An Equation of State for Gases at Extremely High Pressures and Temperatures from the Hydrodynamic Theory of Detonation

Abstract

The hydrodynamic theory of detonation is derived in a convenient form for practical utility by employing the general equation of state pv=nRT+α(T, v)p. Two methods of solution of the general equations based on measured detonation velocity are discussed. In method (a) the detailed form of α(T, v) is unspecified. It is therefore, in principle, at least, a general solution. However, in practice one finds that it is impossible due to the experimental error in detonation velocities to evaluate the heat capacity at constant volume and hence the detonation temperature without specifying a particular form of α(T, v). The postulate (used only in the calculation of temperature) is α=α(v). Method (b) employs the approximation α=α(v) throughout. Methods (a) and (b) lead to identical results which one will find in view of the comparative nature of the two methods, is good evidence (but not conclusive proof) for the validity of the above approximation. This is supported also by the discovery that the same α vs. v2 curve applies to all explosives yet considered. As a matter of fact, it has been found that the detonation velocities may themselves be computed within experimental error, evidently for explosives of all types (where sufficient heat data are available) by employing the α(v) function evaluated from a few selected explosives. Several additional arguments supporting the above approximation are discussed. Data on the detonation properties of several explosives are presented and correlated with similar data obtained by other investigators.