The maximum isothermal entropy change in a magnetic refrigerant with a second-order phase transition is shown to depend on applied magnetic field $H$ as follows: $(\ensuremath{-}\ensuremath{\Delta}S){}_{\mathrm{max}}$ $=$ $A$($H$ $+$ ${H}_{0}$)${}^{2/3}$ -- ${\mathit{AH}}_{0}^{2/3}$ $+$ $\mathit{BH}$${}^{4/3}$. Here $A$ and $B$ are intrinsic parameters of the cooling material and ${H}_{0}$ is an extrinsic parameter determined by the purity and homogeneity of the sample. This theoretical prediction is confirmed by measurements on variously pure poly- and single-crystalline samples of Gd. The Curie point of pure Gd is found to be 295(1) K; however, the maximum of $\ensuremath{-}\ensuremath{\Delta}{S}_{\mathrm{M}}$ is attained at a lower temperature: The higher the quality of the sample, the closer the peak position to 295 K. Further tests are reported for a series of melt-spun LaFe${}_{13\ensuremath{-}x}$Si${}_{x}$ alloys. These are found to follow the same field dependence, despite the fact that for certain compositions ($x$ 1.8) they experience a phase transition of first, rather than second, order.