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Statistical mechanics/Thermodynamics two spin-1/2 subsystem
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[QUOTE="S_Flaherty, post: 4521710, member: 359865"] [h2]Homework Statement [/h2] Consider two spin-1/2 subsystems with identical magnetic moments (μ) in equal fields (B). The first subsystem has a total of N[SUB]A[/SUB] spins with initially "a" having magnetic moments pointing against the field and (N[SUB]A[/SUB] - a) pointing along the field, so that its initial energy is U[SUB]iA[/SUB] = μB(a - (N[SUB]A[/SUB] - a) = μB(2a - N[SUB]A[/SUB]). The second subsystem has a total of N[SUB]B[/SUB] spins with "b" having moments initially pointing against the field so that its initial energy is U[SUB]iB[/SUB] = μB(2b - N[SUB]B[/SUB]). Now suppose that the two subsystems are brought together so that they can exchange energy. Assume that B = constant and a, b, N[SUB]A[/SUB], N[SUB]B[/SUB] >> 1. Show that in equilibrium, a[SUB]0[/SUB]/N[SUB]A[/SUB] = b[SUB]0[/SUB]/N[SUB]B[/SUB], and this implies that the two subsystems will have the same "magnetization," i.e. total magnetic moment/spin. [h2]Homework Equations[/h2] I'm not really sure what equations are useful in this case because I'm having trouble understanding what I need to be doing. I think I need to use multiplicity so Ω(N,n) = N!/(n!(N-n)!) [h2]The Attempt at a Solution[/h2] I think that I have to first figure out the most probable macrostate because that is where the systems would be in equilibrium(?). So do I go along the lines of solving Ω(N[SUB]A[/SUB], a) and Ω(N[SUB]B[/SUB], b)? I don't even know if that makes sense or what a[SUB]0[/SUB] and b[SUB]0[/SUB] represent in this question. [/QUOTE]
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Statistical mechanics/Thermodynamics two spin-1/2 subsystem
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