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Title: Complete Mie-Gruneisen Equation of State

Abstract

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 Gruneisen coefficient, {Lambda} = -V({partial_derivative}{sub e}P){sub 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 {Lambda} 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-Gruneisen EOS in which the pressure is linear in both the specific energy and the temperature. Such an EOS has previously been used to model liquid nitromethane.

Authors:
 [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
DOE/LANL
OSTI Identifier:
1045381
Report Number(s):
LA-UR-12-22592
TRN: US201215%%182
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICAL METHODS AND COMPUTING; ISOTHERMS; NITROMETHANE; SPECIFIC HEAT; TEMPERATURE DEPENDENCE; THERMODYNAMICS

Citation Formats

Menikoff, Ralph. Complete Mie-Gruneisen Equation of State. United States: N. p., 2012. Web. doi:10.2172/1045381.
Menikoff, Ralph. Complete Mie-Gruneisen Equation of State. United States. doi:10.2172/1045381.
Menikoff, Ralph. Thu . "Complete Mie-Gruneisen Equation of State". United States. doi:10.2172/1045381. https://www.osti.gov/servlets/purl/1045381.
@article{osti_1045381,
title = {Complete Mie-Gruneisen Equation of State},
author = {Menikoff, Ralph},
abstractNote = {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 Gruneisen coefficient, {Lambda} = -V({partial_derivative}{sub e}P){sub 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 {Lambda} 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-Gruneisen EOS in which the pressure is linear in both the specific energy and the temperature. Such an EOS has previously been used to model liquid nitromethane.},
doi = {10.2172/1045381},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {6}
}

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