| The only region of the
electromagnetic spectrum to which our eye is sensitive is the
"visible" range identified in the diagram by the rainbow colors.
The sun is not the only object that
provides radiant energy; any object whose temperature is greater than 0 K
will emit some radiant energy. The challenge to scientists was to show how
this radiant energy is related to the temperature of the object.
If an object is placed in a container whose
walls are at a uniform temperature, we expect the object to come into
thermal equilibrium with the walls of the enclosure and the object should
emit radiant energy just like the walls of the container. Such an object
absorbs and radiates the same amount of energy. Now a blackened surface
absorbs all radiation incident upon it and it must radiate in the same
manner if it is in thermal equilibrium. Equilibrium thermal radiation is
therefore called black body radiation.
The first relation between temperature and
radiant energy was deduced by J. Stefan in 1884 and theoretically
explained by Boltzmann about the same time. It states:
where the total energy is per unit area per
second emitted by the back body, T is its absolute (thermodynamic)
temperature and  is the
Stefan-Boltzmann constant.
The great question at the turn of the
century was to explain the way this total radiant energy emitted by a
black body was spread out into the various frequencies or wavelengths of
the radiation. Maxwell's "classical" theory of electromagnetic
oscillators failed to explain the observed brightness distribution. It was
left to Max Planck to solve the dilemma by showing that the energy of the
oscillators must be quantized, i.e. the energies can not take any
value but must change in steps, the size of each step, or quantum, is
proportional to the frequency of the oscillator and equal to hv,
where h is the Planck constant. With this assumption, Planck derived the
brightness distribution of a black body and showed that it is defined by
its temperature. Once the temperature of a black body is specified, the
Planck law can be used to calculate the intensity of the light emitted by
the body as a function of wavelength. Conversely, if the brightness
distribution of a radiating body is measured, then, by fitting a Planck
curve to it, its temperature can be determined.
The curves illustrated below show that the
hotter the body is, the brighter it is at shorter wavelengths. The surface
temperature of the sun is 6000 K, and its Planck curve peaks in the
visible wavelength range. For bodies cooler than the sun, the peak of the
Planck curve shifts to longer wavelengths, until a temperature is reached
such that very little radiant energy is emitted in the visible range.
 This
figure (adapted from Adkins' "Thermal Physics") shows several
Planck curves for black bodies. The Intensity is in units of energy per
unit area per unit solid angle per unit time per unit wavelength interval.
The broken line illustrates the variation with wavelength and temperature
of the peaks of the curves.
This is a graphical representation of
Wien's law, which states:
 (max)
~ 0.29/T,
where (max)
is the wavelength of maximum brightness in cm and T is the absolute
temperature of the black body.
The human body has a temperature of about
310 K and radiates primarily in the far infrared. If a photograph of a
human is taken with a camera sensitive to this wavelength region, we get a
"thermal" picture. This picture is courtesy of the Infrared
Processing and Analysis Center, Jet Propulsion Laboratory, NASA.
A page developed by Compix gives a fine
description of thermal images and their uses.
John E. Will has pointed to several thermal
images obtained during research in antenna pattern measurements, as
another example of the use of thermal images. |
