# Rose–Vinet equation of state

The Rose–Vinet equation of state are a set of equations used to describe the equation of state of solid objects. It is an modification of the Birch–Murnaghan equation of state.[1][2] The initial paper discusses how the equation only depends on four inputs: the isothermal bulk modulus $B_0$, the derivative of bulk modulus with respect to pressure $B_0'$, the volume $V_0$, and the thermal expansion; all evaluated zero pressure ($P=0$) and at a single (reference) temperature. And the same equation holds for all classes of solids and a wide range of temperatures.

Let the cube root of the specific volume be

$\eta=\sqrt[3]{\frac{V}{V_0}}$

then the equation of state is:

$P=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}$