The Fortuitous Discovery and Derivation of the Stefan-Boltzmann Law for Thermal Energy Emission

Kirchhoff's work thus set up a systematic empirical investigation of thermal radiation by physicists. By 1875 the results of this research was appearing in textbooks of physics, notably in the textbook of A. Wullner, Die Lehre von der Wärme vom Standpunkte der mechanischen Wärmetheorie (2nd edition). In that text book Josef Stefan read that John Tyndall had found that the total radiant energy emitted by a platinum wire at a temperature of 1200 °C is 11.7 times that radiated at 525°C. A temperature of 1200° C is an absolute temperature of 1473° K and 525°C is equivalent to 798°K. Josef Stefan noted that

1473/798 = 1.849
and
(1.849)⁴ = 11.61
which is very close to 11.71

f E=σT^β then

E₁/E₂ = (T₁/T₂)^β
and
β = log(E₁/E₂)/log(T₁/T₂)

For the above data

β = log(11.7)/log(1.849) = 4.0016

Stefan conjectured on the basis of that one piece of data that the total emission E of radiant energy over all wavelengths from a body at absolute temperature T is proportional to the fourth power of T; i.e.,

E = σT⁴

Stefan published this speculation in an article in a journal of physics in 1879. Stefan's discovery was fortuitous because Tyndall's result was in error. Tyndall was not using test equipment approximating a black body. The result Tyndall should have obtained was a ratio of 18.6 rather than 11.7.

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