According to QM, a diatomic gas molecule possesses rotational energy levels given by En = (1/2I)(h^2)n(n + 1). h is meant to be h-bar, Planck's constant over 2π here and I = moment of inertia. Energy level n has a degeneracy of 2n + 1.(adsbygoogle = window.adsbygoogle || []).push({});

Find the partition function of the rotational motion of a single such molecule.

Z = Σ gn.exp(-En/kT) = Σ (2n + 1)exp[-(n(n + 1)h^2)/kT]

Suppose T is sufficently small so that only the first 2 energy levels need to be considered. Find an expression for the mean rotational energy.

Here's where I'm stuck as I don't know which equation to use. Some of my notes say E avg = (1/Z)Σ En.gn.exp(-En/kT). In some of my other notes, there's an example for finding out the mean vibrational energy. E avg = (1/Z)(kT^2)dZ/dT. Obviously for rotation, the Boltzmann factor will be different as there's a different expression for En, but can I use this equation anyway?

Edit: I worked out Z for the first 2 states as Z = 1 + 3exp[-(h^2)/IkT].

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Statistical Physics question

**Physics Forums | Science Articles, Homework Help, Discussion**