Thermodynamic properties are essential for the design of chemical processes, and they are most useful in the form of an equation of state (EOS). The motivating force of this work is the need for accurate prediction of the phase behavior and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis in the improved Most General Cubic Equation of State theory and forecasts the behavior of pure molecules over a broad range of fluid densities at both high and low pressures in both single and multiphase regions. With the new EOS, it is possible to make accurate estimations for saturated densities and vapor pressures. The density dependence of the equation results from fitting isotherms of test substances while reproducing the critical point, and enforcing the critical point criteria. The EOS includes analytical functions to fit the calculated temperature dependence of the new EOS parameters.

Thermodynamic properties are essential for the design of chemical processes, and they are most useful in the form of an equation of state (EOS). The motivating force of this work is the need for accurate prediction of the phase behavior and thermophysical properties of natural gas for practical engineering applications. This thesis presents a new cubic EOS for pure argon. In this work, a theoretically based EOS represents the PVT behavior of pure fluids. The new equation has its basis in the improved Most General Cubic Equation of State theory and forecasts the behavior of pure molecules over a broad range of fluid densities at both high and low pressures in both single and multiphase regions. With the new EOS, it is possible to make accurate estimations for saturated densities and vapor pressures. The density dependence of the equation results from fitting isotherms of test substances while reproducing the critical point, and enforcing the critical point criteria. The EOS includes analytical functions to fit the calculated temperature dependence of the new EOS parameters.

A multiparametric and fundamental equation of state is presented for the fluid thermodynamic properties of helium. The equation is valid for temperatures from the λ- line (~2.17 K) to 1500 K and for pressures up to 2000 MPa. The formulation can calculate all thermodynamic properties, including density, heat capacity, speed of sound, energies, entropy and saturation properties. A new equation of state is necessary to overcome difficulties associated with the current standard in the asymptotic region between the λ -line and 3 K and also difficulties related to lack of data, extrapolation performance, and accuracy at higher temperatures. Below 50 K, the uncertainties in density are 0.20% at pressures up to 20 MPa. From 50 K to 200 K the uncertainties decrease to 0.05 % at pressures up to 80 MPa. At higher temperatures the uncertainties in density are 0.02 % up to pressures of 80 MPa. At all temperatures and at pressures higher than listed here, the uncertainties may increase to 0.3% in density. The uncertainties in the speed of sound are 0.02%. The uncertainties in vapor pressure are less than 0.02% and for the heat capacities are about 2%. Uncertainties in the critical region are higher for all properties except vapor pressure.

The speed of sound in various gases between 250 and 350 K has been obtained from measurements of the frequencies of the radial modes of spherical acoustic resonators; two resonators were used and both apparatus are described. The radius of each resonator was obtained from the speed of sound in argon. Measurements with the 60 mm radius resonator were made below 115 kPa on the six substances: n-butane; methyipropane; n-pentane; methylbutane; dimethylpropane; and, methanol. Perfect gas heat capacities and second and third acoustic virial coefficients for these substances have been calculated from the results, and estimates are given for the second and third (p,Vm,T) virial coefficients. A sealed resonator of radius 40 mm was used to obtain acoustic results below 7 MPa on argon and the industrially important gases methane, a natural gas, and air. Measurements with argon provided an opportunity to study the model used to account for acoustic energy losses in the resonator. The speed of sound, for the industrially important gases, was compared with estimates obtained from several equations of state.

No description available.

The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state (EOS). One way to facilitate the mapping of observables to the EOS is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EOS. We use mock EOS that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables of mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EOS with five fiducial densities between similar to 1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EOS to within less than 0.5 km for the extreme mock EOS and to within less than 0.12 km for 95% of a sample of 42 proposed, physically motivated EOS. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M-circle dot and the moment of inertia of a 1.338 M-circle dot. neutron star to within less than 10% for 95% of the proposed sample of EOS.

Thesis (Ph.D.)--Auburn University, 2007. / Abstract. Includes bibliographic references (ℓ. 163-)

Black hole-neutron star (BH-NS) mergers are promising candidates for the progenitors of short-duration gamma-ray bursts (GRBs). With the right initial conditions, the neutron star becomes tidally disrupted, eventually forming a dense, accreting disk around the black hole. The thermal energy of this black hole-disk system can be extracted via neutrino processes, while the spin energy of the black hole can be extracted via magnetic processes. Either (or even a combination of these) processes could feasibly power a relativistic jet with energy ≥~ 10 49 erg and duration ≤~ 2 s, hence producing a short-duration GRB. In this thesis, we investigate BH-NS mergers with three-dimensional, pseudo-Newtonian simulations. We use the simulation code Charybdis, which uses a dimensionally-split, reconstruct-solve-average scheme (i.e. using Riemann solvers) to solve the Euler equations of hydrodynamics. Although the code is based on a Newtonian framework, it includes pseudo- Newtonian approximations of local gravitational wave effects and the innermost stable circular orbit of the BH, which are both general relativistic phenomena. The code also includes the effects of global neutrino emission, shear viscosity and self-gravity. This thesis comprises two main projects. The first project is a parameter study of the equation of state, which encapsulates the relationship between the pressure of a fluid and its other thermodynamic properties. Although the EOS is well understood at low densities, it is yet to be constrained at supranuclear densities, and so must be treated as a parameter in numerical studies of BH-NS mergers. We present simulations using three existing EOSs, in order to investigate their effect on the merger dynamics. We find that the EOS strongly influences the fate of the NS, the properties of the accretion disk, and the neutrino emission. In the second project, we begin upgrading Charybdis to include magnetic field effects, in order to investigate the magnetic processes described above. We implement existing reconstruction and Riemann solver algorithms for the equations of magnetohydrodynamics, and present 1D tests to compare them. When modelling magnetic fields in more than one dimension, we must also deal with the divergence-free condition, ∇. B = 0. We develop a new constrained transport algorithm to ensure our code maintains this condition, and present 2D tests to confirm its accuracy. This algorithm has many advantages over existing ones, including easier implementation, greater computational efficiency and better parallelisation. Finally, we present preliminary tests that use these algorithms in simulations of BH-NS mergers.

The Neutron-star Interior Composition Explorer is an X-ray astrophysics payload that will be placed on the International Space Station. Its primary science goal is to measure with high accuracy the pulse profiles that arise from the non-uniform thermal surface emission of rotation-powered pulsars. Modeling general relativistic effects on the profiles will lead to measuring the radii of these neutron stars and to constraining their equation of state. Achieving this goal will depend, among other things, on accurate knowledge of the source, sky, and instrument backgrounds. We use here simple analytic estimates to quantify the level at which these backgrounds need to be known in order for the upcoming measurements to provide significant constraints on the properties of neutron stars. We show that, even in the minimal-information scenario, knowledge of the background at a few percent level for a background-to-source countrate ratio of 0.2 allows for a measurement of the neutron star compactness to better than 10% uncertainty for most of the parameter space. These constraints improve further when more realistic assumptions are made about the neutron star emission and spin, and when additional information about the source itself, such as its mass or distance, are incorporated.

No description available.