Thermodynamics, Statistical Physics, and Quantum Mechanics

141

4.4 3 Diatomic Molecules in Two Dimensions

(Columbia)

a) The partitionfunction may be calculated in theusual way by multi-

plying the individual Boltzmann factors by their degeneracies and summing:

This isdifficult tosum, but we mayconsider theintegral instead, given the

assumption that

b) The energy and heat capacityof the set ofdiatomicmoleculesdescribed
above may be determined from the partitionfunction for theset:

where the N-fold product has been divided by the number of permutations
of theNindistinguishablemolecules. Recallthat

We then find that

Again, for theheat capacity is

A diatomic rotor inthreedimensions would havecontributions to theenergy
of per degree of freedom. Three degrees oftranslation and two
degrees ofrotation(assumingnegligibleinertia perpendicular toits length)
gives for one molecule

THERMODYNAMICS AND STATISTICAL PHYSICS