In the 19th century there was a lot of interest in thermodynamics. One of the areas of interest was the rather contrived idea of a black body: a material kept at a constant temperature T, and absorbing any radiation that falls on it. Thus all the light that it emits comes from its thermal energy, non of it is reflected from other sources. A very hot metal is pretty close to this behaviour, since its thermal emission is very much more intense than the environmental radiation. A slightly more realistic device is an oven with a small window, which we need to observe the emitted radiation. The laws of thermal emission have been well tested on such devices. A very different example is the so-called 3 K microwave radiation (Nobel price 19xx). This is a remnant from the genesis of our universe, and conforms extremely well to the black-body picture, as has been shown by the recent COBE experiment.
The problem with the classical (Rayleigh-Jeans) law for black-body
radiation is that it does suggest emission of infinite amounts of energy,
which is clearly nonsensical. Actually it was for the description of this
problem Planck invented Planck's constant! Planck's law for the energy
density ate frequency
for temperature T is given by
| (1.2) |
If we look at Planck's law for small frequencies
h
kT, we find
an expression that contains no factors h (Taylor series expansion of
exponent)
| (1.3) |
| E = |
(1.4) |