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At low temperature, the vibrational degrees of freedom of diatomic molecules do not contribute to the heat capacity of the gas. When the temperature is higher than the vibrational characteristic temperature of diatomic molecules, the vibrational degrees of freedom are excited. The vibration of this diatomic molecule is actually a simple harmonic approximation of the interaction between atoms. However, the simple harmonic approximation criteria given in the literature are all mechanical results, and these results are qualitative. In this study, the statistical physics criterion is given: the validity of the harmonic approximation is that the temperature must be much lower than the molecular bond energy characteristic temperature.
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