THE DETONATION PROCESS 83 



the constants h, c, d being adjusted to give the same pressure and 

 curvature as the equation for a higher pressure at an intermediate value 

 of V. 



These results are of course based on data for nitrogen at a low tem- 

 perature. Jones makes the assumptions that the effect of interaction 

 at high temperatures and comparable densities will not be appreciably 

 different and that the same interaction can be applied to other gaseous 

 products. With these assumptions the total energy of the products of 

 an explosion becomes 



E = J: [NaEa +(N - N.) (Eo + ^ Rt\ 



In this equation Na represents the number of moles of each molecular 

 species, whether solid or gas, and Ea is the energy per mole exclusive of 

 interaction of molecules in the gas phase. N = ^Na is the total num- 

 ber of moles; Ns is the number of moles of solid products. The last 

 term thus represents the energy of interaction for the gas molecules 

 plus vibrational energy 3/2 RT per mole. 



In addition to the interaction term it is therefore necessary to 

 evaluate the energies Ea and the composition variables Na. The ener- 

 gies Ea are evaluated from specific heat data at ordinary pressures, as 

 interaction effects at high pressures are represented by Eo. The final 

 problem is therefore determination of the equilibrium composition con- 

 sistent with the Rankine-Hugoniot and Chapman-Jouget conditions. 

 In order to determine the equilibrium of possible reactions as a function 

 of temperature, the activities of the various products are introduced, 

 which can be evaluated as a function of pressure from the equation of 

 state. This procedure is made practical by the simplifying assumption 

 that all molecules have the same field of force. The activity can how- 

 ever be expressed in terms of the composition variable Na and the equi- 

 librium constants for the assumed reactions as a function of tempera- 

 ture at normal pressures to which ideal gas conditions are applicable. 

 Elimination between these equations and the decomposition equations 

 for the particular explosive then permits determination of the Na for 

 various temperatures. 



The increase in internal energy of the products must be the sum of 

 the chemical energy Q released by the reaction and the work done by 

 the pressure at the detonation front. A knowledge of E, the energy 

 release Q, and the equation of state therefore provides sufficient infor- 

 mation to solve the detonation front equations. 



Although it is evident from this sketch that Jones' procedure in- 

 volves several fairly drastic simplifying assumptions, the calculation is 

 of importance because the results give an idea of the success obtainable 



