3. Theoretical equations of state

Theoretical models are developed from an interpretation of the forces that exist between molecules. In principle, these forces can be calculated from quantum mechanics, however, as the actual potential energy function is unknown, it is generally assumed that these forces obey an empirical potential such as the hard sphere or Lennard-Jones potential. Statistical mechanics links quantum mechanics and continuum mechanics, to take into account statistical averages using molecular variables, in order to obtain observable quantities on a macroscopic scale. The usual method consists in summing up the Boltzmann energies of all possible states of the system in the canonical partition function. Many simplifying assumptions are introduced when formulating the partition function. However, once an expression has been chosen for the partition function, all thermodynamic quantities can be determined by...