The Velocity of Sound in an Absorptive Gas

The theory of velocity propagation in a gas as conditioned by internal energy exchanges is considered in detail for the simplest case in which the "lags" may be different—namely, the model with three sets of states. This "second order" theory is required for the interpretation of experimental results where the wave period is of the order of the lag for some states. Assuming the first vibration state of C${\mathrm{O}}_2$ to have the largest lag in accordance with Kneser's interpretation of his recent experiments, the necessary approximations are given explicitly and the results are directly applicable to C${\mathrm{O}}_2$. The apparent lag as measured in sound velocity experiments is not the simple stationary state mean "collision life" nor the mean life of the energy quantum except under special conditions and then for only one of the states. The velocity increment in the "resonance" region is given more accurately in terms of transition probabilities and is not described completely by the specific heats as might be expected from the "first order" theory. Contrary to the indications of the simple theory with an empirical constant the external energy is always merely the translation term. The status of the assumed lag assignment in C${\mathrm{O}}_2$ is discussed in the light of the results and underlying theory of this paper.