MOTION MOUNTAIN

light sources 143
Ref. 104
Vol. I, page 244
Challenge 149 d
Ref. 105
Vol. IV, page 17
Ref. 106
The essence of black bodies is that the colour they have, i.e., the light they radiate, is
independent of the surface. Black bodies are thusideal in this sense. Real bodies, which
do show surface effects, can be classified by theiremissivity.The emissivity gives thedegreetowhichabodyapproachesablackbody.Mirrorshave
emissivities of around 0.02,
whereas black soot can have values as high as 0.95. Practically all bodies at everyday temperaturearenotblackbodies:theircolourisnotdeterminedbyemission,butmostlyby
theabsorptionandreflectionoflightattheirsurface.
Blackbodies,asthesectiononquantumtheorywillshow,havesmooth light emission
spectra. An example for a spectrum of a black body, and for a spectrum of a real body –
in this case, the Sun – is shown in Figure 90.
Black bodies are also used to define the colour white. What we commonly call pure
white is the colour emitted by the Sun. The sun is not a good black body, as Figure 90
shows (its effective temperature is5780 K). Because of these problems, pure white is now
defined as the colour of a black body of6500 K, e.g. by the Commission Internationale
d’Eclairage. Hotter black bodies are bluish, colder ones are yellow, orange, red, brown or
black. The stars in the sky are classified in this way.
Black bodies are thus bodies that glow perfectly. Most real bodies are only rough approximationsofblackbodies,even
at temperatures at which they shine yellow light. For
example, the tungsten in incandescent light bulbs, at around2000 K, has an emissivity of
around 0.4 for most wavelengths, so that its spectrum is a corresponding fraction of that
of black body. (However, the glass of the light bulb then absorbs much of the ultraviolet
and infrared components, so that the final spectrum is not at all that of a black body.)
Black body radiation has two important properties: first, the emitted light powerincreaseswiththefourthpowerofthetemperature.Withthisrelationaloneyoucancheck
the temperature of the Sun, mentioned above, simply by comparing the size of the Sun
with the width of your thumb when your arm is stretched out in front of you. Are you
able to do this? (Hint: use the excellent approximation that the Earth’s average temperatureofabout14.0°C
isduetotheSun’s irradiation.)
The precise expression for the emitted energy densityuper frequencyνcan be deducedfromtheradiation
‘law’ forblackbodiesdiscovered by Max Planck*
u(ν,T)= 8πh
c 3 ν 3
e hν/kT −1 . (76)
He made this important discovery, which we will discuss in more detail in the quantum
part of our mountain ascent, simply by comparing this curve with experiment.The new
constanthis called thequantumofaction orPlanck’sconstant and turns out to have the
value6.6⋅10 −34 Js, and is central to all quantum theory, as we will find out. The other
* Max Planck (b. 1858 Kile, d. 1947Göttingen), professor of physics in Berlin, was a central figure in thermodynamics.
He discoveredand named Boltzmann’s constantk and the quantum of actionh, often called
Planck’sconstant.Hisintroductionofthequantumhypothesisgavebirthtoquantumtheory.Healsomade
the works of Einstein known in the physical community, and later organized a job for him in Berlin. He
received the Nobel Prize for physics in 1918. He was an important figure in the German scientific establishment;
he also was one of the very few who had the courage to tell Adolf Hitler face to face that it was
abad idea tofireJewishprofessors. (Hegot an outburst ofanger asanswer.) Famouslymodest,with many
tragediesin hispersonallife,hewasesteemedbyeverybodywhoknewhim.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net