When a blackbody system is heated to a suitable high temperature it emits radiation of all possible wavelengths, energy. This radiation is called blackbody radiation.

The closest system which follows with approximation the blackbody properties is an isothermal cavity (Figure 3) whose surface has uniform temperature. When the radiation enters the cavity through a small opening, suffers multiple reflections at the inner walls. After a few reflections, the radiation will be almost entirely absorbed by the cavity.

The distribution of energy among the different wavelengths of the spectrum of blackbody radiation is not uniform. Since blackbody emission is diffuse, the spectral intensity of radiation leaves the cavity independent of the direction.

The radiation from a constant temperature cavity depends only on the temperature of the cavity and it does not depend on the nature of the substance.

 

The Plank distribution

The intensity of radiation from a blackbody at temperature T is given by the Planck's Law of Radiation:

                                           Equation 1

where h represents the Plank constant and has the value h=6.626x10^-34Js, k is the Boltzmann constant and has the value k=1.381x10^-23 J/K respectively, c₀ is the speed the light in vacuum c₀=2.998x10⁸ m/s and T is the absolute temperature of the blackbody (K).

The spectral emissive power of a blackbody is:

                            Equation 2

where the first and the second radiation constants are C₁ = 2πhc₀² = 3,742x10⁸Wμm⁴/m² and C₂= hc₀/k= 1.439x10⁴ μmK. Equation 2 is known as Plank distribution.

This is the formula that is used in general in practical application, remote sensing, heat transfer, radioastronomy.

Those formulas can be taken into consideration only if we have a transparent medium.

Wien’s Displacement Law

The wavelength at which the radiation is strongest is given by Wien's law and corresponds to a λ_max which depends on the temperature T.

In the Wien displacement law equation (Equation 3), C₃represents the third radiation constant: C₃ = 2897,8mK

    λ_max = C₃ / T                                                                                      Equation 3

So, from this relation we can see that the maximum value of radiation intensity increases in proportion to temperature to the fifth power.

The Stefan-Boltzmann Law

Overall power emitted per unit area is given by the Stefan-Boltzmann law:

     E_b= σ xT⁴                                                                                                                               Equation 4

where σ represent the Stefan-Boltzmann constant: σ=5.67ßx10^-8 W/m²K⁴    .

 

Related link:

If you are interested to see and hear another approach of those 3 lows you can have a look to the link below:

http://www.youtube.com/watch?v=jbxty6aDfhU

http://www.youtube.com/watch?v=R2Af_VMTxZY