Problems and Solutions on Thermodynamics and Statistical Mechanics

164 Problems EI Solutions on Thermodynamics El Stati~ticd Mechanic8

NT and the number of particles with spin -1/2 whose direction is opposite
to H be Ni; then the component of the total spin in the direction of H is

M, = -(NT - NL). By NT + Ni = N, we can obtain Nt = - + M, and

Ni = - - M,. The number of states of the system is

1 N

2 2

N

2

Using Stirling’s formula, one obtains

N!

Nt! NL!

In Q = In ___

BY

a In Q

-=-InNt+In(N-Nt)=O,

a Nt

N

2

we get NT = -, i.e., M, = 0 when the number of states of the system is

maximum.

(b) See Question 2009.

2005

There is an one-dimensional lattice with lattice constant a as shown

in Fig. 2.1. An atom transits from a site to a nearest-neighbor site every

7 seconds. The probabilities of transiting to the right and left are p and

q = 1 - p respectively.

Fig. 2.1.