Vibrational Relaxation Equation for Polyatomic Gases and Its Application to CO₂

Abstract

The vibrational relaxation equation for polyatomic gases is formulated in consideration of the translation-vibration and the vibration-vibration energy transfers. The multi-quanta transitions of vibrational states and the simultaneous couplings among any numbers of vibrational modes are allowed in the vibrational energy transfers. On the basis of this relaxation equation, the energy relaxation of each vibrational mode in CO₂ is analyzed. The effect of the V−V couplings between mode ν₃ and modes ν₁+ν₂ on the relaxation of mode ν₁(ν₂) is not appreciable due to the small vibrational heat capacity of mode ν₃, and the apparent relaxation rate for mode ν₁(ν₂) is nearly equal to a mean rate constant K_∞ of the T−V processes of modes ν₁ and ν₂. If the rate of the intramolecular V−V couplings of mode ν₃ with modes ν₁+ν₂ is comparable to or larger than K_∞, the apparent relaxation rate of mode ν₃ is also very close to K_∞. This is the reason why a multiple relaxation has not been found experimentally in CO₂.