[MatteoFrigo]

See https://www.feynmanlectures.caltech.edu/I_40.html specifically Sections 40-5 and 40-6, for a discussion of why classical physics fails to explain the specific heat of gases.

As a sibling poster commented, the blackbody spectrum was also inexplicable from a classical point of view (see https://www.feynmanlectures.caltech.edu/I_41.html Section 41-2), but I think that the specific-heat problem was known before the blackbody problem.