Matches in DBpedia 2014 for { ?s ?p The Mie-Grüneisen equation of state is a relation between the pressure and the volume of a solid at a given temperature. It is used to determine the pressure in a shock-compressed solid. The Mie-Grüneisen relation is a special form of the Grüneisen model which describes the effect that changing the volume of a crystal lattice has on its vibrational properties. Several variations of the Mie–Gruneisen equation of state are in use.The Grüneisen model can be expressed in the formwhere V is the volume, p is the pressure, e is the internal energy, and Γ is the Grüneisen parameter which represents the thermal pressure from a set of vibrating atoms. If we assume that Γ is independent of p and e, we can integrate Grüneisen's model to getwhere p0 and e0 are the pressure and internal energy at a reference state usually assumed to be the state at which the temperature is 0K. In that case p0 and e0 are independent of temperature and the values of these quantities can be estimated from the Hugoniot equations. The Mie-Grüneisen equation of state is a special form of the above equation.. }
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- Mie–Gruneisen_equation_of_state abstract "The Mie-Grüneisen equation of state is a relation between the pressure and the volume of a solid at a given temperature. It is used to determine the pressure in a shock-compressed solid. The Mie-Grüneisen relation is a special form of the Grüneisen model which describes the effect that changing the volume of a crystal lattice has on its vibrational properties. Several variations of the Mie–Gruneisen equation of state are in use.The Grüneisen model can be expressed in the formwhere V is the volume, p is the pressure, e is the internal energy, and Γ is the Grüneisen parameter which represents the thermal pressure from a set of vibrating atoms. If we assume that Γ is independent of p and e, we can integrate Grüneisen's model to getwhere p0 and e0 are the pressure and internal energy at a reference state usually assumed to be the state at which the temperature is 0K. In that case p0 and e0 are independent of temperature and the values of these quantities can be estimated from the Hugoniot equations. The Mie-Grüneisen equation of state is a special form of the above equation.".