The Cooling of a Gas By Radiation

Cover The Cooling of a Gas By Radiation
The Cooling of a Gas By Radiation
Ernest Bauer
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with the initial conditions Substituting (33) in (31) and (32), we find that at t = 0, we have N„=N° of equation (?), and also d N^/St = - Api^o* Both these results are eminently reasonable, and show that the initial conditions (33) are satis- factory for describing how radiative 2-1 transitions disturb the initial statistical equilibrium.
- 12 - X - x^, 8x/3t - 0, at t - 0, (37) We shall take (2f (x)^ e""" (38) as an approximation, bearing in mind that while the precise form of F(T) is not kn
...own, yet an approximation such as (38) does yield the basic, exponential, T-dependence of equation (17) • 3. 1 Solution of the system (3$) - (37) A standard way of solving two coupled equations is to eliminate one of the two dependent variables: here it is clearly convenient to eliminate n rather that x ♦ If we carry out the elimination, we get ^ ^ 0/3X)(l/x) H0 (x) 1+g.

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