Theory of the Fireball

violet, (3.17) is not valid; these wave lengths are strongly absorbed by
cold or cool air ( Sec . kc) . For example, at p = po and T = 2000°, the
mean free path is less than 1 meter for all light16 of hv > 4.7 ev
(A < 0.26 p). Since the emission of light of such short wave length from
such cool air is negligible, the fireball will not emit such radiation at
all.
A detailed discussion of the absorption coefficient in the visible
will be given in Sec. 4b. As can be seen from the tables of Meyerott
16
et al. and from our Table VI, for a density p = po the mean free path
is of the order of 5 meters at about 6000~. This corresponds to a pres-
sure13 of about 25 bars. For p = O.lpo the requisite mean free path of
a few meters is obtained for about 10,OOOo, with p M 7 bars. Thus for a
J
relatively modest decrease in pressure, the effective temperature of
radiation increases from 6000 to 10,OOOo, corresponding to a very sub-
stantial increase in radiation intensity. This is the mechanism of the
increase in radiation tarard the second maximum. A more detailed dis-
cussion w ill be given in Sec. 5f.
d. Energy Supply
As long as the radiating temperature is low, not much energy w ill
be emitted as radiation, and this emission will only slightly modify the
cooling of the material due to adiabatic expansion. However, when the
radiating temperature increases, the radiation cooling will exceed the
adiabatic cooling to an increasing extent. It then becomes necessary to
supply energy from the interior to the radiating surface.