Theory of the Fireball

From y = 1.18,
y=l-A
Y=
-1
2.2 - 0*4/y
X 2.2-0.4/y
12.2 - x
1-85
11.2
and the isothermal sphere disappears for
l/1 . e6
x = 12.2 = 3.811-
2
For these higher altitudes, then, the time when the isothermal sphere
(6 -18)
(6.20)
disappears is a fixed multiple of the time when it is first reached by
the cooling wave. This multiple depends only on y, and on the ratio
Hc/Hl of internal to external ent'nalpy at time ta. Tne pressure at the
time x is
2
1/3
-1.2
P2 = PaX2 .= 1.0 ($) (6.21)
For sea level, f (x) increases more slovly (the pressure decreases
more slovly) with time; hence it takes somewhat longer to use q the iso-
tnemal sphere. Conversely, t'ne pressure at the time t = t x will have
2 aa
decreased by a smaller factor from pa.
For the simple case of nigher altitude, we can use (6.19) to calcu-
late the fraction of the mass y 3 which -
will still be in the isothermal