Finding the probabilities of macrostates for paramagnetic dipoles

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SUMMARY

This discussion focuses on calculating the probabilities of macrostates for a system of 10 paramagnetic dipoles in a magnetic field B. The key equation used is the multiplicity formula, Ω(Nv) = Ntot! / (NΛ! * Nv!), which allows for determining the probability of each microstate. The participant seeks to identify the microstate with the highest probability and the one with the highest entropy, noting that the alignment of dipoles with the magnetic field complicates the analysis. The conclusion emphasizes that energy does not play a significant role in this context.

PREREQUISITES
  • Understanding of statistical mechanics and thermodynamics
  • Familiarity with the concept of microstates and macrostates
  • Knowledge of the multiplicity formula in statistical physics
  • Basic principles of magnetism and dipole behavior in magnetic fields
NEXT STEPS
  • Study the derivation and application of the multiplicity formula in statistical mechanics
  • Explore the relationship between entropy and probability in thermodynamic systems
  • Learn about the behavior of paramagnetic materials in external magnetic fields
  • Investigate the concept of energy states and their relevance in statistical mechanics
USEFUL FOR

Students and researchers in physics, particularly those studying statistical mechanics, thermodynamics, and magnetism, will benefit from this discussion.

Minish
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Homework Statement


Hi!
So I am given two different microstates of a system with 10 dipoles in a magnetic field B.
I am asked to find the microstate that belongs to the macrostate with the highest probability, and to give that probability. I am also asked to find the same but with the highest entropy.
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Homework Equations


Ω(Nv) = Ntot! / ( NΛ! * Nv! )

The Attempt at a Solution


So I can find the multiplicity of the states here and find the probability of each one simply using the multiplicity of that state over the total number of all microstates. However since there is a field and these dipoles will tend to allign with the field, I am unsure of how to answer the given questions.

Thank you very much
 

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Minish said:
However since there is a field and these dipoles will tend to allign with the field, I am unsure of how to answer the given questions.
Energy plays no special role here. Considering Ω(Nv) is the same as considering Ω(E).
 

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