Ultrasonic and Relaxational Spectroscopy of Fast Reactions. I. Gas

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Abstract
As a method of ultrasonic spectroscopy in gas, ultrasonic absorption and dispersion in gas due to multiple reactions are treated theoretically and the interaction of the relaxations is examined. The complex velocity of sound is calculated from the changes of the number of moles, the pressure, the volume, the internal energy, and the rates of the reactions by sound wave. The heat capacities for gases at constant pressure and at constant volume are composed of the terms of a simple mixture, the terms due to each reaction, and the terms due to the mutual interaction of the reactions. The latter two terms depend on the sound frequency, and the last terms are pointed out for the first time. Examples involving one and two reactions are shown, and Einstein's equations are derived as a special case of one reaction. The characteristics of the ultrasonic spectrum and a numerical example will be treated in a later paper.