Thermodynamics Quantities are classified in two groups.

Extensive

These quantities increase by a factor when size of system under consideration is increased by some factor. e.g., Entropy

Intensive 

These quantities remain same when system under consideration is increased. e.g; pressure, Temperature.

These functions described the statistical properties for a system in thermodynamics equillibrium. It defines system by variables such as total energy, free energy entropy and pressure. All variables can be expressed in term of partition funtions. Mainly used partition functions include.

  1. Canonical partition function
  2. Grand canonical partition function
The canonical partition function applies to canonical ensemble in which system is allowed to exchange heat with enviornment at fixed tempoerature volume and Chemical potential.

In Grand canonical partition function system can exchange both heat and particles with enviornment at fixed temperature volume and chemical potential.

Significance of partition functions

With help of this function one can fixed microstate energies from other thermodynamics variables and then can fixed partition function. This function will allow to calculate other thermodyanamics variables.

Equipartition Theorem

It states that mean value of every independent quadratic term in energy is equal 1\2 KT. If all the terms in energy is equal to 1\2 KT. If all the terms in energy are quadratic then mean energy is sprerad over all degree of freedoms.