Thermodynamics, Statistical Physics, and Quantum Mechanics

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We see that this is the same asfound in (S.4.44.12).Since we expecta heat

capacity per degree of freedom of 1/2, we see that there are two degrees of

freedom foreachmolecule since

Theycorrespond to the tworotational degrees offreedom of aclassicalrod.

(There are no spatial degrees of freedom since the molecule is considered

fixed.)

4.45 Two-Level System (Princeton)

a) There is nothingto prevent givingeach atom itslarger energy hence,

has a maximum of 1 with Clearly, thesystem would

not be in thermal equilibrium. To compute the problem inequilibrium,

we need todetermine the partitionfunction,Z. For distinguishable non-

interactingparticles, thepartitionfunctionfactors, so foridenticalenergy

spectra

The free energywould be

The energy isthen

or

where Obviously, sinceboth and arepositive, cannot be
largerthan 1. On theother hand, is a monotonicfunction which

SOLUTIONS