233 
Sec. 10 -22- Eq. 66-73 
Substitution of these into the basic equation for D, Eq. (39), yields the 
expression 
DeVy y® YovoNaFo = (vyMe) \/ FoncRtare Mt (66) 
This equation can be substituted into Eq. (42) for Pp to obtain 
Po = Py Voya(Vy-Vp) / VoF 
or 
where the subscripts 1 and 2 indicate the initial and final states, 
respectively, This equation is very useful in connecting Xp and Xj. 
b. Ratio D/D;. Division of Eq. (66) for D by Eq. (47) for Dy gives 
/ 
Ae Orett  / i2. Te. oy, (68) 
Le ieee pea Fetoiwes 
It should be noted that Vo, To and Xo differ in the ideal and real final 
states. It is found that tables of D/Dy can be constructed so that it is 
not necessary to carry out a detailed calculation for each explosive and 
density. 
c. Calculation of v2/ Daa: From thermodynamics one obtains the fol- 
lowing equation for the actual heat capacity in terms of the ideal heat 
capacity Cy; (per M grams). 
Vie a 
C=C, + Mr J (a P/at’ ),av. (69) 
‘i oy (2) A), . (70) 
When the equation of state (62) is inserted in these expressions, the result 
is 
Also 
of 
il 
Cy = Cy; + nO (z-1)R, (71) 
and 
Y= 14 mz /o,y) , (72) 
in which 
z=F -ax (dF/dx) Sse ean @ x°. © * 5 (73) 
