Murnaghan

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The Murnaghan EoS (Murnaghan, 1937) can be derived from the assumption that the bulk modulus varies linearly with pressure, . This results in a relationship between P and V of:


               


or as:


               


This illustrates the attraction of the Murnaghan EoS: it is ‘invertible’ (Freund & Ingalls, 1989), which means that it can be written as either a simple function of V, or as a simple function of P. This makes it very attractive for use in thermodynamic databases and calculations in which both functions and their integrals are frequently required. However, the Murnaghan EoS only reproduces P-V data and the correct values of the room pressure bulk modulus for small compressions up to about 10% (i.e. V/V0 ~ 0.9). It fails at greater compression because it has K''PT  , in contrast to experimental data which indicate that most solids exhibit a small negative value for K''0T   of the order of (e.g. Jackson & Niesler, 1982). The obvious simple extension of the Murnaghan EoS to include an additional term in the expression for the bulk modulus, results in an extremely complex and impractical function for volume as a function of pressure (Freund & Ingalls, 1989).