Dulong-Petit law
The Dulong-Petit law was discovered in 1819 by two French chemists, Pierre Louis Dulong and Alexis Thérèse. Initially, it stated that the molar heat capacity of solids was equal to 3R, where R is the ideal gas constant.
Later it was shown that this law does not hold at low temperature, and that the molar heat capacity reduces to cancel out at absolute zero. This fact remained puzzling until Einstein explained it using the laws of quantum theory.
If it is considered that the atoms behave as harmonic oscillators in 3D during their thermal agitation around their equilibrium position, the theorem of the equipartition of energy from classical statistical mechanics does yield the Dulong-Petit law.
The fact that it no longer holds at low temperature was a mystery, but retrospectively this was one of the first indications leading to the discovery of quantum theory.