The Bean-Rodbell model is used to study the temperature and field dependences of the magnetization M, magnetic entropy Sm, total entropy Stotal and magnetic specific heat Cm in case of first - order phase transition in the elemental Gd system. For magnetic fields ≤ 5 T and temperature range up to 400 K, the isothermal entropy change ΔSm and the adiabatic temperature change ΔTad are determined. For a magnetic field change of 5 T, the maximum values of ΔSm and ΔTad are 4.599 J/mol. K and 20.1 K, respectively. As the magnetic field changes, the value of the Curie temperature Tc changes slightly. In contrast to the second- order phase transition, the maximum values of the magnetocaloric effect (MCE) for first order transition are larger. The temperature and field dependences of the magnetization, magnetic heat capacity, entropy, ΔSm and ΔTad, in addition to Arrott-plots are indicative of first - order phase transition (FOPT).