228 
Sec, © -17- 
to 10° Atm., the ratio Pyp/Py>0 is greater than unity so long as carbon is 
present. The assumption that the reaction goes completely to the right 
means an overestimation of the detonation rate because the heat absorption 
is overcompensated by an increased mole number of gaseous products. The 
following examples in Table 7-1 demonstrate the masnitude of the effect 
on D of the extreme assumptions concerning this equilibrium. It is seen 
that ideal rates calculated with no carbon and those calculated with no 
hydrogen differ only by 3% or less. In actudlity the first case is approached 
closely almost always and hence the error resulting from thse extreme assump- 
tion must be smll. 
Table 7-1. Effect of equilibria on ideal detonation rates.* 
Compound Decomposition equation TK D; m/sec. 
Picric 6 CO+ H0+ 3H, + 12N 3u0 2140 
Acid 2 = 
BeiCO'+ 15° H.0 45404 13 Np 3615 2120 
TNT 6 CO+ 23 In + C+ 13 Np 2830 2070 
33 CO+ 241504 55 C+ 13 Ny 3650 2005 
Tetryl 7 CO+ HO + 13 H, + 23 N, 3950 2360 
5zCO+ 23 H0+15C+ 2ENy Hobs 2290 
d. Summary. Summing up the results of this discussion it is found 
that the effects of chemical equilibria in the detonation wave are divers. 
and aitogether may effect a decrease of the rate with increasing pressure (or 
density of loading) amounting to perhaps 10 or at the very most 15%. This 
conclusion is interesting from the theoretical point of view since it 
indicates that the study of detonation rates for solids does not provide 
crucial evidence as to whether chemical equilibria are establishad in the 
wave or not. For the detonation to comply with the present theory it is 
only necessary to postulate that the reaction is "complete" in the sense 
that the oxygen combines with all the carbon to form CO, the excess oxygen 
combines with hydrogen to form water and if any is still left over, it 
combines with CO to form COp. 
8, The Equation of State 
If the ideal gas law is used, the calculated detonation velocity does 
not depend on the density of loading, as is seen from mM. (47). This is found 
* Calculated usin;; ideal gas law. 
