Thermodynamics - Work done on a paramagnetic material

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Discussion Overview

The discussion centers on the work done on a paramagnetic material, specifically examining the expressions for work related to changes in magnetization and magnetic field. Participants explore the differences between two formulations: \(\hat{d}w = -MdB\) and \(\hat{d}w = -BdM\), questioning their validity and applicability in thermodynamic contexts.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the validity of two expressions for work done on a paramagnetic material, noting that their textbook supports \(-MdB\) while other articles reference \(-BdM\).
  • Another participant suggests consulting a specific paper that discusses the form of magnetic work in thermodynamics, indicating that it may provide clarity on the topic.
  • A participant inquires about the relationship between magnetic field \(B\) and magnetic field strength \(H\), suggesting a potential link to the differing expressions for work.
  • Reference is made to Landau and Lifshitz's work as a source for a comprehensive discussion on the topic, implying that it may contain relevant insights.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the two formulations for work done on a paramagnetic material, indicating that multiple competing views remain without a consensus on which expression is correct.

Contextual Notes

There are unresolved assumptions regarding the definitions and relationships between the variables \(B\) and \(H\), as well as the conditions under which each expression for work is applicable.

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

[itex]\hat{d}[/itex]w = -MdB
[itex]\hat{d}[/itex]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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