Thermodynamics
We now wish to relate our expression energy conservation to the magnetocaloric effect \(\Delta T\left(\frac{dH}{dT}\right)\), which depends on the temperature dependence of the magnetization \(\frac{dM}{dT}\), the system magnetic-field dependent heat capacity \(C\left(H\right)\), and thermal conductance \(\kappa\).
From classical thermodynamics, we have the definition of heat capacity (for the spin system)