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In the classical model of blackbody radiation, the Rayleigh-Jeans Law takes into account that cavity atoms are modeled as oscillators emitting electromagnetic waves of all wavelengths: dI 2πckT. = I(λ, T ) = (3) dλdΩ λ4 where k is Boltzmann’s constant and c is the speed of light in free space.
Electromagnetic waves emitted by a blackbody are called blackbody radiation. Figure \(\PageIndex{2}\): The intensity of blackbody radiation versus the wavelength of the emitted radiation. Each curve corresponds to a different blackbody temperature, starting with a low temperature (the lowest curve) to a high temperature (the highest curve).
To begin analyzing heat radiation, we need to be specific about the body doing the radiating: the simplest possible case is an idealized body which is a perfect absorber, and therefore also (from the above argument) a perfect emitter. For obvious reasons, this is called a “black body”.
An object that absorbs all radiation falling on it at all wavelengths is called a blackbody. It is well known that when an object, such as a lump of metal, is heated, it glows; first a dull red, then as it becomes hotter, a brighter red, then bright orange, then a brilliant white.
A blackbody is a hypothetical object that absorbs all incident electromagnetic radiation while maintaining thermal equilibrium. No light is reflected from or passes through a blackbody, but radiation is emitted, and is called blackbody radiation.
The universal microwave background radiation, peaked at @ mm, 1 fits the Planck curve for a black body of T = 2.728 K to great precision. (The deviation, of order 6 parts in 106 is, of course, of great interest.) Illustration source: http://www.bc.cc.ca.us/programs/sea/astronomy/light/lightb.htm#A2.1.
8.1 A Basic Radiation Model. We consider the wave equation with radiation, for simplicity in one space dimension assuming periodicity: Find u = u(x t ) such that ... u′′ u = f x t (8.1) 1. where (x t ) are space-time coordinates, _v @v = @t , v′ = forcing in the form of incoming waves, and the term.
