397 
zero for such a eae rarefaction wave 
Pee sy ye Oo , 
' 
o*(p) = [pico (2.5) 
pre P(e st) ) 
where ¢ * is the velocity of sound in the gas, The integral defining the 
function c~ is to be taken along the initial adiabatic of the gas from 
its initial density ft a density f,* determined as a function of p 
along the adiabatic of entropy hy by the equation of state of the gas. 
Eqse 2.5 therefore provide a second relation between Py and Uy» 
ob) +U,=0. (2.6) 
Simultaneous solution of Eqs. 2.4 and 2,6 determines the initial values 
of py and uy, on the gas sphere. This solution is most conveniently car- 
ried out by graphical determination of the intersection point of the curves 
F(p) and = g(p). The pressure p is generally much less than Pee 
The calculation of the pressure p, for adiabatic constant volume 
conversion of the explosive to its products is a straightforward problen 
in thermodynamics. For this process, 
a Is de 
SL aes oe SAT Fae rae Av C7) 
where E; is the molar heat of formation at constant volume and temperature 
T, of the i-th product constituent, E, is the specific heat of formation at 
constant volume and temperature T, of the intact explosive, n; is the number 
of moles of the i-th product constituent per gram of explosive, and Cc. is 
the zero=epressure specific mean heat capacity over the temperature range of 
an 
