Research and derivation for Wien’s displacement law by using catastrophe theory

Abstract

In this paper, Wien’s displacement law as one of the most important laws of thermal radiation, for which Wien has won the Nobel Prize in Physics, is studied and derived from the perspective of phase transition by using catastrophe theory. This paper describes in detail how the control variable causes the phase transition of the system potential function and the main indexes for judging whether the phase transition occurs. By extending the control variable in the catastrophe theory affecting the thermal radiation into multi-parameters form, the function equilibrium curve of the blackbody radiation is solved, and then the two expressions of Wien’s displacement law including wavelength-temperature and wavelength-temperature are derived theoretically. Furthermore, a phase transition method is proposed to study the thermal radiation of blackbody. This not only provides a new perspective for the research of thermal radiation, but also provides a new idea for the study of other phase transitions.