The fluorine nuclei of a calcium fluoride crystal carry magnetic moments of magnitude
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Electricity, Magnetism & Electromagnetism · Statistical foundations and the equilibrium ensembles
Thermal Physics, Ch Two-level systems, paramagnets and the Einstein solid
Problem
The fluorine nuclei of a calcium fluoride crystal carry magnetic moments of magnitude μm=1.32×10−26JT−1, each with two allowed orientations of energy −μmB along the applied field and +μmB against it. The crystal sits in B=0.65T and the nuclear moments are in equilibrium with the lattice at 295K. The field direction is then reversed in a time far shorter than the moments need to respond, so the populations of the two orientations are unchanged while the labels "along" and "against" swap. The moments are weakly coupled to everything else, and the field energy is excluded from U.
((a)) Before the reversal, by what fraction does the population of the lower level exceed that of the upper level, that is, find N↑/N↓−1.
((b)) What temperature fits the populations immediately after the reversal?
((c)) The crystal is now coupled weakly to a copper block held at 295K. Which way does energy flow, and is the spin system colder than absolute zero? Justify your answer with the slope rule for (∂S/∂U)B,N.