Stefan's -Boltzmann Law

This law states that the total amount of radiant energy emitted by a black body per second per unit area is directly proportional to the fourth power of its absolute temperature i.e. E∝T⁴ or E=𝜎T⁴ where 𝜎 is called Stefan's constant. It has a value of 5.67 x 10⁻⁸ Wm⁻²K⁻⁴. This law is strictly true only when the medium surrounding the black body is vacuum.

The same law was established later by Boltzmann theoretically from thermodynamical considerations. Hence, this law is known as Stefan-Boltzmann law.

Consider the case of black body 'A' at absolute temperature 'T1' which is surrounded by another black body at absolute temperature 'T2'.

Now, 

Heat lost by black body 'A' is 𝜎T1⁴ 
Amount of heat absorbed by black body 'A' from black body 'B' is  𝜎T2⁴.

Therefore, Net amount of heat emitted by body 'A' per second per unit area is 𝜎(T1⁴ - T2⁴).

This is the form of "Stefans Boltzman Law". 

Note: This law is true only when medium surrounding the body is vacuum.

What is Statistical Mechanics?

When we consider bodies at macroscopic level they consist of uncountable atoms or molecules i.e. about 10²³ atoms/gm.mole. In such cases we cannot predict the result of interactions between atoms with the help of ordinary classical laws of motion.

Statistical Mechanics is the branch of Science which establishes the interpretation of macroscopic behaviour of system in terms of its microscopic properties.

The main theme is that it doesn't deal with motion of each particle but it takes into account the average or most probable properties of system without going into interior details of characteristics of its constituents.

The larger is the number of particles in the physical system considered, the more nearly correct are the statistical predictions. The smaller is the no. of particles (no. of degrees of freedom) in a mechanical system, the methods of mechanical system cease to have meaning.

Before the advent of quantum theory Maxwell, Boltzmann, Gibbs etc applied statistical methods making the use of classical physics. These statistical methods are known as Maxwell Boltzmann Statistics.

These statics explained successfully many observed physical phenomenon like temperature, pressure, energy etc; but couldn't explain adequately several other experimentally observed phenomenon like black body radiation, specific heat at low temperature etc.

In order to explain such phenomenon "quantum statistics" was introduced and developed by Fermi, Dirac, Bose, Einstein with new approach by using new quantum idea of discrete exchange of energy between system.

i) Bose-Einstein Statistics
ii) Fermi-Dirac Statistics