94 THE DETONATION PROCESS 



Jones has also made calculations (52), applicable to oxygen-rich 

 explosives, by which the equation of state and adiabatic expansion are 

 related to the variation of detonation velocity with loading density (as 

 previously noted, this variation would not occur were the products 

 ideal gases). An interesting result of these calculations, noted by 

 Jones, is that the predicted compressibility of the gaseous products is 

 quite similar to Bridgman's experimental data for nitrogen mentioned 

 in section 3.3. 



In addition to a knowledge of the pressure and density resulting 

 from adiabatic explosion, the evaluation of conditions at the gas sphere 

 boundary requires a knowledge of the sound velocity, Riemann function 

 (7, and other parameters for the initial adiabatic in the gaseous products. 

 The determination of these variables for any explosive is a quite straight- 

 forward derivation from the equation of state and heat capacity data. 

 The explicit form of the necessary relations is, however, rather compli- 

 cated and the description of them here is restricted to indicating the 

 method of approach. The internal energy and entropy can be expressed 

 as functions of density p and temperature T by means of the Wilson- 

 Kistiakowsky equation of state in the form: 



E{p, T) = Eo + NCv {T - 300) + aNRTxe^' 



T 



S{p, T) = S. + N f ^ clT - NR flog ,p + \ {e^^ - 1) - axe^^l 

 J 300^ LP J 



where Eo, So are the ideal values for unit density and temperature 300° K. 

 The sound velocity, given by c^ = (dP/dp)s, is then obtained from the 

 equation of state and entropy expression by standard thermodynamics, 

 it being assumed adequate for this purpose to use a constant heat ca- 

 pacity Cv for temperatures T not greatly different from To, the initial 

 temperature of the products. The pressure-density relation can also be 

 expressed as a function of temperature T and the equation of state 

 variable x, as can the Riemann function o- and enthalpy co. These lat- 

 ter are in the form of definite integrals, conveniently computed using 

 the function x = (p/M) KT-"" as independent variable. 



3.6. The Form of the Detonation Wave 



When the Chapman-Jouget condition is satisfied, a specification of 

 the adiabatic pressure-density relation in the products of explosion pro- 

 vides the necessary data for determining the form of the detonation 

 wave behind its front. G. I. Taylor (106) has considered the general 

 problem and o})tained detailed results for TNT, using the detonation 

 conditions calculated by H. Jones. Before describing these results it is 



