Thermodynamics, Statistical Physics, and Quantum Mechanics

136

where we have expressedGas a function of P. The chemical potential
so we obtain, from (S.4.39.3),

Thisapproximation isvalid when thetemperature ismuchlowerthan the
energydifference between the electronicground state and the first
excitedstate; since this iscomparable to theionizationenergy
this condition isequivalent to However, even attemperatures
the gas is almost completely ionized(seeLandau andLifshitz,
Statistical Physics, Sect. 106). Therefore (S.4.39.4) isalways valid for a
nonionizedgas.

Gas in HarmonicWell(Boston)

a) The partitionfunction isgiven by astandard integral (compare with
4.38,where themolecules areindistinguishable):

The HelmholtzfreeenergyFfollowsdirectly fromthe partitionfunction:

b) We may find the force from F:

4.4 0

SOLUTIONS