Engineering



Engineering

Introduction

Maxwell Boltzmann Statistics is used to predict various number of atoms in the thermal equilibrium. It also predicts the proportion of atom in the given energy level. It determines how many atoms will stay in the ground state and how many will remain in the excited state, hence it gives an idea about the level at which the atom will stay.

Discussion

Maxwell Boltzmann Statistics

In physics, the Maxwell-Boltzmann statistics is a statistic function developed to model the behavior of physical systems governed by classical mechanics. This feature of classical statistical physics was originally formulated by JC Maxwell and L. Boltzmann. It governs the distribution of a set of particles, according to the possible values of energy. For each thermodynamic system , the Maxwell-Boltzmann distribution is not simply the application of collective canon of statistical mechanics , but it also assume the non-quantum occupation numbers available in each state as compared to the maximum number of occupation.

The Maxwell-Boltzmann distribution has been applied especially to the kinetic theory of gases, and other physical systems as well as in econo physics to predict the distribution of income. In reality the Maxwell-Boltzmann distribution, is applicable to any system consisting of N "particles" or "individuals".

When Maxwell Boltzman theory and statistics is applied to the container that is filled with the gas, having relevant energy levels. They are obtained by solving the issue of time independent Schrodinger equation. This equation is carried out for the atom found inside the container. Thus, for gas atoms in a one-dimensional box, the probability that a given atom will be occupying the nth state is proportional to f'XP :-E ..... I L;Td. Maxwell-Boltzmann statistics predict that the number of particles with energy, tj, is Nj:

Where Ni= number of particles in state i

?i = energy of the ith state

gi = the degeneracy of state I, the number of microstates with energy ?i

µ = the chemical potential

k = boltzmann's constant

T= absolute temperature

N = total number of particles

Z = partition function

These statistics are known as the statistics of “distinguishable”, based on classical particles. For example, we have a collection of 10 particles to go with 2 possible energy states that could be occupied. If these particles are distinguishable, it means that one can give different names to these particles like particle 1, particle 2 etc. Suppose, particles 1,2,3,4,5 are in state 1 and particles 6,7,8,9,10 are in state 2, that gives a different distribution than if you were to switch between particle 6 and particle 1. It is important to understand the fact that these particles could be arranged for 2^10 = 1024 ways. That is these 10 particles could be arranged in 1024 ways among the 2 states.

These statistics are very helpful, when one deals with gases of high temperature and low density.

Fermi Dirac Statistics

Fermi Dirac Statistics is one of the most important ways in which these indistinguishable particles could be distributed among different energy states. Only one particle can occupy these discrete ...