Statistical Mechanics

PHYS 222

Dr. P. Misra

Fall 2002

Homework #7

Due: 10/30/02

1.

Consider a gaseous system of N noninteracting diatomic molecules, each having an electric dipole moment μ, placed in an electric field of strength E.  The energy Є of a molecule will be given by the kinetic energy of transition plus the kinetic energy of rotation plus the energy of orientation in the applied field:

Є = +-,

where I is the moment of inertia of the molecule, and L_i is the i^th component of angular momentum.

a.       Calculate the energy of the system to order E².

b.      Calculate the linear electric polarization and the dielectric constant ε of the system.

c.      Calculate ε for gaseous HCl at P = 1 atm and T = 0ºC, and compare your result with experiment.

2.

A box of volume V contains 2N atoms of type B.  (B is a symbol with no particular chemical meaning.)  The walls of the box have total area A and n_s sites per unit area where single atoms of type B may either be adsorbed with binding energy ε_s or not adsorbed at all.  Two B atoms may combine via the reaction B₂2B to form B₂ molecules.  Take ε_B to be the unique binding energy of the B’s (i.e., the B₂ molecule has a single bound state).  Let 2m and I be the mass and moment of inertia of the B₂ molecule.  Assume that all the gases are ideal and classical.  Find the probability that one of the wall sites is occupied by a B atom at temperature T.