Physics 3333
Homework Set 3
Due October 4,
1999
email
to: phcox@tamuk.edu
1.Entropy
and temperature.
Suppose g(U) =CU3N/2, where C
is a constant and N is the number of particles.(a)
Show that 
.
(b) Show that 
is
negative. This form of g(U) actually applies to an ideal
gas.
2.Paramagnetism. Find
the equilibrium value at temperature t
of the fractionalmagnetization
M/Nm
= 2<s>/N
of
the system of N spins each of magnetic moment m in a magnetic
field B. The spin excess is 2s. Take the entropy as the logarithm
of the multiplicity g(N,s) to be:
,
for
|s| << N. Hint: Show that in this approximation
,
withs0
= log g(N,0). Further, show that 1/t
=– U/m2B2N,
where U denotes <U>, the thermal average energy.