As this fascinating documentary shows, the attempt to answer this question has produced a dramatic series of insights and breakthroughs in our understanding of the universe, such as the relationship between temperature and pressure, the development of thermometers and standards of measures, the development of the laws of thermodynamics and the principle of conservation of energy, among many others.
This pursuit has also involved some of the greatest scientific minds of the past four hundred years, such as Cornelius Drebbel (who invented an air conditioner in the early 1600's, as well as the first navigable submarine!), Francis Bacon, Robert Boyle, Daniel Farenheit, Anders Celsius, Guillaume Amontos, Antoine Lavoisier, Count Rumford, Michael Faraday, Lord Kelvin, James Prescott Joule, and even the botanist and taxonimist Carl Linnaeus.
I never knew Madame Lavoisier ended up marrying Count Rumford!
If you want to learn more about Lavoisier and Faraday's scientific contributions to Einstein's formulation of E=mc2, check out this other fascinating documentary.
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