Equation of state based on the first principles

Abstract

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

37 pages, 5 figures

References in corpus (4)

• Instability of cumulation in converging cylindrical shock wave
• Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 turbulence spectrum of breaking waves
• Limitation in velocity of converging shock wave
• Energy density balance during shock wave implosion in water