Statistical Mechanics

This branch of statistical mechanics which treats and extends classical thermodynamics is known as statistical thermodynamics or equilibrium statistical mechanics.

We apply statistical mechanics to solve real systems (a system for many particles). We can easily solve Schrodinger’s equation for 1 particle, atom or molecule. For many particles, the solution will take the form:

total = linear combination of  a(1) b(2) c(3)…

Where  a means a particle in state a with an energy E_a.

For example, we consider particles conned in a cubic box of length L. From quantum mechanics, the possible energies for each particle is :E= 22m2L2(n2x+n2y+n2z)

For example in an ideal gas, We assume that the molecules are non-interacting, i.e. they do not affect each other’s energy levels. Each particle contains certain energy.

At T > 0, the system possesses total energy, E.

So, how is E distributed among the particles? Another question would be, how the particles are distributed over the energy levels.

We apply statistical mechanics to provide the answer and thermodynamics demands that the entropy is maximum at equilibrium.

Thermodynamics is concerned with heat and the direction of heat flow, whereas statistical mechanics gives a microscopic perspective of heat in terms of the structure of matter and provides a way of evaluating the thermal properties of matter, for e.g., heat Capacity.