Statistical Mechanics

Quantum mechanics deals with the individual atoms and molecules of a system by assigning definite values of the wave functions (eigen functions to each of these particles at any instant of time (as these may be changing with time)*.On the other hand, thermodynamics deals with the properties like internal energy, enthalpy, entropy, free energy etc, of the matter in bulk and not with the individual particles. It was, therefore, realized that by suitable averaging method, it should be possible to calculate the thermodynamic/properties of the bulk matter from those of its individual atoms and molecules. This led to the need for the study of the new branch of science, called as ‘statistical mechanics’.

It is interesting to mention here that just as the quantum mechanical wave function contains all the information about a particle, similarly in statistical mechanics, we introduce thermodynamic information about the system.

As explained above, in thermodynamics we deal with properties such as temperature, pressure, energy etc, for the whole system, called the ‘macroscopic system’. The value of any thermodynamic property such as energy depends upon the variables of the system such as temperature, value and the number of moles. These variables are said to define the ‘state of the system’. So long as these variables remain unchanged, the value of the thermodynamic property remains the same. In the later part of the nineteenth century, it was though that since a macroscopic system is made up to consider the properties of the individual atoms and molecules and then find their sum for the whole system and calculate theoretically the thermodynamic properties of the system and these calculated values could be compared with the experimentally determined value. The method of averaging the behavior of a large number of individuals is called ‘statistical method’. Further laws of mechanics (classical or quantum mechanism) can be applied to the particles of the system. That is why this branch of science is called ‘statistical mechanizes’. Thus, statistical mechanics is that branch of science which helps us to calculate the macroscopic properties of the system for its microscopic properties by statistical methods and using the laws of mechanics.

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