40 
THERMODYNAMICS OF RADIATION 
heat escapes from or is admitted to the chamber, so that the change is 
adiabatic (dQ = 0) ; (2) it eliminates the ordinary processes (absorption 
and emission) by which radiation in an enclosure attains equilibrium 
constitution, so that we have not the usual guarantee that after the 
alteration of volume there will be equilibrium radiation in the chamber. 
Let us for the moment accept the first consequence, but evade the 
second by inserting in the chamber a speck of absorbing matter of 
negligible heat capacity; this re-introduces absorption and emission and 
the radiation will be brought into equilibrium with the matter just as 
though it formed the walls*. 
Now let the chamber undergo any number of expansions and contrac 
tions and return to its original volume. As it is subject to the adiabatic 
condition the pressure is a function of the volume only; in fact, setting 
dQ = 0 in (30-2) we have = constant. Hence the radiation has re 
turned to its original pressure and therefore to its original energy-density ; 
and as it is still equilibrium radiation it is exactly in its original state. 
Thus the entropy of the radiation is unaltered. Since dQ = 0 no entropy 
has been removed from it to its surroundings. Therefore no entropy has 
been created in it. 
The function of the speck of matter was to convert the radiation to 
equilibrium constitution as fast as any divergence was produced. But 
we have seen that this process is irreversible and that non-equilibrium 
radiation has less entropy than equilibrium radiation (§ 29), so that the 
conversion involves creation of entropy. Since no entropy has been created 
it follows that the speck of matter has not functioned at all—it has never 
in the whole process found any non-equilibrium radiation to convert. 
This shows that the adjustment is made automatically and reversibly by 
the reflecting walls without the help of any absorbing matter. 
33 . In these conditions the only cause of a change of constitution is 
the Doppler effect at the moving mirrors enclosing the radiation—moving 
when the chamber alters in size. When the walls recede the wave is re 
flected with lower frequency than the incident wave, so that there is a 
general conversion to lower frequencies accompanying the lowering of 
energy-density and temperature. 
Let waves of energy-density E and frequency v fall normally on a 
reflector receding with velocity V. Let E ', v be the energy-density and 
frequency of the reflected waves. The well-known formula for the Doppler 
effect is 
y' c-V 
v c + V 
(33-1). 
* The argument is equally valid if the continual conversion of non-equilibrium 
into equilibrium radiation is accomplished by the fiat of the mathematician.