Theory of the Fireball

pressure is larger than pa, (5.50) . Then the radiating surface is in
the adiabatic region described in Sec. 3c. The condition for its posi-
tion is, (3.21), t = R/5O. From Brode's curves, the position of a point
of temperature T ' near 1 is given approximately by
1/3 r-0.10
R = 0.78
-1/4
Y T P
This expression comes purely from the numerical calculation, except thct
the correct dependence on yield is inserted. Y is in megatons, p in bars,
R in kilometers. Equation (5.51) holds from p = 5 to 100 bars within
about 5%. The absorption coefficient is given in (4.10), which yields
using t'ne equation of state (4.11). Equating this to 1/50 of (5.51)
gives
Tr408 = 4.5 y -1/3 P -1.20
Thus the radiating temperature increases as the pressure decreases.
64
b