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 -ΔS_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-xSi_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.