Consider a system having 1024 spin-1/2 particles. The z-component of the magnetic moment of each is ±µB (µB = 9.27 × 10-24 J/T). They are sitting in a magnetic field, in the +z direction, of 0.5 tesla.
(a) If 70% of the particles are spin up, what is the temperature of the system? (Hint: Use classical statistics.)
(b) If in state 1 70% of them are spin up, and in state 2 69.9% are spin up, find the change in entropy in going from one state to the other.
(c) What is the change in the magnetic interaction energy between the two states?
(d) If you use 1/T = ?S/?E, do you get the same temperature as in part (a)?
(e) If the system is insulated from its environment and the magnetic field is reduced to 0.000 001 tesla, the magnetic moment remaining unchanged, what is the new temperature of the system?