Equation of state based on the first principles

An alternative to the well-known complete form of Mie-Gr\"uneisen equation state (EOS) for water is suggested. A closed analytical description self-consistent EOS an arbitrary medium based only on first law thermodynamics and a new virial theorem obtained. This (allowing variable power-law exponent particles interaction potential) result generalization known method similarity (Feynman et al., 1949). In EOS, internal potential energy as solution nonlinear Riemann-Hopf type proposed.