A theory of the response of a burning solid to a sound wave is developed, based on time-dependent solutions of the transport equations relevant to a combustible having idealized physical and chemical properties. The development is restricted to small perturbations about the steady-state conditions for a rather simple model whose parameters have either a direct physical significance, or are experimentally determinable. The introduction of ad hoc time delays, or other phenomenological parameters has been entirely avoided. Time-dependent reaction rate chemistry also has been avoided, by considering only sufficiently fast reactions that the volumetric rate of reaction corresponds to the steady-state rate appropriate to the instantaneous local conditions as described by solution of the time-dependent transport equations. The predictions of the theory are discussed briefly, and several rather general observations are made. However, in view of the complexity inherent in the phenomenon and the present state of inadequate available empirical knowledge regarding this phenomenon, it is not yet possible to make a quantitative comparison between the theory and experiment.

The second virial coefficients of ethane, propane, n-butane, n-heptane, ammonia, methyl chloride, and the freons are computed from available experimental data. The causes for sizeable errors in second virial coefficients are considered. At temperatures above the critical, the second virial agrees with the theorem of corresponding states. Below the critical temperature, molecules with dipoles have unusually large virials and the values of their reduced dipole moment, μ/(TcVc)½, determine the discrepancy. The data for isomeric hydrocarbons show that the second virial is not sensitive to the shape of the molecule. This makes it impossible to determine the exact laws of intermolecular interaction from the temperature variation of the second virial. The imperfections of a gas are considered to arise from the presence of double molecules which exist for the duration of a collision. The equilibrium constant for the formation of double molecules is related to the second virial and its temperature variation gives the entropy ΔS and the energy ΔE of their formation. These may be interpreted qualitatively in terms of the intermolecular forces. The second virial coefficient for all substances fits the equation: B(T) = ba(1 — c exp (—ΔE/RT)) where ba, c, and ΔE are taken as constants. Here bac=exp (ΔS/R). A corresponding states equation is given for estimating second virials when no experimental data are available.

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