General form of the Mie–Grüneisen equation of state

Abstract

The Mie–Grüneisen equation of state is defined in an incomplete form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> which does not allow access to temperature and entropy. We show here how we can extend it to a complete equation of state in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>S</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> form by providing an additional independent function which defines the heat capacity variations and then gives access to all the thermodynamic properties.