Nonequilibrium Contributions to the Rate of Reaction. IV. Explicit Time-Dependent Solutions

Abstract

The explicit time dependence of the corrections to the equilibrium rate of reaction and the equilibrium rate of change of the temperature in one‐component monatomic systems is obtained by integrating the nonlinear Boltzmann equation with a moment method. The calculations are carried out for the model systems employed in the earlier studies. For sufficiently small values of the ratio of the elastic and reactive relaxation times ${\mathrm{(\tau }}_{{E}}{\mathrm{\hspace{0.17em}/\hspace{0.17em}\tau }}_R{\text{\hspace{0.17em}≲\hspace{0.17em}10}}^{\text{−2}})$ , it was found that in a time ${\tau }_{{E}}$ the time‐dependent corrections increased rapidly from zero to an asymptotic value. For times greater than ${\tau }_{{E}}$ , the asymptotic values of the corrections increased or decreased slowly and approximately linearly with time. The maximum values of the corrections as a function of time (in instances where a maximum value was obtained) were compared with the corresponding result obtained employing the Chapman–Enskog solution of the Boltzmann equation. This qualitative comparison indicates that for ${\tau }_{{E}}{\mathrm{\hspace{0.17em}/\hspace{0.17em}\tau }}_R{\text{\hspace{0.17em}≈\hspace{0.17em}10}}^{\text{−2}}$ the Chapman–Enskog result differs from the present result by 10%. For ${\tau }_{{E}}{\mathrm{\hspace{0.17em}/\hspace{0.17em}\tau }}_R{\text{\hspace{0.17em}≈\hspace{0.17em}10}}^{\text{−4}}$ , the deviation between the two results is reduced to 1%–3%. In the limit as ${\tau }_{{E}}{\mathrm{\hspace{0.17em}/\hspace{0.17em}\tau }}_R\text{\hspace{0.17em}→\hspace{0.17em}0}$ , the present results coincide exactly with the Chapman–Enskog result.