The Partition Function

According to Boltzmann distribution law (Eqn. 2.7.18), the fraction of molecules which in the most problem state at temperature T possesses the energy is given by

                                      
Where n_i is the number fo molecules having energy at temperature T,N is the total number of molecules and g_i is the degeneracy (or statistical weight of the energy level .

The denominator of the above equation which gives the sum of the terms for all the energy levels is called the partition function. (It was originally called the Zustandssumme’ by Planck which means the “sum over the states” but this term is know rarely used). It is usually represented by Q.
Thus
                        
The partition function is so called because it indicates the particles, are distributed among the various energy states.

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