In the syllabus of electromagnetism and electrodynamics, the polarization of the medium is a very important part. To explain the microscopic mechanism of polarization to students, textbooks often adopt the physical image of the Lorentz model. This physical image is clear and simple, which is helpful for beginners to quickly understand the physical nature of polarization. However, the Lorentz model has a certain degree of inconsistency. In addition, paradoxes arise when using the Lorentz model to solve physics competition problems. In this paper, we first review this classic paradox in the physics competition problems, and then introduce a more rigorous definition of the medium polarization vector, describe the microscopic physical processes that occur during the polarization of the medium, and on this basis, explain the reasons and solutions for the appearance of the paradox using thermodynamics. Finally, we briefly introduce the geometric phase theory for calculating the polarization of the medium.