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The equations of state for the ideal classical gas are generalized with two characteristic constants known as the state indices. A simple and complete representation is developed for the super-ideal gas, with explicit results which are general enough to cover a wide range of equilibrium systems and states. Evidence and justification are provided in terms of examples and results of statistical physics. The new model should prove useful for treating problems involving physical behavior and properties which might otherwise call for specialized or advanced methods of statistical mechanics.

On the basis of the well‐established relationship U = A + Bu (U denoting shock velocity, u particle velocity, and A, B experimental constants), it is shown that the following explicit formula can be used for the evaluation of the Gruneisen parameter: γ = {U(2U − A)[A + (B − 1)U] − (13AU)(U − A) − BA3} / U(U − A)(U + A). This is a short cut of its kind. Although its resultant values of γ reflect some differences similar to those between the Slater and Dugdale–MacDonald schools, the present method of computation can lead to a satisfactory evaluation of the equation‐of‐state data. In addition, direct calculation of sound velocity behind the shock front turns out to exhibit an interconnection between static and dynamic compressibilities. Such a link should be of value for pursuit to gain basic understanding of high pressures.

Shock waves in solid craters and effects of high speed impact of particles on space vehicles

This paper presents an analytic method for evaluating the effect of shock compression on metals. A lattice potential of the Born-Mayer type is used for calculating the pressure, compressibility, Gruneisen coefficient, entropy, temperature, and energy. A general equation of state is determined in the form of p ( v , T ) = f ( v ) + Tg ( v ). Except for the use of a few well-established thermodynamic properties of the metal, no experimental data from shock-wave measurements are required for the theoretical calculation in this paper. Comparison between the calculated and cited experimental results is made only to test the accuracy of the analysis, and agreement turns out to be fairly close. The analysis also establishes a validity range for shock compressibility of solids, and the material model considered is sensitive to its lattice structure as compared with a continuum model.

Shock‐wave behavior and properties of solids are described on the basis of a quadratic representation for the shock velocity and with results of considerable generality and simplicity. An implicit treatment is provided by coupling the Hugoniot adiabat with the isentrope in the Gruneisen equation of state for solids. This also leads to correlations between data and results of shock and hydrostatic measurements for high pressures.

Investigations show that static compressibility of a Debye solid can be deduced from shock‐compression data and vice versa. In this paper three different approaches are considered for the evaluation of static and dynamic compressibilities. Except for the linear law of shock propagation and the Born—Mayer type of energy function, which are semianalytical, all other equations are derived on a full analytic basis. It is of interest to show that the entropy and temperature are implicit functions of shock compression. These implicit functions are then determined in closed form, and they turn out to provide a means for the calculation of thermal properties of the Debye solid at high pressures in terms of purely mechanical parameters. Some calculated results are given according to the pseudo‐Hugoniot approach only, and the validity range covers pressures from 104−107 atm and temperatures from 102−103K.

An average value of 11 / 6 is taken to represent the Gruneisen constant of these eighteen metals: Li, Na, K, Rb, Cs, Fe, Mo, Ta, W, Al, Co, Ni, Cu, Pd, Ag, Pt, Au, and Pb. An analytical model is formulated for the interpretation of shock‐wave behavior of the_e metals. The model is shown to be as heuristic as the classical model of gas dynamics, and the adiabatic indices and compression ratios of both models at shock infinity may now be arranged as orderly spectra (53, 32, 75, 43) and (4, 5, 6, 7), respectively. The investigation seeks to emphasize the interrelation between shock and isentropic compressibilities, and it also provides favorable evidence for the use of Slater formula to evaluate γ at high pressure.

In this paper the compressibility equation of Tait is generalized in a basic form with three arbitrary parameters. Data-fitting of these parameters can be made correct to the third order. Thus, the generalized Tait yields a more flexible equation of state that is also related simply to several other well-known equations of high pressure, all accurate only to the second order.

This essay is motivated to add a useful note to the contemporary literature of ideal gases. For brevity, a new description is given for a special class of ideal quantum gases (the “qsuper ideal gases”) which are characterized here by two compact equations of state. Within such a framework all fundamental properties of these gases are readily expressed in terms of two constants known as the state indices. In order to test our results of deduction, six typical examples are given with comparable numerical values. While all the examples must otherwise have resort to statistical calculations, our evaluation for them turns out to be straightforward as well as heuristic.

In the framework of a simple compression wave and a weak shock wave, an isentrope of the Tait type and a Hugoniot adiabat based on the linear velocity relation are shown to verify each other consistently. Thus, the two empirical equations of state are given a semianalytical treatment on favorable terms.