A closer look at planck's blackbody equation

Abstract

The spectral distribution of blackbody radiation is given by Planck's blackbody equation. This can be integrated across the complete spectrum to obtain the total blackbody emissive power (the Stefan-Boltzmann law). In some circumstances we shall want to investigate behaviour only in a band of the spectrum. For example, rare earth oxides which are commonly used in thermophotovoltaic devices typically emit significantly only in a single narrow band. The complexity of Planck's blackbody equation is such that it appears to require significant computing prowess to be able to obtain useful results. In a recent paper in this journal, Jain (1996) calculated the emissive power of the visible region using the high-powered mathematical software package Mathematica. The requirement of advanced numerical techniques and/or a powerful piece of software limit the range of students who can study spectral blackbody effects. However, by taking a closer look at Planck's equation we find that it is possible to learn much about spectral blackbody effects (including all of Jain's results) by careful use of mathematical techniques covered in A-level and a spreadsheet (or other simple computational tool). This opens a study of Planck's equation to all undergraduates. © 1997.