Theory of the Fireball

where t is in seconds, p in bars, ad Y in megatons, ad pl is the den-
sity of tine mbient, undisturbed aLr. Then (> 36) becomes
Tne right hand side of (5.38) gives the co&plete dependence on Y and p1
since, deriving (5.36), we have only used tne opacity 'law (3.33) and
the adisbatic cooling of air, (5.32), both of which zre independent of
the explosive yield Y and of tne ambient density of the air.
iY0r.r insek-t u from (5. X,9) ; then we obtain
Tnis equation gives the radiating temperature in teas of tne central
(5.39)
temperature T and of the quantities on the right hand side. The radi-
at in2 temperature is proportional to a low power of the central temper-
eture ( about tne 1/6 '
C
pover); tnus as the inside coo1s, tne radiation
decreases (see Sec. 5e for details). It also decreases slowly with time
due to the pressure factor on tile right nand side, T 1-P
For given
p and T the radiation temperature is higher for lower yield, T ' - Y
and for nigher altitude, Ti - p,
-0.032
C' 1 9
-1./21 .
For sea level, for Y = 1, and for p = 5 bars (cf. Sec. >e for this
choice) Brode's calculations give T' M 3.6; then (5.39) yields Ti = 1.08,
C
59
c