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Molten salts thermodynamic properties, discussing pure salts corresponding states and binary mixtures conformal solution theories, using model ionic melt
A previous calculation of the thermodynamic properties of interstitial solid solutions based on the technique of Kirkwood expansions has been extended to include the effects of second nearest neighbor solute atom mutual interactions. The error inherent in the first order (or quasi-chemical) counting of the degeneracy of the solution crystal is avoided. It is shown that, at high temperatures, even strong second nearest neighbor solute mutual interactions have a negligible effect on the entropy of the solution and a small, temperature-dependent effect on the solute partial enthalpy.
The development of thermodynamics and statistical mechanics is very important in the history of physics, and it underlines the difficulty in dealing with systems involving many bodies, even if those bodies are identical. Macroscopic systems of atoms typically contain so many particles that it would be virtually impossible to follow the behavior of all of the particles involved. Therefore, the behavior of a complete system can only be described or predicted in statistical ways. Under a grant to the NASA Lewis Research Center, scientists at the Case Western Reserve University have been examining the use of modern computing techniques that may be able to investigate and find the behavior of complete systems that have a large number of particles by tracking each particle individually. This is the study of molecular dynamics. In contrast to Monte Carlo techniques, which incorporate uncertainty from the outset, molecular dynamics calculations are fully deterministic. Although it is still impossible to track, even on high-speed computers, each particle in a system of a trillion trillion particles, it has been found that such systems can be well simulated by calculating the trajectories of a few thousand particles. Modern computers and efficient computing strategies have been used to calculate the behavior of a few physical systems and are now being employed to study important problems such as supersonic flows in the laboratory and in space. In particular, an animated video (available in mpeg format--4.4 MB) was produced by Dr. M.J. Woo, now a National Research Council fellow at Lewis, and the G-VIS laboratory at Lewis. This video shows the behavior of supersonic shocks produced by pistons in enclosed cylinders by following exactly the behavior of thousands of particles. The major assumptions made were that the particles involved were hard spheres and that all collisions with the walls and with other particles were fully elastic. The animated video was voted one of two winning videos in a competition held at the meeting of the American Physical Society's Division of Fluid Dynamics, held in Atlanta, Georgia, in November 1994. Of great interest was the result that in every shock there were a few high-speed precursor particles racing ahead of the shock, carrying information about its impending arrival. Most recently, Dr. Woo has been applying molecular dynamics techniques to the problem of determining the drag produced by the space station truss structure as it flies through the thin residual atmosphere of low-Earth orbit. This problem is made difficult by the complex structure of the truss and by the extreme supersonic nature of the flow. A fully filled section of the truss has already been examined, and drag predictions have been made. Molecular dynamics techniques promise to make realistic drag calculations possible even for very complex partially filled truss segments flying at arbitrary angles.
A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).
Independent differential relationship, virial theorem and linear dependence set among thermodynamic functions in statistical atom model for arbitrary temperature
The gap in explicit resolution of phenomena between global climate models and cloud resolving models is shrinking at a steady pace with global integrations of several km in resolution now practical for at least some time scales. In moving toward finer resolution the long standing problem of convective parameterization is being examined along with the assumption of convective quasi-equilibrium and how this can be reconciled with the stochastic and intermittent nature of convection. In this context we examine the nature of parameterized convection in the NASA Goddard Earth Observing System (GEOS-5) Atmospheric General Circulation Model. Our analysis uses both coarse (2.5 degree) and fine scale 0.25 degree spatial resolution integrations. Two basic formulations are compared: the default option is the Relaxed Arakawa-Schubert (RAS) scheme which invokes a sequence of linearly entraining plumes and quasi-equilibrium closure. An optional modification of this method (the "Stochastic Tokioka" constraint) places a random lower limit on plume entrainment. An alternative representation is the Kain-Fritsch parameterization which was originally developed for mesoscale numerical modeling strategies. Here entrainment is determined by a crude buoyancy sorting approach that allows the plume spectrum to be more responsive to ambient vertical stratification of moisture. Diagnostics of the model behavior are referenced to recent observational evidence of continuous phase transition behavior. In particular we examine the relationship between column water vapor and probablility of convective presence and intensity. Sensitivity of the statistics of convective behavior to parcel mixing/entrainment formulations and parcel initial thermodynamics are considered. Observational statistics from A-Train and TRMM sensors provide validation of the model integrations.
Theoretical models of stellar atmospheres and the process of forming a spectrum are reviewed with particular reference to the spectra of B stars. In the case of classical models the stellar atmosphere is though to consist of plane parallel layers of gas in which radiative and hydrostatic equilibrium exists. No radiative energy is lost or gained in the model atmosphere, but the detailed shape of the spectrum is changed as a result of the interactions with the ionized gas. Predicted line spectra using statistical equilibrium local thermodynamic equilibrium (LTE), and non-LTE physics are compared and the determination of abundances is discussed. The limitations of classical modeling are examined. Models developed to demonstrate what motions in the upper atmosphere will do to the spectrum and to explore the effects of using geometries different from plane parallel layer are reviewed. In particular the problem of radiative transfer is addressed.
The fluctuation of energy is discussed in all thermodynamics textbooks because of the crucial role it plays in bringing to light the statistical uncertainties of all thermodynamic quantities.
NASA's Space Shuttle utilizes atmospheric thermodynamic properties to evaluate structural dynamics and vehicle flight performance impacts by the atmosphere during ascent. Statistical characteristics of atmospheric thermodynamic properties at Kennedy Space Center (KSC) used in Space. Shuttle Vehicle assessments are contained in the Cape Canaveral Air Force Station (CCAFS) Range Reference Atmosphere (RRA) Database. Database contains tabulations for monthly and annual means (mu), standard deviations (sigma) and skewness of wind and thermodynamic variables. Wind, Thermodynamic, Humidity and Hydrostatic parameters 1 km resolution interval from 0-30 km 2 km resolution interval 30-70 km Multiple revisions of the CCAFS RRA database have been developed since initial RRA published in 1963. 1971, 1983, 2006 Space Shuttle program utilized 1983 version for use in deriving "hot" and "cold" atmospheres, atmospheric density dispersions for use in vehicle certification analyses and selection of atmospheric thermodynamic profiles for use in vehicle ascent design and certification analyses. During STS-114 launch preparations in July 2005 atmospheric density observations between 50-80 kft exceeded density limits used for aerodynamic ascent heating constraints in vehicle certification analyses. Mission specific analyses were conducted and concluded that the density bias resulted in small changes to heating rates and integrated heat loading on the vehicle. In 2001, the Air Force Combat Climatology Center began developing an updated RRA for CCAFS.
First order statistical model for temperature dependence of carbon activity in austenite
Results of quantum statistical mechanical calculations and thermodynamic evaluation of the structure of H2CO3 and its stability against dissociation are reported. Under temperature and pressure conditions near the surface of Venus, carbonic acid would predominatly dissociate into H2O and CO2 and, hence, could not contribute to any significant absorption there.
A description is given of the methods used to establish the statistical parameters and models for wind and various thermodynamic quantities at an altitude of 0-70 km for nine geographical locations. It is noted that wind is modeled as a vector quantity using the bivariate normal probability function. With the five parameters of the bivariate normal distribution, the distribution for wind speed is derived as a generalized Rayleigh distribution. In addition, the frequency of wind direction is derived, and the conditional distribution of wind speed given the wind direction is derived. It is pointed out that these and other wind models are consistent with the rigorous mathematical properties of the bivariate normal probability theory. The thermodynamic quantities are consistent with the hydrostatic equation and the equation of state for the mean values. With these methods, many statistical relationships can be derived.
A quasiparticle ensemble ( Q ensemble) is constructed in which the number of quasiparticles with momentum k in the ensemble is conserved. The thermodynamic properties of this ensemble are related to those of the grand canonical ensemble. By comparison with explicit microscopic predictions of the theory, it is shown that this formulation is necessary if the third law of thermodynamics is to be satisfied, and that in this case, the Landau theory of a Fermi liquid follows as a natural consequence.
A fully second-order closure model for turbulent reacting flows is suggested based on Favre statistics. For diffusion flames the local thermodynamic state is related to single conserved scalar. The properties of pressure fluctuations are analyzed for turbulent flows with fluctuating density. Closure models for pressure correlations are discussed and modeled transport equations for Reynolds stresses, turbulent kinetic energy dissipation, density-velocity correlations, scalar moments and dissipation are presented and solved, together with the mean equations for momentum and mixture fraction. Solutions of these equations are compared with the experimental data for high heat release free mixing layers of fluorine and hydrogen in a nitrogen diluent.
A fully second-order closure model for turbulent reacting flows is suggested based on Favre statistics. For diffusion flames the local thermodynamic state is related to a single conserved scalar. The properties of pressure fluctuations are analyzed for turbulent flows with fluctuating density. Closure models for pressure correlations are discussed and modelled transport equations for Reynolds stresses, turbulent kinetic energy dissipation, density-velocity correlations, scalar moments and dissipation are presented and solved, together with the mean equations for momentum and mixture fraction. Solutions of these equations are compared with the experimental data for high heat release free mixing layers of fluorine and hydrogen in a nitrogen diluent.
The Kennedy Space Center (KSC) Range Reference Atmosphere (RRA) is a statistical model that summarizes wind and thermodynamic atmospheric variability from surface to 70 km. The National Aeronautics and Space Administration's (NASA) Space Shuttle program, which launches from KSC, utilizes the KSC RRA data to evaluate environmental constraints on various aspects of the vehicle during ascent. An update to the KSC RRA was recently completed. As part of the update, the Natural Environments Branch at NASA's Marshall Space Flight Center (MSFC) conducted a validation study and a comparison analysis to the existing KSC RRA database version 1983. Assessments to the Space Shuttle vehicle ascent profile characteristics were performed by JSC/Ascent Flight Design Division to determine impacts of the updated model to the vehicle performance. Details on the model updates and the vehicle sensitivity analyses with the update model are presented.
The 2006 Cape Canaveral Air Force Station (CCAFS) Range Reference Atmosphere (RRA) is a statistical model summarizing the wind and thermodynamic atmospheric variability from surface to 70 kin. Launches of the National Aeronautics and Space Administration's (NASA) Space Shuttle from Kennedy Space Center utilize CCAFS RRA data to evaluate environmental constraints on various aspects of the vehicle during ascent. An update to the CCAFS RRA was recently completed. As part of the update, a validation study on the 2006 version was conducted as well as a comparison analysis of the 2006 version to the existing CCAFS RRA database version 1983. Assessments to the Space Shuttle vehicle ascent profile characteristics were performed to determine impacts of the updated model to the vehicle performance. Details on the model updates and the vehicle sensitivity analyses with the update model are presented.
Magnitudes and scales of atmospheric perturbations about the monthly mean for the thermodynamic variables and wind components are presented by month at various latitudes. These perturbation statistics are a revision of the random perturbation data required for the global scale atmospheric model program and are from meteorological rocket network statistical summaries in the 22 to 65 km height range and NASA grenade and pitot tube data summaries in the region up to 90 km. The observed perturbations in the thermodynamic variables were adjusted to make them consistent with constraints required by the perfect gas law and the hydrostatic equation. Vertical scales were evaluated by Buell's depth of pressure system equation and from vertical structure function analysis. Tables of magnitudes and vertical scales are presented for each month at latitude 10, 30, 50, 70, and 90 degrees.