### Equipartition theorem

Posted:

**Thu Jan 07, 2016 8:05 pm**Just out of curiosity, how high does the temperature have to be to use the equipartition theorem in calculations of vibrational motion? Thank you in advance!

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=130&t=9156

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Posted: **Thu Jan 07, 2016 8:05 pm**

Just out of curiosity, how high does the temperature have to be to use the equipartition theorem in calculations of vibrational motion? Thank you in advance!

Posted: **Fri Jan 08, 2016 2:00 am**

The vibrational modes start to have an effect when k_{b}T becomes greater than the vibrational energy gap. The size of this gap depends completely on the specific molecule but it can be approximated easily by quantum mechanics. Just for example, the vibrational gap in HCl is about 5.7*10^-20 J per molecule (35 kJ/mole). Dividing by k_{b} gives about 4000 K. So you need a very high temperature to get the vibrational modes.