THE LIGHT-QUANTUM 365a simple form, as do all functions which do not depend on the properties of indi-
vidual bodies and which one has become acquainted with before now' [K2].
Kirchhoff's emphasis on the experimental complexities turned out to be well
justified. Even the simple property of / that it has one pronounced maximum
which moves to lower v with decreasing T was not firmly established experimen-
tally until about twenty years later [K3]. Experimentalists had to cope with three
main problems: (1) to construct manageable bodies with perfectly black properties,
(2) to devise radiation detectors with adequate sensitivity, and (3) to find ways of
extending the measurements over large frequency domains. Forty years of exper-
imentation had to go by before the data were sufficient to answer Kirchhoff's
question.
Kirchhoff derived Eq. 19.1 by showing that its violation would imply the pos-
sibility of a perpetuum mobile of the second kind. The novelty of his theorem was
not so much its content as the precision and generality of its proof, based exclu-
sively on the still-young science of thermodynamics. A quarter of a century passed
before the next theoretical advance in blackbody radiation came about.
In 1879 Josef Stefan conjectured on experimental grounds that the total energy
radiated by a hot body varies with the fourth power of the absolute temperature
[SI]. This statement is not true in its generality. The precise formulation was
given in 1884, when Boltzmann (then a professsor of experimental physics in
Graz) proved theoretically that the strict T^4 law holds only for bodies which are
black. His proof again involved thermodynamics, but combined this time with a
still younger branch of theoretical physics: the electromagnetic theory of Maxwell.
For the case of Hohlraumstrahlung, the radiation is homogeneous, isotropic,
and unpolarized, so that
one had come as far as possible on the basis of thermodynamics and general elec-
tromagnetic theory. (Proofs of Eqs. 19.3 and 19.4 are found in standard texts.)
Meanwhile, proposals for the correct form of p had begun to appear as early
as the 1860s. All these guesses may be forgotten except for one, Wien's exponential
law, proposed in 1896 [W2]:
(19.4)
This law was the very first thermodynamic consequence derived from Maxwell's
theorem, according to which the numerical value of the radiation pressure equals
one third of the energy per unit volume. When in 1893 Wilhelm Wien proved his
displacement law [Wll
(19.3;
where p(v,T), the spectral density, is the energy density per unit volume for fre-
quency v. In this case, the Stefan-Boltzmann law reads (V is the volume of the
cavity)