A Multi-Dimensional Exploration of Black-Body Radiation: Laws, Applications and Significance

This paper studies the black-body radiation and related laws, providing a background inquiry into black body radiation as one of the important sources of modern physics. The problems to be tackled include derivation of Planck's formula, and derivation of Wien's displacement law and Stefan-Boltzmann law from Planck's formula. This work also mentions applications in cosmology, such as cosmic background radiation. In a methodical way, it introduces the derivation of the black-body formula, provides calculation of average energy and number of vibrations of vibrating particles inside the cavity with a certain frequency, and comes to the black-body radiation formula. Limit method falls into place in order to arrive at Wien formula, and Rayleigh-Jeans formula from Planck’s law. The results and conclusions are illustrated on the derivation of Stefan-Boltzmann law and Wien's Law, along with applications in cosmology. This work is significant in that it will help readers get a clear view of the black body radiation formula and its importance. It serves as a guide for the new physicists in their study and seems to be helpful for professionals in other fields.