A New Modified Form of Murnaghan Thermodynamic Equation of State

Abstract

An equation of state (EOS) denotes the relationship between the pressure and the volume, involving two quantities, the isothermal bulk modulus (B₀) and its first pressure derivative (B′), both at zero pressure. An accurate representation of P-V relationship in solids is provided by the modified Murnaghan equation (MME) in which B′ is assumed to be a linear function of pressure. We have derived a new equation of state by assuming B′ to be constant plus a weakly dependent function p of P and solving the resulting differential equation by the perturbation method. If the weak pressure-dependent part is chosen to be proportional to P, a situation exactly analogous to that of the MME, our perturbation solution acquires an algebraic structure somewhat simpler to the MME. As far as numerical applications are concerned, the two equations do not differ much. Our treatment has the additional advantage that it can be easily generalized to include higher order terms if desired. We have reported the V/V₀ versus P values of NaCl and the same have been compared with Freund–Ingalls three-parameter equation and the Birch equation.