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Paramagnetic system: computing number of microstates
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[QUOTE="Fred Wright, post: 5447201, member: 570722"] To find the number of microstates of N distinguishable objects with spin up or spin down you need to divide the N spins into two smaller groups of n[SUB]u[/SUB] and n[SUB]d[/SUB]. There are N distinguishable states so N! possible arrangements, but there are n[SUB]u[/SUB] indistinguishable states so there are n[SUB]u[/SUB]! arrangements of these. By simple combinatory analysis the total number of microstates is, Ω = N!/ (n[SUB]u[/SUB]!(N- n[SUB]u[/SUB])!). The total energy is E = n[SUB]u[/SUB](-μH) + n[SUB]d[/SUB](μH) and from this, n[SUB]u[/SUB] = (1/2)(N-E/(μH)) = (N/2)(1-E/(NμH)) n[SUB]d[/SUB] = N - (1/2)(N-E/(μH)) = (N/2)(1+E/(NμH)) In order to find β and magnetization I suggest you use the basic thermodynamical relations: (∂S/∂E)[SUB]H,N[/SUB] = 1/T and (∂S/∂H)[SUB]E,N[/SUB] = m/T where the entropy is S = k[SUB]B[/SUB]ln(Ω) [/QUOTE]
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Paramagnetic system: computing number of microstates
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