Statistical Mechanics

PHYS 222

Dr. P. Misra

Fall 2002

Homework #9

Due: 11/15/02

1.

a.       Evaluate the canonical partition function for two free particles in a box of volume V.  Treat the cases where both particles are either spin-½ fermions or spin-zero bosons.

b.      For the systems considered in part ‘a’, evaluate the probability  that one particle will be found at  and another at .

Be careful when dealing in spin degrees of freedom.

2.

For perfect gases in two dimensions, find

a.       The Fermi degeneracy temperature T_F.

b.      The Bose condensation temperature.

c.      The heat capacity at constant area in the low-temperature limit for both the Fermi and Bose cases.