## Equipartition theorem

$\Delta U=q+w$

Michelle Dela Rosa 1D
Posts: 25
Joined: Fri Sep 25, 2015 3:00 am

### Equipartition theorem

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!

Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times

### Re: Equipartition theorem

The vibrational modes start to have an effect when kbT 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 kb gives about 4000 K. So you need a very high temperature to get the vibrational modes.