Theory of the Fireball

Table 11. Adiabats
( 'Present" density, 0. 1-p shock density, lopo)
0;
T 4,000 6,000 8, ooo 12,000
T 9,000 10,500 18,000 28,000
S
y' - 1 0 213 0.194 0.144 0 1-53
Y; - 1 0.208 0 190 0.190 0.20
z 1-13 1.27 - 1.68 2.06
=S 1-03
. 1.6 2.06 3
Assming an adiabat of constant 7 = y', the density of a mass
element is
P = PS(k)1/Y (3.5)
Now ps is a constant, and at any given time, p is the s&e for all mass
elements except those very close to the shock, hence
4 7
P - Ps
(w means proportional- to)
If we now introduce the abbreviation
3
m = r (3.7)
which is proportional to the mass inside the mass element considered,
and if we use ( 3.2), we find that at any given time
21