On the Trail of Blackbody Radiation by unknow

Author:unknow
Language: eng
Format: epub
Tags: Planck’s constant; quantum physics; blackbody; blackbody radiation; spectral energy density of blackbody radiation; Stefan-Boltzmann law; Wien’s displacement law; Einstein’s theory of quantum radiation; history of physics
Publisher: MIT Press
Published: 2022-08-16T00:00:00+00:00

(8.12)

Planck then correctly deduced from (8.6), that is, from , that

(8.13)

Using (8.11) and (8.12) to substitute for both sides of (8.13) one arrives at a relation,

(8.14)

between the second derivatives and evaluated at the equilibrium energy .

At this point Planck made a mistake—perhaps an understandable mistake. He incorrectly assumed that the two functions, and , are the same function of their arguments so that (8.14) is equivalent to

(incorrect)(8.15)

where . The functional form

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