231 
Sec. 9 -20- Eq. 55-5 
d. Calculation of the ideal temperature. If the empirical formula 
given above is substituted for Cx in Eq. CG) and this equation is solved 
for Toy, the result is 4 
-Q + AT 
il 
Tei = -(apR/2¥ 53) + AFB (Toy-T}) (55)* 
Here the subscript i denotes the ideal state. In the above equation To4 
occurs on the right so that the equation is properly a quadratic equation 
but it is easier to solve it by successive approximations. A trial value of 
Toy (say 4000°) is inserted in the denominator and the right hand side 
evaluated, The value of To; thus obtained is substituted in the denominator 
in place of the original trial value and a new value of T,; obtained. Usually 
two trials are sufficient. 
Strictly speaking, Jo; will vary with Tp and also with the composition. 
In practice, however, XY oyhas a range of only 10% for the substances con- 
sidered in this report. Furthermore the term noR/2 Soi has a value only about 
10% of the total denominator. Therefore, less than 0.5% error in To; will 
be introduced if the constant mean value of 0.80 is used for R/2 Soi in 
Iq. (55). 
The heat of reaction Q can be obtained from the heat of formation Hf, 
of the explosive, since 
-Q@=HP,- <n, Hf, (56) 
2 , 
where Hf, denotes the heat of formation of the th product species (per 
mole) and ny, the number of moles of that species. The heats of combustion 
of most explosives are known so that the heats of formation are available. 
e. Calculation of Dj. Eq. (47) can now be used to calculate the ideal 
detonation velocity D;. The heat capacity ratio Yoy could be determined 
directly from the Imown heat capacities of the products and the temperature, 
but this is rather tedious so an approximation has been adopted which 
yields values of D; about 2% low. This error is larzely removed by the 
method in which d/D; is determined. The approximation consists in calculating 
Y using the mean value C instead of the heat capacity at Toy. A very con- 
venient equation is 
nee 
~~ 
Oo, > 14+ ay Blo, 
(57) 
3 
A and B having been obtained already for use in Eq. (55). 
With the values of To; from Eq. (55) and Bn; as given above, D; is 
easily computed from Eq. (47), repeated below: 
