86 THE DETONATION PROCESS 



for each type of molecule are adjusted to give best agreement for selected 

 data on heats of formation and specific heats, and the detonation prob- 

 lem can then be solved for given equilibrium conditions. The second 

 problem, of determining the equilibrium composition, is attacked in 

 either approach by standard thermodynamic methods. The equation 

 of state and energy conditions are of course not independent of the equi- 

 librium and the final solution must thus be obtained by simultaneous 

 solution of the two problems. The formal solution of the equilibrium 

 problem is essentially the same in the two approaches but differs in de- 

 tail because of different reaction constants assumed and the different 

 equations of state emploj^ed. In order to indicate the nature of the 

 equilibrium calculation a short summary of the steps in the procedure of 

 Brinkley and Wilson is given here. 



The work content A of a mixture of M grams of gases of sufficiently large volume 

 Vo and temperature T is given by standard thermodynamics as 



A{Vo, T) = UNiHio + RT ^N log I + llNi log A^- - A^J 



where A^» is the number of moles of the ^th product gas and A^ the total number of 

 moles. The chemical potential fxi for a gas is defined in general as 



^' \dN-)T,v, 



Nj 9^ Ni 



and ixio is its value for the pure gas at standard pressure and temperature T. At 

 any other volume and the same temperature, the work content is given by 



A{V,T) = A{Vo, T) - M i PdV 



Introduction of the modified Wilson-Kistiakowsky equation of state to eUminate V 

 gives on integration 



+ RT \J^. ^eP' - loge ^'i-^) ] 



In this equation, F{x) is the function in the equation of state 

 ,,^, NRT ,,, , NRT .^ , ^ , 



