Consider a system of N distinguishable non-interacting spins in a magnetic filed H. Each spin has a magnetic moment of size μ, and each can point either parallel or antiparallel to the field.
(a) Determine the internal energy of this system as a function of β, H, and N by emplying an ensemble characterized by these variables.
(b) Determine the entropy of this system as a function of β, H, and N.
(c) Determine the behavior of the energy and entropy for this system as T→0.