Statistical Physics 199(c) For low temperatures, we need only take the first two terms of z,
i.e., z = 1 + 3e-'lT, where 6 = h2/4a2ma2k.
so
2036
The quantum energy levels of a rigid rotator areej = j(j + l)h2/8n2ma2 ,
where j = 0,1,2,... , m and a are positive constants. The degeneracy of
each level is gJ = 2j + 1.
(a) Find the general expression for the partition function 20.
(b) Show that at high temperatures it can be approximated by an(c) Evaluate the high-temperature energy U and heat capacity C,,.
(d) Also, find the low-temperature approximations to zo, U and C,.integral.
( s UN Y, Bufulo)
Solution:
(a) The partition function iswhere,
h2
8a2ma2k *
6=