A molecule with a magnetic dipole moment and the partition function.

A molecule possessing a magnetic dipole moment has squared spin angular momentum 3/4 h^2. Give an expression for the energy of the molecule when it is stationary in a magnetic field of flux density B.

Write down the molecule's partition function Z and show that

(deltaZ/deltaB)_T = -T/B (deltaZ/deltaT)_B

A crystal is formed out of such molecules. With M the magnetic moment of the crystal, the work done during an infinitesimal change in B is - MdB. Assuming that magnetic interactions between molecules are negligible, give a general expression for the change in the crystal's Helmholtz free energy in terms of changes in other thermodynamic variables. Show that the entropy S and magnetic moment of the crystal are related by

(deltaS /deltaB) = -B/T(deltaM/deltaB)_T.

Explain physically why there is a minus sign in this equation. If the crystal is thermally isolated, how will its temperature change when B is increased?

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