Vibrational Partition Function for the Multitemperature Theories of High-Temperature Flows of Gases and Plasmas

The vibrational partition function is calculated using the classical method of integration over the whole phase space. The calculations were done for the ground electronic state of a carbon monoxide molecule. The main focus is on temperature in the range 5000-20 000 K, which is common in hypersonic flows of gases and plasmas. The method presented here, because of the exclusion of the noninteracting part of canonical partition function according to the ideas of T.L. Hill, is applicable at temperatures of tens of thousands of Kelvins, where the standard expression for the vibrational partition function fails. At lower temperatures (here 1000-6000 K), the correct quantum results can be obtained with the help of Wigner-Kirkwood expansion. The influence of vibrations on the rotational partition function by bond-length elongation is examined, and the results are compared with the exact ro-vibrational partition function.