THE DETONATION PROCESS 79 



nRT 



PV = 



M 



where n is the number of moles of gas in M grams of the final gases 

 (which we assume to be a mixture of products). The adiabatic expan- 

 sion law is then 



PV'^ = constant, dS = 



where y is the ratio of specific heats and the velocity of sound c is given 



by 



=^^^<-f) = ^^^ 



The increase in internal energy E — Eo may be written 



MiE - Eo) = Q + C. {T - To) 



where Q is the heat absorbed in the reaction of M grams at the initial 

 temperature T and final composition and Cv is the mean specific heat at 

 constant volume of the final composition for the temperature range. 



The Rankine-Hugoniot requirement for energy change at the shock 

 front may be combined with these thermal data to give 



(3.11) £ - £. = i(P + P„) (V'-V)=~+^{T- T.) 



In order to solve for the final temperature it is necessary to eliminate 

 P, V from this equation. The conditions of mass and momentum con- 

 servation at the shock front and Chapman-Jouget condition may be 

 written 



Eliminating Z), u by the first and third relations we obtain for the second 



