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: (-ΔS)max = A(H + H0)2/3 – AH02/3 + BH4/3. Here A and B are intrinsic parameters of the cooling material and H0 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 -ΔSM 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 LaFe13-xSix 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.