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p - p_0 = \frac{\Gamma}{V} (e - e_0)
</math>
where ''p''<sub>0</sub> and ''e''<sub>0</sub> 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 ''p''<sub>0</sub> and ''e''<sub>0</sub> are independent of temperature and the values of these quantities can be estimated from the [[Rankine–Hugoniot conditions|Hugoniot equations]]. The Mie–Grüneisen equation of state is a special form of the above equation.
== History ==
From Grüneisen's model we have
{{NumBlk|:|<math> p - p_0 = \frac{\Gamma}{V} (e - e_0) </math>|{{EquationRef|1}}}}
where ''p''<sub>0</sub> and ''e''<sub>0</sub> are the pressure and internal energy at a reference state. The [[Rankine–Hugoniot conditions|Hugoniot equations]] for the conservation of mass, momentum, and energy are
:<math> \begin{align}
\rho_0 U_s &= \rho (U_s - U_p) \,, \\[1ex]
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