Thermodynamics, Statistical Physics, and Quantum Mechanics

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The average force is given by

whereFis the freeenergy. So,

The minus signindicates an average attraction between the dipoles.

Entropy of Ideal Gas (Princeton)

a) For an ideal gas thepartitionfunctionfactors;however, we must take

the sum of N identical molecules divided by the number of interchanges N!

to account for thefact that onemicroscopicquantumstate corresponds to

a number ofdifferentpoints inphasespace. So

Now, the Helmholtz free energy,F,is given by

Using theexplicit expression for the molecular energy we canrewrite
(S.4.38.3) in theform

4.38

Using Stirling’s formula, ln we obtain

THERMODYNAMICS AND STATISTICAL PHYSICS