Thermodynamics, Statistical Physics, and Quantum Mechanics

204 SOLUTIONS

4.84 Three Ising Spins (Tennessee)

a) Define and where The definition of the

partition function is

A direct calculation gives

b) The average value of spin is

c) The internal energy is

4.85 N Independent Spins (Tennessee)

a) The partition function is given by

where Each spin is independent, so one has the same result as
for one spin, but raised to the Nth power

b) The internal energy is the derivative of ln Z with respect to

c) The entropy is derivative of ln Z with respect to