Abstract
In this work we discuss the thermodynamics of the magnetocaloric effect around the first- and second-order magnetic phase transitions. We show that, around the second-order phase transition, the magnetocaloric potential $\ensuremath{\Delta}S$ can indeed be determined by using magnetization data through the Maxwell relation. However, around the first-order phase transition, the Maxwell relation is not valid so that the determination of $\ensuremath{\Delta}S$ by using magnetization data is somewhat more complex and should be done very carefully. These statements were verified in a simple model of interacting spins with two energy levels including an extra term to account for the first-order phase transition.
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