Ultrasonic Propagation in Liquids. II. Theoretical Study of the Free Volume Model of the Liquid State

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Abstract
The free volume theory of liquids is applied to problems connected with sound propagation. The equation of state derived by Tonks for assemblies of hard elastic spheres may be written pVa≅3NkT, where the available volume Va is the difference between the actual volume and the volume corresponding to the closest possible packing. It is shown that the molar available volume is approximately given by the increase in molar volume of a substance on heating from 0°K to the temperature considered, so that the pictorial concept of the available volume has a real physical basis. Using the Tonks equation, expressions are derived for the sound velocity, and the temperature and pressure coefficients of sound velocity. These expressions are compared with experimental results. Expressions are also given for the cubic expansion coefficient and the difference of the specific heats on the free volume model. The Herzfeld‐Rice derivation of the sound absorption caused by phase shifts in the vibrational specific heat is carried through for the Tonks equation of state. The temperature and pressure coefficients of sound absorption are discussed. Remarks are made on the relation of molecular structure to sound absorption.