Editing Magnetocaloric effect (section)

=== Equation ===

The magnetocaloric effect can be quantified with the following equation:

<math display="block">\Delta T_{ad}=-\int_{H_0}^{H_1}\left(\frac {T}{C(T,H)}\right)_H{\left(\frac {\partial M(T,H)}{\partial T}\right)}_H dH</math>

where <math>\Delta T_{ad}</math> is the adiabatic change in temperature of the magnetic system around temperature T, H is the applied external magnetic field, C is the heat capacity of the working magnet (refrigerant) and M is the [[magnetization]] of the refrigerant.

From the equation we can see that the magnetocaloric effect can be enhanced by:

* a large field variation
* a magnet material with a small heat capacity
* a magnet with large changes in net magnetization vs. temperature, at constant magnetic field

The adiabatic change in temperature, <math>\Delta T_{ad}</math>, can be seen to be related to the magnet's change in magnetic [[entropy]] (<math>\Delta S </math>) since<ref>{{Cite journal| last1=Balli|first1=M.|last2=Jandl|first2=S.|last3=Fournier|first3=P.|last4=Kedous-Lebouc|first4=A.|date=2017-05-24| title=Advanced materials for magnetic cooling: Fundamentals and practical aspects| journal=Applied Physics Reviews| volume=4|issue=2|pages=021305| doi=10.1063/1.4983612| bibcode=2017ApPRv...4b1305B|arxiv=2012.08176|s2cid=136263783}}</ref>

<math display=block> \Delta S(T) = \int_{H_0}^{H_1}\left(\frac{\partial M(T,H')}{\partial T} \right)dH'</math>

This implies that the absolute change in the magnet's entropy determines the possible magnitude of the adiabatic temperature change under a thermodynamic cycle of magnetic field variation. T