# 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:

- 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}

}