Isentropic Compressibilities-Experimental Origin and the Quest for their Rigorous Estimation in Thermodynamically Ideal Liquid Mixtures

In this review, attention is initially focused upon the evolution of the Newton–Laplace Equation, that links the measured speed of sound in a fluid in conjunction with its density, to a reliable estimate of its isentropic compressibility κS. Definitions of ideal and excess isentropic quantities are formulated on the premise that the thermodynamic properties of an ideal mixture are mutually related in the same manner as are those of a real mixture or a pure substance. It is shown that both intensive and extensive properties can be derived from the ideal Gibbs energy. Different approaches previously used to calculate ideal isentropic quantities are examined and some subtle errors are identified. The consequences of using conflicting definitions are pointed out. Isentropic pressure derivatives obtained under different conditions and empirical models for estimating the differences between ultrasonic speeds in real and ideal liquid mixtures are discussed. Drawing ultrasonics and thermodynamics together can simplify studies on intermolecular forces and therefore has a enormously wide application; the nature of the link has, however, been widely disputed. In this Review, such differences are clarifed and a thermodynamically sound procedure for evaluating the key parameter, the thermodynamic excess isentropic compressibility (κS)E, is given. The open circles in the graph give values of (κS)E for a model water/1‐propanol mixture; deviations arising from earlier methods—approximations on the mass‐fraction (filled circles), volume‐fraction (open squares) and mole‐fraction (filled squares) averages of pure component values—are shown.