Answer to Question #320712 in Molecular Physics | Thermodynamics for Sam

Question

1) Classify three kinds of statistics, their need, applicability, the idea of phase space, macro-microstates.

Answer 1

Answer

The three types of statistics used in statistical mechanics are :

1) Maxwell Boltzmann statistics :

Particles which are regulated by Maxwell-Boltzmann Statistics have to be

distinguishable each other and one energy state can be occupied by two or

more particles. Distinguishable means that if we have 2 particles, let say A

and B, also two states, 1 and 2, and we put A to state 1 and B to state 2, it

will be different with the distribution A to state 2 and B to state 1. It

means that A and B are distinct.

2) Fermi Dirac statistics :

Particles which are regulated by Fermi-Dirac Statistics have to be

indistinguishable each other and one energy state can be occupied by only

one particle. So we have to fill it to another state when a state has just

been occupied by another particle.

3) Bose Einstein statistics :

Particles which are regulated by Bose-Einstein Statistics have to be

indistinguishable each other and one energy state can be occupied by two

or more particles. So instead of saying it as particle A or B, we call it as

just “particle” since they are the same thing.

Applicability of different types of statistics :

 Maxwell Boltzmann statistics is applicable to identical, distinguishable particle

of any type spin. The molecules of gas are particle of this type.

 Bose Einstein statistics is applicable to the identical, indistinguishable particles

of zero or integral spin. These particles are called Bosons. Example photons,

Helium atom.

 Fermi Dirac statistics is applicable to the identical, indistinguishable particles

of half integral spin. These particles obey Pauli Exclusion Principle .Ex

Electron, proton etc.

Now let's jump into the idea of phase space ,

It's just a space containing all sets of points representing the position and momentum which the system can possibly have ,For example when you plot phase space of a classical harmonic oscillator it comes out to be an Ellipse when you plot it's position on x-axis and velocity on y-axis , that's what we call phase space of classical harmonic oscillator.

Let's now discuss Microstates and Macrostates :

In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations.

Whereas ,the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density .