Statistical Thermodynamics: Current Perspectives and Limitations of Fluid Property Estimation

Abstract

Statistical thermodynamics provides a simple formal connection between the thermodynamics of a system, as represented by its free energy A, and the molecular properties of a system, as represented by its canonical partition function Q [1]:

$${{\rm{A}}^{{\rm{(T,V,\{ }}{{\rm{N}}_{\rm{j}}}{\rm{\} )}}}}\,{\rm{ = }}\,{\rm{ - }}\,{\rm{kT}}\,{\rm{ln}}\,{\rm{Q(T,V,\{ }}{{\rm{N}}_{\rm{j}}}{\rm{\} ),}}$$

((1))

where k is Boltzmann’s constant, T is the thermodynamic temperature, V the volume, {N_j} the total amount of molecule numbers of the various components, and

$${\rm{Q}}\,{\rm{ = }}\,\mathop {\rm{\Sigma }}\limits_{\rm{i}} \,{\rm{e}}{\,^{{\rm{ - E}}{}_{\rm{i}}{\rm{/kT,}}}}$$

((2))

Here E_i, the molecular energy of the system in its quantum state i, is the key quantity.