Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 47

d)Find the low-temperature limit of the heat capacity and explain why

it is reasonable in terms of the model.

4.102 Gas Adsorption (Princeton, MIT, Stanford)

Consider a vapor (dilute monatomic gas) in equilibrium with a submono-

layer (i.e., less than one atomic layer) of atoms adsorbed on a surface.

Model the binding of atoms to the surface by a potential energy

Assume there are possible sites for adsorption, and find the vapor pres-

sure as a function of surface concentration (N is the number of

adsorbed particles).

4.103 Thermionic Emission (Boston)

a) Assume that the evaporation of electrons from a hot wire (Richard-

son’s effect) is thermodynamically equivalent to the sublimation of a

solid. Find the pressure of the electron gas, provided that the elec-

trons outside the metal constitute an ideal classical monatomic gas

and that the chemical potential of the electrons in the metal (the

solidphase) is a constant.

b) Derive the same resultby using the Clausius–Clapeyronequation

where L is the latent heat of electron evaporation. Neglect the volume

occupied by the electrons in the metal.

4.104 Electrons and Holes (Boston, Moscow

Phys-Tech)

a)

b)

c)

Derive a formula for the concentration of electrons in the conduction

band of a semiconductor with a fixed chemical potential (Fermi level)

assuming that in the conductionband (nondegenerate

electrons).

What is the relationship betweenhole and electron concentrations in

a semiconductor with arbitrary impurity concentration and band gap

Find the concentrationof electrons andholes for anintrinsicsemi-

conductor (no impurities), and calculate the chemical potential if the

electron mass is equal to the mass of the hole: