# 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 ${\displaystyle B_{0}}$, the derivative of bulk modulus with respect to pressure ${\displaystyle B_{0}'}$, the volume ${\displaystyle V_{0}}$, and the thermal expansion; all evaluated zero pressure (${\displaystyle P=0}$) 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

${\displaystyle \eta ={\sqrt[{3}]{\frac {V}{V_{0}}}}}$

then the equation of state is:

${\displaystyle P=3B_{0}\left({\frac {1-\eta }{\eta ^{2}}}\right)e^{{\frac {3}{2}}(B_{0}'-1)(1-\eta )}}$

A similar equation was published by Stacey et al. in 1981.[3]

## References

1. ^ Pascal Vinet, John R. Smith, John Ferrante and James H. Rose (1987). "Temperature effects on the universal equation of state of solids". Physical Review B. 35: 1945–1953. doi:10.1103/physrevb.35.1945.
2. ^ "Rose-Vinet (Universal) equation of state". SklogWiki.
3. ^ F. D. Stacey; B. J. Brennan; R. D. Irvine (1981). "Finite strain theories and comparisons with seismological data". Surveys in Geophysics. 4 (4): 189–232. doi:10.1007/BF01449185.