Some magnetic materials undergo a first-order phase transition when a magnetic induction field B is applied. These materials are of interest because some of them have a strong magnetocaloric effect, which could be used for refrigeration applications [134]. In these materials, at any given temperature T, there is a critical magnetic induction field B in which the two phases coexist. The two phases, labelled 1 and 2, are characterised by their molar magnetisation m₁ and m₂ and their molar entropies per unit volume s₁ and s₂. Show that the temperature derivative of the magnetic induction field B satisfies the magnetic Clausius–Clapeyron equation,which is analogous to the Clausius–Clapeyron equation (6.49).

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dB dT -($182) (m₁m₂)¯¹