THE DETONATION PROCESS 87 



and the h are the empirical covolume constant* for the various species determined 

 from detonation data. 



If at equihbrium for the various reactions the number of moles of each species 

 Xi is vi, counted as negative for reactants and positive for products, the reaction 

 may be represented as ZviXi = 0, and for equilibrium we have the condition 



'SvifXi = 



The thermodynamic constant Kp for reactions at various temperatures is defined 

 as 



RT log Kp = - Xvi ixoi 



Summing over the vim and introducing the equilibrium constant gives 



log K, = llvi log A^ + ^vi [log , I + "^^^ - log g F(a;) J 



+ Nxe^^Uvjki 



^NiKi 



= log K — log G 



where log iv represents the first term on the right, log G the other terms. This 

 equation represents the condition imposed on the reactions by their equilibrium con- 

 stants. This expression may be written K = KpG, which in turn may be expressed 



nA'; = nKpyG;, where A^, = HyCA^i)"^ 

 the product being extended over the equilibrium considered. 



The detailed calculation determining both the equilibrium constants 

 and the final state is carried out in two steps: calculation of a hypo- 

 thetical final state, using ideal gas laws, the heats of formation and 

 specific heats of the products, and an estimated final composition and 

 temperature in the Rankine-Hugoniot equations. This first estimate 

 of the final state is improved using the actual equation of state. This 

 revised estimate is employed to calculate approximate equilibrium con- 

 stants K using the thermodynamic equilibrium conditions, this calcu- 

 lation involving solution of a set of simultaneous equations equal in 

 number to the number of products. The whole process is then repeated 

 with successive approximations giving the same equilibrium. 



The complete process is evidently a long and somewhat complicated 

 numerical procedure which will not be described in detail. It is, how- 

 ever, of interest to mention approximate composition rules developed 

 by Brinkley and Wilson, which in most cases agree surprisingly w^ell 

 with the final result. For explosives described by the formula 

 C^HrOsNi the assumed decomposition equations are 



