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The '''multiplicity function''' for a two state paramagnet, W(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the [[Combinations|combinatoric function C(N,n)]]. That is: | |||
<center> | |||
<math>W (n,N) = {N \choose n} = {{N!} \over {n!(N - n)!}}</math> | |||
</center> | |||
It is primarily used in introductory [[statistical mechanics]] and [[thermodynamics]] textbooks to explain the microscopic definition of entropy to students. If the spins are non-interacting, then the multiplicity function counts the number of states which have the same energy in an external magnetic field. By definition, the [[entropy]] S is then given by the [[natural logarithm]] of this number: | |||
<center> | |||
<math>S = k\ln{W }\,</math> | |||
<ref>Schroeder, Daniel V.. An Introduction to Thermal Dynamics. San Francisco: Addison Wesley Longman 2002.</ref> | |||
Where k is the [[Boltzmann constant]] | |||
</center> | |||
==References== | |||
<references/> | |||
[[Category:Thermodynamics]] | |||
Revision as of 16:45, 12 January 2014
The multiplicity function for a two state paramagnet, W(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the combinatoric function C(N,n). That is:
It is primarily used in introductory statistical mechanics and thermodynamics textbooks to explain the microscopic definition of entropy to students. If the spins are non-interacting, then the multiplicity function counts the number of states which have the same energy in an external magnetic field. By definition, the entropy S is then given by the natural logarithm of this number:
[1] Where k is the Boltzmann constant
References
- ↑ Schroeder, Daniel V.. An Introduction to Thermal Dynamics. San Francisco: Addison Wesley Longman 2002.