Solution Found!
Use Stirling’s approximation to find an approximate
Chapter 2, Problem 19P(choose chapter or problem)
Problem 19P
Use Stirling’s approximation to find an approximate formula for the multiplicity of a two-state paramagnet. Simplify this formula in the limit to obtain . This result should look very similar to your answer to below Problem; explain why these two systems, in the limits considered, are essentially the same.
Problem:
Use the methods of this section to derive a formula, similar to below equation, for the multiplicity of an Einstein solid in the “low-temperature” limit, q≪ N.
Questions & Answers
QUESTION:
Problem 19P
Use Stirling’s approximation to find an approximate formula for the multiplicity of a two-state paramagnet. Simplify this formula in the limit to obtain . This result should look very similar to your answer to below Problem; explain why these two systems, in the limits considered, are essentially the same.
Problem:
Use the methods of this section to derive a formula, similar to below equation, for the multiplicity of an Einstein solid in the “low-temperature” limit, q≪ N.
ANSWER:
Step 1:
To find an approximate formula for the multiplicity of a two-state paramagnet.
The total number of dipoles =
The number of dipoles that point down =
The multiplicity of the paramagnet is