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b3 HANDWRITTEN THEN BOX THE FINAL ANSWERS (DO NOT USE AI) III. PARAMAGNET [40 pts] Consider / non-interacting spins 1/2 with dipole mo- ments u

b3 HANDWRITTEN THEN BOX THE FINAL ANSWERS (DO NOT USE AI)

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III. PARAMAGNET [40 pts] Consider / non-interacting spins 1/2 with dipole mo- ments u in a uniform magnetic field B at thermal equi- librium. Each spin can have two possible energies tuB. 10 pts In the canonical ensemble, calculate the partition function of the magnet at temperature T. 10 pts Calculate the average energy of the magnet. 20 pts Calculate the heat capacity of the magnet

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