Thermomagnetic motors serve as energy harvesters by converting low-grade thermal wastes into useful mechanical power. This paper proposes a mathematical model based on the first law of thermodynamics for assessing the specific work produced by thermomagnetic motors utilizing first and second-order magnetocaloric materials. After initial verification of the results against data from open literature for the ideal Ericsson and Brayton cycles, the model then explores the impact of losses and irreversibilities on the output work. It was found that internal demagnetizing fields reduce the available work up to 42% for the simulated conditions, while heat losses and magnetic hysteresis are complex to implement and show minor impacts. Thermal hysteresis, in turn, may enhance the specific work, but prolong cycle periods. The model provides a cost-effective means to compare magnetocaloric materials and evaluate motor performance, aiding in component selection for thermomagnetic motors.