7 
RADIATIVE EQUILIBRIUM 
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Let there be a circulatory current conveying heat between two pressure 
levels. As the mass rises to a level of lower pressure its temperature 
changes according to the adiabatic law 
P oc T yliy ~ 1 \ 
For stability y > |, so that P <x T (<4) . Hence the material which has 
ascended is cooler than its surroundings and receives heat from them; the 
material which has descended is hotter than its surroundings and gives 
up heat to them*. The circulatory current transfers heat against the 
temperature gradient, and by the second law of thermodynamics it can 
only do this at the expense of its mechanical energy. The currents there 
fore tend to die out, and there is nothing to restart themf. 
Radiative equilibrium has a natural precedence over convective 
equilibrium, since in radiative equilibrium convection ceases, whereas in 
convective equilibrium radiation remains and tends to destroy it. In 
fact convective equilibrium is only approached automatically from one 
side; to reach it from the other side extraneous mechanical energy of 
stirring must be supplied. 
Equation of Radiative Equilibrium. 
71. We admit now that the only mode of transfer of heat is by radia 
tion, and develop the equation of radiative equilibrium. We require three 
results reached in Chapter n— 
(1) The momentum of radiation is E/c, where E is the energy and c 
the velocity of light. The momentum is in the direction in which the waves 
are travelling. 
(2) Radiation in an enclosure with absorbing walls maintained at 
uniform temperature T is isotropic as regards direction of flow and has 
an energy-density 
E = aT\ 
where a = 7-64 . 10 -15 in c.g.s. units and degrees Centigrade. 
(3) With the same conditions radiation exerts a hydrostatic pressure 
vr = \e = &T*. 
To a very high degree of approximation the last two results are im 
mediately applicable to the interior of a star. It is true that the radiation 
* E.g. let y = |, and let a current ascend from a level where the pressure and 
temperature are P and T to a level where they are j^^-P> jo^' > un( fer the diminished 
pressure the temperature of the convected material falls adiabatically to 
(t ffihnyF = 0-025T, 
so that it is much below the temperature O'lT of its surroundings. Cf. H. N. Russell, 
Astrophys. Journ. 54, p. 293. 
f Except that in a rotating star a small circulation is maintained as explained 
in § 199. 
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