Temperature and the Sackur–Tetrode Equation

Let's figure out what temperature is, and derive one of the most complicated formulas I know of!

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Visuals and background music were made by me

This video was made for the Summer of Maths Exposition. Check out the other entries:
https://some.3b1b.co
#some4

References mentioned in the video:
W. Grimus: On the 100th anniversary of the Sackur-Tetrode equation
https://arxiv.org/abs/1112.3748
J. Mellor: Let’s Derive the Ideal Gas Law from Scratch!
https://www.cantorsparadise.org/lets-...

00:00 What is temperature?
06:32 An oversimplified model
13:19 Multiplicity of an ideal gas
20:40 The Sackur–Tetrode equation
24:01 Extra things