Relation between surface tension and isothermal compressibility: application of statistical mechanical equation of state

A statistical mechanical equation of state is used to establish relation between liquid isothermal compressibility κ and surface tension γ with length parameter L, order of surface thickness, in the form of functional κf·γf = CL, where subscript f stands for freezing point. The proportionality constant C depends on the structure and molecular shape of a fluid, and for liquid hydrocarbons varies by a factor of 2-3. Pervious universal relation between second virial coefficient and surface tension at freezing point is used to derive the above relation. The length parameter is a measure of surface thickness and found as the size of (ρfN)−1/3, where ρf is the liquid density at freezing point and N is the Avogadro's number. Pure theoretical treatment for numerical calculation of the proportionality constant is in reasonable agreement with literature, for which experimental data on isothermal compressibility and surface tension have been used.