The critical compressibility factor of fluids from the Global Isomorphism approach

The relation between the critical compressibility factors $Z_{c}$ of the Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the global isomorphism approach. On this basis we obtain the alternative form for the value of the critical compressibility factor which is different from widely used phenomenological Timmermans relation. The estimates for the critical pressure $P_c$ and $Z_c$ of the Lennard-Jones fluid are obtained in case of two and three dimensions. The extension of the formalism is proposed to include the Pitzer's acentric factor into consideration.