Development of the Liquid Equation and the Partial Structure of Water

In a previous publication where the derivation of the Tait equation for liquids is given, the number average degree of association and the volume of holes depended on a sum $$\mathrm{\phi =}{\displaystyle \sum _{\text{x=1}}^{\infty }}{s}_x{\text{(1/v)}}^x·$$ This sum is transformed here into a closed expression. Hence, these quantities can now be evaluated numerically along any isobar or isotherm in terms of one undetermined constant at a particular reference temperature. In terms of this development, the structure of water is analyzed along an isobar (1 atm) from 20°—75°C and along an isotherm (20°C) from 1–200 atm.