La0.7Ca0.3−xBaxMnO3 nanoparticles with the crystalline size d = 38 and 39 nm for x = 0.025, and 0.05, respectively, were synthesized by utilizing the solid-state reaction and mechanical ball milling methods. We have used the Banerjee's criteria, the mean-field, and the thermodynamic theories, and isothermal magnetization, M(H), data around Curie temperature (TC) to investigate the magnetic phase transformation and the temperature (T) and magnetic field (H) dependences of magnetic entropy change, ΔSm(T, H), for nanoparticles. These exhibit the samples undergoing a second-order magnetic phase transition with an existence of the short-range ferromagnetic order in the samples. Under an applied magnetic field change ΔH = 30 kOe, the maximum value of ΔSm (denoted as |ΔSmax|) are obtained about 4.4 J kg−1 K−1 corresponding to a relative cooling power (RCP) value about 140 J kg−1. Field dependences of |ΔSmax| and RCP can be expressed by the power laws, |ΔSmax| = a × Hn and RCP = b × HN, where a and b are coefficients, n and N are the field exponents, respectively. Interestingly, all the ΔSm(T, H) curves measured at different applied fields are collapsed onto a universal curve, ΔSm(T, H)/ΔSmax versus θ = (T − TC)/(Tr − TC), where Tr is the reference temperature.
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