Some Simple Isothermal Equations of State

Abstract

Previous work on the Tait equation of state, usually applied to liquids, is discussed together with a review of work on a closely related simple equation arising both from the theory of finite strain and from microscopic considerations. The latter equation has been primarily used for fitting hydrostatic compression pressure-volume data for solids. A detailed discussion of methods for assessing goodness-of-fit of data to equations of state is presented along with an analysis of ways to help decide which of two similar equations is the more applicable for given data. Nonlinear least squares fitting of the above two-parameter equations of state is carried out for the first time using published $P-V-T$ data for water, a very compressible hydrocarbon liquid, zinc, lithium, sodium, potassium, and rubidium and the results compared with those of previous analyses of these data. Careful fitting of the present type can lead to new conclusions and insights not so apparent from less careful fitting of the present equations or from fitting with other equations. For most of the materials and data considered here the finite-strain equation was found to be superior to the Tait equation. Reasons are advanced, however, why both equations should be primarily considered only as empirical, with theoretical justifications for them applicable only over limited pressure-volume ranges.