Theory of the Fireball

t
For p1 = po, T = 0.8, this is 14 bars.
At higher temperature (T' > 1) , the ultraviolet can be transported
as easily as the visible although it will not escape to large distances
(Sec. kc). Then it
(,),,
is reasonable to use the full black body radiation
(3.33) for the emission. Inserting this into (3.32) gives
$8/3
(3.39)
1 .O, this is 40 bars.
Thus for p greater than 14 to 40 bars, the radiation is '
only a
fraction of the adiabatic cooling, for lower pressure radiation cooling
is more important. At the lower pressures then, energy must be supplied
from the inside to maintain the radiation. This gives rise to a "cooling
wave" moving inwards as will be discussed in Sec. 5.
It is interesting that the condition (3.38) refers to the pressure
alone. Neither the local density nor the equation of state enters. The
opacity of air enters only insofar as it determines the radiating temper-
ature T ' through the condition ( 3 *21)
.
A more accurate expression for the limiting pressure will be derived
in Sec. 5e. It will turn out to be considerably lower, about 5 bars.