simulations carried out in this work shows that the theory gives excellent thermodynamic results for these systems. The present theory also gives a physically reasonable hard-sphere diameter over the entire fluid range.

Stationary nonequilibrium states by molecular dynamics. Fourier's law

We have developed a technique to produce stationary nonequilibrium states in a molecular-dynamics system; this method is based on the introduction of stochastic boundary conditions to simulate the contact with a thermal wall. The relaxation times involved in such contact are short enough (\ensuremath{\sim}${10}^{\ensuremath{-}11}$ sec) to make the technique suitable for computer experiments. The method allows the simulation of bulk properties in a system coupled with a heat reservoir and the study of the local thermodynamical equilibrium. Furthermore, it gives a physical description of the heat transfer near a thermal wall. The method has been applied to simulate high thermal gradients in a region of dense fluids ranging from the gas-liquid coexistence line to the freezing line, to check the validity of the linear thermal response (Fourier's law). We have found that the linear region extends at least up to gradients of the order of 1.8\ifmmode\times\else\texttimes\fi{}${10}^{9}$ K/cm for argon. In the bulk region where boundary effects are negligible we have verified the validity of the local equilibrium hypothesis for all simulated gradients.

Universality of the bridge functions and a semiempirical freezing criterion in two and three dimensions

A model for systems interacting via soft inverse-power potentials enables one to express the bridge function at the origin, $B(O)$, directly in terms of the equation of state, and to find its physical meaning. The Lindemann, Ross, and van der Waals empirical melting criteria are unified by the empirical finding that $B(O)$, calculated along the freezing line, is nearly independent of the pair potential and is nearly the same in two and three dimensions.

The density dependence of the self-diffusion coefficient of liquid methane

Self-diffusion coefficients for liquid methane obtained by the NMR spin-echo technique are reported at 110, 140 and 160 K. The density range extends to the freezing line at 110 and 140 K, and to 30 mol/dm 3 at 160 K. Using the hard sphere diameter as a single temperature dependent parameter it was found that the reduced diffusivity isotherms fall on a common curve when plotted against reduced density [ n ∗#620.26, 0.58⩽T r⩽1.70 ]. Literature viscosities could also be correlated in this way using diameters obtained from the diffusion data. The experimental results are in good agreement with molecular dynamics calculations for the hard sphere fluid, except at densities above n ∗ = 0.87 . This difference at high densities is similar to deviations from the rough hard sphere model observed for more complex molecular liquids (CCl 4, C 6H 6). The diffusion data are also compared with the results of molecular dynamics and other calculations for more sophisticated potential models.

Variational equation of state and entropy of liquid argon

Two consequences of Gibbs-Bogoliubov variational theory are examined as applied to liquid argon: the choice of a hard-sphere reference system leads to an equation of state if the packing fraction is used as the variational parameter, the non-ideal part of the entropy is only a function of eta . Calculations are performed along the freezing and vapour-pressure lines. Excellent agreement with experimental results is obtained if the Lennard-Jones potential is regarded as an effective pair potential and its parameters are appropriately chosen, and for the hard-sphere reference system the empirical radial distribution function proposed by Verlet and Weis (1972) is used together with the Helmholtz free energy derived from the Carnahan and Starling equation of state (1969).

Dense-fluid shear viscosity via nonequilibrium molecular dynamics

A novel fluid-transport calculation by computer simulation, via nonequilibrium molecular dynamics, of laboratory methods of transport measurement is described. Shear viscosity of soft-sphere (${r}^{\ensuremath{-}12}$ potential) and Lennard-Jones particles (${r}^{\ensuremath{-}12}\ensuremath{-}{r}^{\ensuremath{-}6}$ potential) has been obtained from molecular dynamic modeling of Couette flow. Soft-sphere deviations from Enskog theory are similar to those found for hard spheres by Alder, Gass, and Wainwright, using time-correlations of equilibrium molecular dynamic system fluctuations. For the Lennard-Jones shear viscosity near the triple-point region, there is agreement between the equilibrium calculation of Levesque, Verlet, and Kurkijarvi and the nonequilibrium results using 108 atoms in a cube. However, systems two and three cubes wide give lower results, which, when extrapolated with inverse width, yield close agreement with the experimental argon shear viscosity. Comparison of the Lennard-Jones shear viscosity with experimental argon data along the saturated vapor-pressure line of argon confirms our successful simulation of macroscopic viscous flow with few-particle nonequilibrium molecular dynamic systems. A new result of the nonequilibrium molecular dynamics is the characterization of nonequilibrium distribution functions, which might provide the basis for a perturbation theory of transport. Since momentum transport is primarily accomplished by the repulsive potential core for high temperatures, the Lennard-Jones shear viscosity must behave like the soft-sphere system for high temperatures [viscosity divided by ${(\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e})}^{\frac{2}{3}}$ is a function of density divided by ${(\mathrm{temperature})}^{\mathrm{\textonequarter{}}}$]. In fact, the calculated excess shear viscosity (that part above the zero-density temperature dependence) has been successfully correlated in terms of the 12th-power scaling variables for temperatures as low as the critical value (along the freezing line). The utilization of soft-sphere scaling variables yields relatively simple functions for describing both the excess shear viscosity and the thermal-conductivity behavior throughout the fluid phase. The introduction of these scaling variables also clearly reveals two features: (i) weak temperature dependence, and (ii) the sign of the temperature derivative at constant density (negative for shear viscosity and positive for thermal conductivity). While both of these features have been experimentally observed in simple fluid experimental data, their cause has not been previously traced to the dominance of the core potential. Thus, the soft-sphere scaling variables should be useful for correlating experimental data.

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63 K to 2000 K with Pressures to 10,000 Bar

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000 K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity (Cv), isobaric heat capacity (Cp), velocity of sound, the isotherm derivative (∂P/∂ρ)τ, and the isochor derivative (∂P/∂T)ρ. The thermodynamic property tables are based on an equation of state, P=P (ρ,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-ρ-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-ρ-T data and, simultaneously, to Cv data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.

Near Surface Soil Temperature Measurements At Resolute Bay, Northwest Territories

Based on daily readings 1951-1955 by meteorological observers at Resolute, supplemented by author's measurements in summers 1953-1955 and winter 1953-1954. Pt. 1 concerns soil temperatures within the six-ft. overburden of frozen gravel and shattered rock overlying limestone bedrock. Daily, monthly and annual average soil temperatures and the influence on them of air temperatures, isolation, and precipitation are discussed. Pt. 2 is a preliminary report on a special study made in fall 1955 on the freezeback in the active layer. Readings were taken at four-hourly intervals, Aug. 28-Oct. 1. The period of the "zero curtain" (period necessary for soil water to freeze) penetration of the 32 F freezing line, and moisture content and migration are discussed.

The melting point diagram of the two‐component system diphenylamine‐acetamide

AbstractThe melting point curve of the binary system diphenylamine‐acetamide has been investigated.The freezing line for the equilibrium Sacetamide ⇋ L has an inflexion point. Probably a metastable separation into two liquid phases would occur below the freezing line. In practice this separation itself has not been observed.

凍上の實驗的研究

This investigation was carried out in order to co_??_firm the theory that the frost heaving is caused by the ice filaments occured under the ground. An apparatus was designed for producing the frost heaving and was used in the cold chamber belonging to the Low Temperature Laboratory.The paocess of the segregation of ice in the f_??_ozen soil is found to be as follows. As the freezing of soil proceeds, hair cracks. take place just below the freezing line, the cracks are filled with ice, thin ice layers are formed, they becomes thicker, the next cracks take place below the ice layers thus produced, the second cracks are again filled with ice. When the freezing line stops to descend for a long while and the water is continuously supplied from the unfrozen soil below, the ice layers grow into thick ones which the composed of ice filaments.Adjusting the temperature of the atmosphere and that of subgrade water, any specified form of segregation of ice are produced in the laboratory.