When introducing Planck's switch to looking at black-body radiation, a number of sources -- like MinutePhysics, the Economist, random online encyclopaedias and even here on HSM.SE (plus many popular history accounts: 1, 2, 3, 4, etc.) -- propose motivations analogous to the following:
In 1894, Planck had been commissioned by electricity companies to discover how to generate the greatest luminosity from light bulbs with the minimum energy.
Depending on the source, it is a single company, a local company, a consortium, or the government. But I haven't traced any of these mentions to an actual historical reference or document. Nor have I seen mentions of particular companies.
The above story also rings several alarm bells:
- Why commission a theoretical physicist for an engineering problem if there are several other well-qualified experimentalists (say Lummer or others at the Physikalisch-Technische Bundesanstalt) in Berlin that could be commissioned instead?
- More reputable accounts (like Helge Kragh's (pdf)) do not mention light bulb companies but suggest that Planck was motivated by the universality of Kirchhoff's law of black body radiation. That law was introduced in 1859, before incandescent light-bulbs were important. This suggests that the motivation for studying black body radiation, in general, had little to do with light bulbs (although we can use those theories now to think about them).
- Tying the previous two points together: Planck seems to have been much more concerned about universal, abstract, and foundational questions and doesn't seem like the kind of character that would take on a clearly practical chore like making light bulbs more energy efficient (even if they were all the rage at that time).
Did light bulbs directly motivate Planck? Was he provided funding in 1894-1900 by anybody related to light bulbs? Were researchers close to him (like Lummer, Rubens, or Wien) motivated by making incandescent light bulbs more efficient? Or even by measuring their efficiency?
Or is this simply one of the many myths made up after-the-fact by history textbooks? (If so, bonus question: who originated it?)
The most convincing story that I've found so far in this direction is on the wikipedia page for the Physikalisch-Technische Bundesanstalt:
The first outstanding scientific achievement at the PTR was also closely connected with Max Planck. To decide whether electricity or gas would be more economic for street lighting in Berlin, the PTR was to develop a more precise standard for luminous intensity. For this purpose, in 1895, Otto Lummer and Wilhelm Wien developed the first cavity radiator for the practical generation of thermal radiation.
But this is again stated without a reliable reference. Jorg Hollandt's article in this collection (pdf) might be able to corraborate the above story, but I cannot read German to verify.