Thermodynamics, Statistical Physics, and Quantum Mechanics

(^232) SOLUTIONS
4.102 Gas Adsorption (Princeton, MIT, Stanford)
For two systems inequilibrium, thechemicalpotentials should be equal.
Consider one of the systems as an ideal gas(vapor) in a volume, and another
as asurfacesubmonolayer film. For an ideal gas the free energyF (see
Problem4.38) isgiven by
where and correspond to the energy states and statistical sum associ-
atedwith theinternal degrees of freedom. If the temperature is reasonably
small, where corresponds to theionization energy of the
atoms, sothat theatoms are not ionized and mostly in theground state,
and this state is nondegenerate, we can take and then(S.4.102.1)
becomes
The Gibbsfree energyGis given by
where we haveexpressedGas a function ofPand using The
chemicalpotential so
Now, consider an adsorptionsite: we can apply aGibbs distributionwith
a variable number of particles to thissite: