Stefan's rule as a consequence of cohesive forces

Abstract

This work is concerned with the derivation of Stefan's rule. The treatment is based on the thermodynamic definition of internal pressure and it leads to an expression correlating internal pressure, molar volume and total molar surface energy of pure liquids. Further, the molar internal energy of vaporization is introduced with the help of the definition equation of the solubility parameter and the equation of Stefan results. All the liquid properties that appear in this derivation are closely related to the cohesive forces acting in fluids. The numerical value of the geometric factor k in the final equation is for simple liquids closely equal to three. This is in agreement with the theory, whilst the speculative value suggested by Stefan is equal to two. In liquids in which the intermolecular forces depart greatly from spherical symmetry and in interacting systems k becomes considerably higher.