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 B 0 {\displaystyle B_{0}} , the derivative of bulk modulus with respect to pressure B 0 ′ {\displaystyle B_{0}'} , the volume V 0 {\displaystyle V_{0}} , and the thermal expansion; all evaluated at zero pressure ( P = 0 {\displaystyle P=0} ) 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
η = ( V V 0 ) 1 3 {\displaystyle \eta =\left({\frac {V}{V_{0}}}\right)^{\frac {1}{3}}}
then the equation of state is:
P = 3 B 0 ( 1 − η η 2 ) e 3 2 ( B 0 ′ − 1 ) ( 1 − η ) {\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.
References
