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I assume that there was a single person that at a specific day in time was the first to see and understand perfectly clearly that temperature is somehow identical with the mean kinetic energy of a bunch of molecules or atoms, and who was able to write this done as a mathematical equation.

Even though this idea grew slowly - over generations of physicists and inside the mind of this one physicist - I believe it became clear to him somehow suddenly (accompanied by an eureka effect).

Do we know who this person was, and when it happened (roughly)?

Or do you believe this question doesn't make sense or is unanswerable?

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    $\begingroup$ You romanticise science too much but if one scientist deserved to be singled out here, it has to be Boltzmann. $\endgroup$ – user154997 Oct 18 '17 at 9:47
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    $\begingroup$ And to prove @LucJ.Bourhis first point I would say that if you are going to try and pin the kinetic theory of gasses on one person, I would go for James Clark-Maxwell $\endgroup$ – By Symmetry Oct 18 '17 at 9:56
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    $\begingroup$ May this be better on History of Science and Mathematics? $\endgroup$ – CDCM Oct 18 '17 at 10:00
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    $\begingroup$ @HansStricker Because if you over-romanticise history and try and to paint it as the breakthrough of one individual, people don't agree on who that should be $\endgroup$ – By Symmetry Oct 18 '17 at 10:02
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    $\begingroup$ I'm voting to close this question as off-topic because it is a question about the History of Science (possibly also the Sociology of Science), not a question about a concept of physics. $\endgroup$ – sammy gerbil Oct 18 '17 at 15:34
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A sketchy and incomplete account...

Francis Bacon, in his Novum Organum (1620) referred to heat as a mode of (particle) motion, but that's not to say that he had anything like the modern conception of Kinetic Theory, and he certainly didn't attempt any mathematical treatment. Daniel Bernoulli (1738) developed a version of kinetic theory that we'd recognise today. John James Waterston (1843) derived a kinetic theory equation for gas pressure (without the 1/3 factor). He also related molecular KE to temperature. His ideas weren't taken seriously. In the late 1850s, Maxwell and Clausius, soon joined by Boltzmann, developed Kinetic Theory as we know it today.

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  • $\begingroup$ Thanks a lot for your hint to Waterston: I never have heard of him before, but he is an extremely interesting scientist. $\endgroup$ – Hans-Peter Stricker Oct 18 '17 at 11:38
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    $\begingroup$ He was mentioned by the late Cyril Domb in a series of lectures on statistical mechanics at King's College London, many decades ago. I'd not heard of him before. It might be interesting to compare him with Oliver Heaviside, a much later physicist and engineer, who had a struggle getting his ideas accepted. $\endgroup$ – Philip Wood Oct 18 '17 at 12:49
  • $\begingroup$ Interesting enough, that both Domb and Waterston were concerned with phase transitions and critical phenomena (Waterston especially in the context of mental functions, but maybe I'm just talking rubbish). $\endgroup$ – Hans-Peter Stricker Oct 18 '17 at 13:03

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