A typical amount of material, let's say 1 gram, contains about 6x10^23 molecules: Avogadro's number. ...Continued Below...

The water molecules shown above are randomly placed and randomly oriented.

Statistical Mechanics uses laws of probability to compute AVERAGE properties of both ordinary materials and of exotic elementary particles.

At the root of Stat. Mech. is the Heisenberg Uncertainty Principle.

Macroscopic Quantities are: Energy, Entropy (S), Enthalpy (H), Gibbs Free Energy (G), etc.

Pressure is the result of the molecules all imparting momentum to a wall.

Stat. Mech. is an easy way to treat a very complicated quantum mechanical problem of many particles.

The Fundamental Postulate of Statistical Mechanics.

Each particle can have a different energy - often quantized, as shown below.

Three Systems (Left, Middle, Right) each having available energy levels. The particles in each system are distributed differently among the energy levels.

In the laboratory, we can't measure the indiviual energy levels of each particle. Instead we can only measure macroscopic quantities, such as N, V, T, P.

The probability that a particle lies in energy state "j" is P_j.

The number, N, and total energy, E, of particles is set in a given system.

The total energy of a system is the number of particles times the average energy per particle.