Theory of the Fireball
Theory of the Fireball
Theory of the Fireball
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The equation <strong>of</strong> continuity is<br />
aH aJ<br />
==-ax<br />
(5 *4)<br />
The energy in radiation has been neglected, which is justified in<br />
all practical cases . Using (5.1), (5.4) can be integrated over x to<br />
give<br />
u H + J = C (5 *5)<br />
where C is a constant. This is <strong>the</strong> fundamental result <strong>of</strong> 2,<br />
If <strong>the</strong> opacity increases monotonically with H, <strong>the</strong>n in <strong>the</strong> interior<br />
J w ill be very nearly zero, and <strong>the</strong>refore<br />
c = uH* (5.6)<br />
where Ho is <strong>the</strong> enthalpy. in <strong>the</strong> undisturbed interior, hot region.<br />
Equation (5.5) becomes<br />
J = u(H0 - H) (5.7)<br />
which can be integrated to give x(T), since H(T) md K(T,p) are known<br />
functions. We have put in evidence <strong>the</strong> fact that K depends on pressure<br />
in addition to T. Over most <strong>of</strong> <strong>the</strong> range <strong>of</strong> T, K(T) is <strong>the</strong> most rapidly
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