THERMODYNAMICS OF RADIATION
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Hence by (33-71) and (33-72)
vl(v, T) = F {v/T).
By (33-74) v oc T~ 3 , so that absorbing the constant of proportion in F
1 (y, T) = T S F ( v/T ).
Finally, if /j ( x ) = F ( x)/x s
I (v, T) = V»/, (v/T)
which proves the required theorem.
To review this rather lengthy investigation we note four steps : ( 1) Proof
that the change of constitution of equilibrium radiation with temperature
is brought about by reflection at moving walls independently of absorption
and emission processes ; (2) Proof that the number of quanta is unchanged ;
(3) Formulation and integration of the partial differential equation ex
pressing the fact that there is no correlation between s and v ; (4) Determina
tion of one of the two functions introduced, by the condition that the
total density of the radiation must agree with Stefan’s law.