The effect of the vibrational level of a molecule on the relaxation time of its rotational energy is studied within the state-to-state kinetic theory approach. The rotational levels of molecules are described by the non-rigid rotator model, while the interaction between molecules is described by the variable soft sphere model. This model is used to calculate the N 2 -N, O 2 -O, and NO-O collision cross sections for different vibrational and rotational levels of molecules. The rotational energy relaxation time is introduced for each vibrational level using the methods of the kinetic theory of nonequilibrium processes. The relaxation times are numerically calculated within a broad temperature range and compared with the relaxation time determined by the well-known Parker formula. The effect of various multi-quantum rotational transitions on the accuracy of the rotational relaxation time calculation is analyzed, and the convergence of the solution with an increase in the maximally possible number of quanta transmitted in the course of transition is demonstrated. It has been established that the vibrational state of a molecule has an appreciable effect on the rotational energy relaxation time in the state-to-state approach, and using the Parker formula may lead to a noticeable error in the calculation of state-to-state transport coefficients. The Parker formula provides a satisfactory agreement with the results obtained via the averaging of state-resolved relaxation times with a Boltzmann vibrational energy distribution in the one-temperature approximation at moderate temperatures.
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