Thermodynamics - Work done on a paramagnetic material

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SUMMARY

The work done on a paramagnetic material can be expressed in two forms: \(\hat{d}w = -MdB\) and \(\hat{d}w = -BdM\), where \(B\) represents the magnetic field and \(M\) denotes magnetization. The textbook reference supports the first equation, while various articles cite the second. Clarification is needed regarding the relationship between \(B\) and \(H\), as discussed in Landau and Lifshitz's Volume V, Sections 31 and 32. The paper "The Form of Magnetic Work in a Fundamental Thermodynamic Equation for a Paramagnet" published in Am. J. Phys. 67, 613 (1999) provides further insights.

PREREQUISITES
  • Understanding of thermodynamic principles related to magnetism
  • Familiarity with the concepts of magnetization (M) and magnetic field (B)
  • Knowledge of the relationship between magnetic field (B) and magnetic field intensity (H)
  • Access to Landau and Lifshitz's "Statistical Physics" for advanced concepts
NEXT STEPS
  • Research the derivation and implications of \(\hat{d}w = -MdB\) in thermodynamics
  • Explore the differences between magnetization (M) and magnetic field (B) in paramagnetic materials
  • Study the relationship between magnetic field (B) and magnetic field intensity (H) in detail
  • Review the paper "The Form of Magnetic Work in a Fundamental Thermodynamic Equation for a Paramagnet" for comprehensive understanding
USEFUL FOR

Physicists, thermodynamics researchers, and students studying magnetism and its applications in materials science will benefit from this discussion.

Cantique
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What is the work done on a paramagnetic? I have seen both of the following:

\hat{d}w = -MdB
\hat{d}w = -BdM

Where B is magnetic field and M is magnetisation

Am I missing something here or are these two completely opposite? My textbook says that -MdB is the work done but I am sure I have seen articles where they use HdM as the work done. Could somebody clear this up for me?
 
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See the paper The Form of Magnetic Work in a Fundamental Thermodynamic Equation for a Paramagnet
Am. J. Phys. 67, 613 (1999).

A copy can also be obtained at http://faculty.luther.edu/~macdonal/ .
 
Cantique said:
I have seen articles where they use HdM as the work done. Could

Do you know the relationship between B and H?
 
One of the best discussions is given in Landau, Lifshitz, Vol. V, Section 31 and 32.
 

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