Black-body radiation

black-body radiation

In physics 

black body is an idealized object that absorbs all electromagnetic radiation that falls on it

The term "black body" was introduced by Gustav Kirchhoff in 1860.  

Kirchhoff's Law: 

    emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body. 

The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.  

Super black is an example of such a material, made from a nickel-phosphorus alloy. More recently, a team of Japanese scientists created a material even closer to a black body, based on vertically aligned single-walled carbon nanotubes, which absorbs between 98% and 99% of the incoming light, in the spectral range from UV to far infrared. 

    A typical industrial "extended source plate" type black body.

Equations governing black bodies

Wien's displacement law  

William Wien 

Opened in 1893 
 
 
 
 
 
 
 
 

(1864-1928)

A consequence of Wien's displacement law is that the wavelength at which the intensity of the radiation produced by a black body is at a maximum, λmax, it is a function only of the temperature:  
 
 
 
 
 
where the constant, b, known as Wien's displacement constant, is equal to 2.8977685(51)×10−3 m K.  

Black body spectrum

Stefan–Boltzmann  law

Ludwig Boltzmann

(1844-1906) 
 
 
 
 
 

1884 

Jožef Stefan (1835-1893)  
 
 
 
 
 
 
 
 
1879 

This law states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature. That is  
 
 
where j*is the total power radiated per unit area, T is the temperature and σ = 5.67×10−8 W m−2 K−4 is the Stefan–Boltzmann constant.  
 
 
 
 
 

Graph of a function of total emitted energy of a black body  proportional to the fourth power of its thermodynamic temperature T  according to the Stefan–Boltzmann law.

Planck's law  
 

produced this law in 1900 (published in 1901) 
 
 
 
 
 
 
 
 

(1858-1947)

In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths emitted in the normal direction from a black body at temperature T. As a function of frequency ν, Planck's law is written as:  
 
 
I(ν,T) dν is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν + dν by a black body at temperature T;  
h is the Planck constant;  
c is the speed of light in a vacuum;  
k is the Boltzmann constant;  
ν is frequency of electromagnetic radiation; and  
T is the temperature in kelvins.