Dear David Chukwuma Izuogu!

1. In the beginning, you need to plot the М(T,H) (H=const)  from М(H) (T=const). 

2. Next, perform numerical differentiation of the function M(T,H) (H=const) with respect to temperature.

3. Next,, you need to plot the dМ(T,H)/dT (T=const) from dМ(T,H)/dT (H=const).

4. Next, perform numerical integration of the function dМ(T,H)/dT (T=const) with respect tomagnetic field.

Good luck!

There is no problem in doing the numerical integration (  use trpezium  or Simpson or more elababorate( higher order)  procedures . The problem comes with dealing with/ knowing  the exp. uncertainties in your  (dM/ dT) h    data , especially if those are small quantities eg far away from a phase transition . That is why, many years ago ,I gave up on this approach and built a simple calorimeter to measure small  T (H) directly. .Depending on the temp. regime you are in, small " chip " semiconductors  eg diodes , thermistors etc  will give you more than adequate T resolution . From tihis data you can of course  get S(H) more directly   and, by experience, much more reliably .

Dear Rajendra Kumar,

Thank you for your recommendation. I have the textbook in question but it doesn't really explain how to carry out the numerical calculation which I am looking for.

Luckily for me, Prof. Yury Koshkidko just stated what I am actually looking for which although was given in the textbook but in a confusing way for someone not very good with calculus.

I am trying to use Origin 9.0 to handle the data and wanted to know how to use the software to handle the integration and incorporated partial differentiation. I had ignored the partial differentiation and integrated directly with respect to dH but the graph was looking weird to me.

From what Yury Koshkidko wrote up there, it seems I am getting the weird plot because I didn't carry out the differentiation part. 

Many thanks to you Prof. Yury Koshkidko!!!

Dear Chris Guy,

Thank you for your contribution. Are you saying the numerical integration of the M vs H data is not reliable? The data was obtained using a SQUID machine which I think has a high precision. Do you think that might not give me a reliable result? It will be cool if I can also build such calorimeter you are using or work with you if possible. I can compare results from both my SQUID measurement and that of the calorimeter.

Also, the Trapezium and Simpson are they free software? Can you help me with a link if any is free?

Thanks

That depends on the data !! but essentially yes  because  you almost certainly do not know your T to better than 0.1 ok and H to  better than ~0.5 - 1% . Hence the dM/dT and dM/dH will have significant errors ( depending the size of the effect you are after)   independent of the sensitivity of the Squid..

Trapezium  ... Simpson  cubic etc are standard algorithms you can get from any high school  / UG   maths textbook. My calorimeters  were  no longer used and scrapped over 30 years a ago . Good luck .

Oh is your interest in magnetic cooling ?    If so where is  that topic now. It looked like a silly non-starter 10 years ago  ( effect is way to small to compete with  standard liquid fridges ,at least near room temperature.

@yuriy koshkid'ko

Sir

Do you have any detail about your method of finding entropy change in written detail form. If yes please guide me through. Thanks