High Temperature Classical Equation Of State

A study is made of the effect of potential perturbations on the equilibrium properties of a hard sphere system at both high and low densities. The perturbation is evaluated beyond the first order term for the second and third virial coefficients to estimate the region of convergence. The results of the first order perturbation from the virial expansion, superposition theory and free volume theory are compared. A comparison with experimental data is made to show the applicability of this perturbation from a hard sphere potential to the estimation of the equilibrium properties of a great variety of gases at moderately high temperatures.

The equation of state of an ionized gas has been investigated for electron densities below about 10(22 power) per cubic centimeter and temperatures below about 1,000,000 K. The gas is assumed to be monatomic, electrically neutral, and in thermodynamic equilibrium, but the composition of the gas is arbitrary, that is multiple ionization of any degree is allowed. The perfect gas approximation is found to be valid for electron densities at least as high as 10(16 power) per cubic centimeter, and in some cases, even higher. It is shown that approximations to the perfect gas expressions can be made which will greatly simplify calculations. It is also shown that blackbody radiation may be important at low densities. The classical corrections to the perfect gas expressions due to electrostatic forces and the finite size of particles which are obtained from the theories of Debye and Hucke, Mayer, and others, are investigated, and their limits of validity are determined. In some cases, improved expressions are derived and suitable approximations are suggested. It is noted that a fundamental weakness of the results based on the these theories is that a basic parameter, the distance of closest approach of charged particles, is not known accurately. Several approximate expressions for this distance are given. Quantum corrections for electron degeneracy and electron interactions are also given. Theories which are applicable at higher densities and temperatures than those of interest in this investigation are also discussed briefly. Finally, the equation of state of a dense, slightly ionized gas is derived.

A valuable and complete resource that brings together many of the branches of physics needed in high-energy-density physics. Targeted at research scientists and graduate students in physics and astrophysics, this book begins with basic concepts and develops a detailed explanation of the physics of hydrodynamics and energy transport in plasma.

We started our work on theoretical methods in the phys ics of high pressures (in connec tion with geophysical applications) in 1956, and we immediately encountered many problems. Naturally, we searched the published Iiterature for solutions to these problems but whenever we failed to find a solution or when the solution did not satisfy us, we attempted to solve the problern ourselves. We realized that other investigators working in the physics of high pres sures would probably encounter the same problems and doubts. Therefore, we decided to write this book in order to save our colleagues time and effort. Apart from the descriptions of ex perimental methods, the book deals only with those problems which we encountered in our own work. Allproblems in high-pressure physics have, at present, only approximate solutions, which are very rough. Therefore, it is not surprising that different investigators approach the same problems in different ways. Our approach does not prejudge the issue and we are fully aware that there are other points of view. Our aim was always to solve a glven problern on a physical basis. For example, the concept of the Grüneisenparameter needs further develop ment but it is based on reliable physical ideas. On the other hand, Simon's equation for the melting curve has, in our opinion, no clear physical basis and is purely empirical. Equations of this type are useful in systematic presentation of the experimental material but they are un suitable for any major extrapolation.