Title: Complete Mie-Gruneisen Equation of State (update)

The Mie-Gruneisen equation of state (EOS) is frequently used in hydro simulations to model solids at high pressure (up to a few Mb). It is an incomplete EOS characterized by a GrÂ¨uneisen coefficient, = -V (@eP)V , that is a function of only V . Expressions are derived for isentropes and isotherms. This enables the extension to a complete EOS. Thermodynamic consistency requires that the specific heat is a function of a single scaled-temperature. A complete extension is uniquely determined by the temperature dependence of the specific heat at a fixed reference density. In addition we show that if the domain of the EOS extends to T = 0 and the specific heat vanishes on the zero isotherm then a function of only V is equivalent to a specific heat with a single temperature scale. If the EOS domain does not include the zero isotherm, then a specific heat with a single temperature scale leads to a generalization of the Mie-GrÂ¨uneisen EOS in which the pressure is linear in both the specific energy and the temperature. This corresponds to the limiting case of two temperature scales with one of the scales in the high temperature limit. Such an EOS hasmore » previously been used to model liquid nitromethane.« less