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THERMODYNAMICS OF RADIATION 
37 
s the steady 
3h this equi- 
density and 
le walls. 
materials we 
temperature 
;ain range of 
ily a passage 
iation in the 
of the screen 
B than from 
Las occurred, 
md therefore 
tture T\ the 
temperature, 
ing the walls 
ary quantity 
temperature 
, quantity of 
d exactly to 
should have 
f we suppose 
temperature 
can use B as 
is mechanical 
3rm tempera- 
principles of 
depends only 
dion depends 
lployment in 
is the screen 
,t all essential 
icticable; but 
mtropy, if as 
le. The ideal 
ich are perfect 
i then becomes 
process must not eliminate the random element in the state of the energy. 
If practicable processes are employed, we are on safe ground; with ideal 
processes we have to be on our guard against inadvertently introducing 
a “sorting demon.” At first sight a screen transparent to one particular 
range of wave-length seems to be dangerously like a sorting demon; but 
since highly selective screens exist naturally, it is clear that such selection 
does not imply destruction of entropy; and although we may not be able 
to find a natural screen suitable for the particular range of wave-length 
SA, the lack is due to irrelevant limitations of nature and not to any 
contravention of the laws of thermodynamics. 
Radiation of the density and quality which would be in equilibrium 
with matter at temperature T is said to have the temperature T. A mixture 
of radiation of various wave-lengths in arbitrary proportions is not in 
general in equilibrium with matter at any temperature and has no unique 
temperature; but if it has the same total density as radiation at temperature 
T, T is called its “effective temperature.” If such radiation is placed in 
an enclosure with walls at temperature T it is rapidly transformed into 
radiation with a true temperature T, that is to say, the enclosure becomes 
filled with an equal amount of energy with a true temperature and the 
walls neither gain nor lose heat on balance. Since this conversion is 
irreversible, entropy is increased by the conversion. The excess organisa 
tion of the radiation with no true temperature could in fact be utilised 
by means of selectively transparent screens to raise matter above its own 
effective temperature T. A notable illustration of this is afforded by the 
radiation traversing space due to the stars; its effective temperature is 
about 3° absolute, but it is capable of spontaneously raising selectively 
absorbent matter to far higher temperatures. Radiation at a true tempera 
ture of 3° could not transfer heat spontaneously to matter above 3°. 
The coefficient 6 for radiation having a true temperature T is the same 
as for molecular heat, viz. 1/T. This follows because energy will pass from 
the radiation in an enclosure into the walls or vice versa according as its 
temperature is higher or lower than that of the walls; hence the limiting 
condition of transfer without change of entropy is when the temperatures 
are equal, and the equality of the coefficients d follows from (25T). 
Having proved that radiation at temperature T has a definite density 
and composition, we have to discover the formulae for the density and 
composition. This investigation is made in several stages. First Stefan’s 
law (30-3) is found determining the total density; next Wien’s displace 
ment law (32T) which reduces the problem of determining the composition 
at all temperatures to the determination of the composition at any one 
temperature; then Planck’s law (37-9) giving the form of the function left 
undetermined in Wien’s law; and finally in (40-7) the identification of the 
physical constant contained in Planck’s law.