THERMODYNAMICS OF RADIATION 
39 
/ 
ohimè, and 
} walls (and 
Lperature at 
isity of the 
(30-1), 
(30-2). 
egral on the 
ce that p^\T 
n of T only. 
(30-3), 
is 7-64.10~ 15 
appropriate 
meaning for 
rtic changes, 
at the state- 
does not appear to be any actual failure of Stefan’s Law (or Planck’s Law) 
in this case; but careful definition is required since the energy of material 
polarisation is in some applications appropriately grouped with the radiant 
energy whereas in other applications it is kept separate. Further reference 
to this point so far as it concerns stellar conditions is made in § 164. 
The quantity of isotropic radiation passing in both directions through 
a plane area 8 is \EcS per second. (The factor \ arises through taking the 
average of cos 6 over each hemisphere, the cross-section of an oblique 
beam through S being S cos 6.) The amount passing in one direction is 
\EcS. Hence if in a body at temperature T a cross-section is cut and 
suddenly exposed, radiation of amount \Ec per sq. cm. per sec. will leave 
the body through this section. This is evidently the maximum intensity 
of radiation obtainable from a body maintained at a general temperature 
T. In practice it will be impossible to avoid a slight drop of temperature 
at the surface. This may be minimised by taking a good conductor of heat 
and coating it with a highly absorbent substance; the conductor is re 
quired to maintain the full temperature near the surface, and the absorber 
to secure that the radiation is “enclosed.” Equilibrium radiation is often 
called black-body radiation in reference to this mode of experimenting on 
it. Another method of obtaining nearly the full black-body radiation is to 
make a small opening in a large enclosure maintained at the requisite 
temperature. 
The full radiation of matter at temperature T is accordingly 
\Ec = per sq. cm. per sec (31-1). 
The constant a = \ac is called Stefan’s constant, but we shall generally 
prefer to use the constant a. 
tional to the 
jaw. 
stribution of 
olecules into 
-he molecules 
the volume 
closure must 
. Thus radia- 
laintained at 
not properly 
osure has an 
is concerned, 
rgy of aether 
quate. There 
• Wien’s Law. 
32 . We next deduce from thermodynamical considerations that the 
constitution of equilibrium radiation at temperature T satisfies Wien’s 
displacement law 
I(y, T) = v*f {v/T) (32-1), 
where I (v, T) dv is the energy-density of the radiation of frequency 
between v and v + dv and/is some definite function of v/T. Since the form 
of / is not indicated by this investigation Wien’s law does not determine 
the constitution ; but if the constitution is known for any one temperature, 
it enables us to calculate the constitution for other temperatures. 
Lemma. A chamber with perfectly reflecting walls initially contains 
equilibrium radiation. If the chamber expands or contracts, the radiation 
will be automatically converted into equilibrium radiation for the temperature 
corresponding to its new density. 
The perfect reflection has two consequences: (1) it ensures that no