Consider a system of N non-interacting spin-1/2 dipoles in a magnetic field B in the +z direction. Each dipole has a magnetic moment of size μ, and each can point either parallel or anti-parallel to the field. If the energy of parallel an

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Consider a system of N non-interacting spin-1/2 dipoles in a magnetic field B in the +z direction. Each dipole has a magnetic moment of size μ, and each can point either parallel or anti-parallel to the field. If the energy of parallel and anti-parallel dipoles is given as +μB and -μB respectively, determine:
(a) The internal energy of this system
(b) The specific heat capacity of this system
(c) The entropy of this system as a function of temperature

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