Black-body radiation

Every hot body radiates

A hot object emits light. An ember glows red, a stove element turns orange, the filament of a bulb shines white. This thermal radiation exists at any temperature — even you emit in the infrared, invisible to the eye but very real (it is what thermal cameras see).

The black body: an ideal emitter

To study this radiation without worrying about the particular material, physicists defined an ideal object: the black body. It is a body that absorbs all the radiation it receives (it reflects nothing, hence "black"), and which, when heated, re-emits radiation that depends only on its temperature — not on its composition.

   Concrete model : a cavity with a small hole

        ___________
       /           /|
      /___________/ |       The hole behaves like
      |           | |       a black body : any ray
      |     o<----|-------  that enters bounces around inside
      |   (hole)  | /       and ends up absorbed. When heated, the
      |___________|/        cavity re-emits through the hole.

The spectrum depends on temperature

If we break down the light emitted by a black body, we obtain a curve: the intensity emitted as a function of wavelength. This curve has a characteristic "hump" shape, and its position depends on the temperature:

   intensity
      ^
      |         .-.        high T (high curve,
      |        /   \\           hump toward BLUE/UV)
      |       /     \\
      |      /  .--.  \\
      |     /  /    \\  '.      low T (low curve,
      |    / /       '.  '-.      hump toward RED/IR)
      |   //           '-.  '--..
      |  //               '--..  '''----...
      +--------------------------------------> wavelength
      UV    blue  green  red      infrared

Two essential observations:

1. The hotter the body, the more it emits (the curve rises overall).
2. The hotter the body, the more the maximum shifts toward short wavelengths (toward the blue).

Wien's law: color betrays temperature

This shift of the maximum obeys Wien's law: the wavelength of the peak is inversely proportional to the temperature (in kelvins):

   λ_max × T = constant  (≈ 2,9 × 10^-3 m·K)

This is why the color of a hot object tells us about its temperature:

   Object            Temperature      Dominant color
   ----------------  ---------------  ------------------
   ember             ~1000 K          dark red
   bulb filament     ~3000 K          orange-white
   Sun               ~5800 K          yellow-white
   blue star         ~20000 K         blue

An astronomer can thus read the temperature of a star from its color alone — a direct application of Wien's law.

In summary

Every hot body emits thermal radiation. The black body is the ideal emitter, whose spectrum depends only on temperature: a hump-shaped curve whose maximum shifts toward the blue as the temperature rises (Wien's law: λ_max × T = const). The color of a hot object therefore reveals its temperature. What remains is to explain the shape of this curve — and this is where classical physics is going to collapse.