Physics:Rose–Vinet equation of state

The Rose–Vinet equation of state is a set of equations used to describe the equation of state of solid objects. It is a modification of the Birch–Murnaghan equation of state. The initial paper discusses how the equation only depends on four inputs: the isothermal bulk modulus [math]\displaystyle{ B_0 }[/math], the derivative of bulk modulus with respect to pressure [math]\displaystyle{ B_0' }[/math], the volume [math]\displaystyle{ V_0 }[/math], and the thermal expansion; all evaluated at zero pressure ([math]\displaystyle{ P=0 }[/math]) and at a single (reference) temperature. The same equation holds for all classes of solids and a wide range of temperatures.

Let the cube root of the specific volume be

[math]\displaystyle{ \eta=\left({\frac{V}{V_0}}\right)^{\frac{1}{3}} }[/math]

then the equation of state is:

[math]\displaystyle{ P=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)} }[/math]

A similar equation was published by Stacey et al. in 1981.