Thermodynamics - Work done on a paramagnetic material

[Cantique]

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?

 

[macdonal]

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/ .

 

[256bits]

I have seen articles where they use HdM as the work done. Could

Do you know the relationship between B and H?

 

[DrDu]

One of the best discussions is given in Landau, Lifshitz, Vol. V, Section 31 and 32.

 

[sardar]

The work done on a paramagnetic material is the energy transfer that occurs when the material is placed in a magnetic field. This work can be calculated using the equation \hat{d}w = -MdB, where M is the magnetization of the material and B is the magnetic field. This equation represents the work done on the material as the field changes.

The confusion may arise from the fact that there are two different ways to express the change in magnetization, either as dM or as HdM. Both expressions are valid, but they represent different physical quantities. The first, dM, represents the change in magnetization over a small interval of magnetic field. The second, HdM, represents the product of the magnetic field and the change in magnetization over a larger interval.

In the context of thermodynamics, the work done is typically calculated using the first expression, dM, as it represents the incremental change in the system. However, both expressions can be used depending on the specific problem being studied. It is important to clearly define which expression is being used to avoid confusion.