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explain the thermal radiation
pattern of a black body by figuring
out the entropy of the system.
Entropy is a measure of disorder,
though more strictly it is defined
as a count of the number of ways
a system can organize itself. The
higher the entropy of a system,
the more ways the system has
of organizing and producing the
same overall pattern. For instance,
imagine a room where all the
molecules of air start off bunched
up in the top corner. There are far
more ways for the molecules to
organize themselves so that there
is roughly the same number of
them in each cubic centimeter of
the room than there are for them all
to remain in the top corner. Over
time, they distribute themselves
equally throughout the room as
the entropy of the system rises.
A cornerstone of the second law
of thermodynamics is that entropy
works in one direction only.
En route to thermal equilibrium,
the entropy of a system always
increases or remains constant.
Planck reasoned that this principle
should be evident in any theoretical
black-body model.The Wien–Planck Law
By the 1890s, experiments in
Berlin came close to Kirchhoff’s
perfect black-body, using so-called
cavity radiation. A small hole in a
box kept at a constant temperature
is a good approximation of a black
body, as any radiation entering the
box gets trapped inside, and the
body’s emissions are purely a result
of its temperature.
The experimental results proved
bothersome for Planck’s colleague
Wilhelm Wien, since the low-
frequency emissions recorded did
not fit his equations for radiation at
all. Something had gone wrong. In
1899, Planck arrived at a revised
equation—the Wien–Planck law—
that attempted a better description
of the spectrum of thermal
radiation from a black body.Ultraviolet catastrophe
A further challenge came a year
later, when British physicists
Lord Rayleigh and Sir James Jeans
showed how classical physics
predicts an absurd distribution
of energy in black-body emission.
The Rayleigh–Jeans Law predicted
that, as the frequency of the
radiation increased, the power it
emitted would grow exponentially.
This “ultraviolet catastrophe”
was so radically at odds with
experimental findings that the
classical theory must have been
seriously awry. If it were correct, a
lethal dose of ultraviolet radiation
would be emitted whenever a light
bulb was turned on.
Planck was not too troubled by
the Rayleigh–Jeans Law. He was
more concerned about the Wien–
Planck Law, which, even in its
revised form, was not matchingMAX PLANCK
No real-world object is a perfect
black body, but the Sun, black velvet,
and surfaces coated with lampblack,
such as coal tar, come close.the data—it could accurately
describe the short-wavelength
(high-frequency) spectrum of
thermal emission from objects, but
not the long-wavelength (low-
frequency emissions). This is the
point at which Planck broke with
his conservatism and resorted to
Ludwig Boltzmann’s probabilistic
approach to arrive at a new
expression for his radiation law.
Boltzmann had formulated a
new way to look at entropy by
regarding a system as a large
collection of independent atoms
and molecules. While the secondScience cannot solve the
ultimate mystery of nature.
And that is because, in the
last analysis, we ourselves are
a part of the mystery that we
are trying to solve.
Max PlanckA cavity with a small hole will
trap most of the radiation that enters
through the hole, making it a good
approximation of an ideal black body.