From its beginnings, thermodynamics gave hints that the laws of motion of microscopic particles were not in accord with Newton’s mechanics, even if two centuries passed before these discrepancies became clear in researchers’ minds. The earliest such observation was the existence of an absolute zero of temperature. Next, Carnot’s analysis of the cyclic process indicated that heat capacities should vanish at absolute zero, in apparent contradiction with the molecular hypothesis. More precise attempts at a statistical description encountered the problems of extensivity and heat capacity of diatomic gases. Even though extensivity can be explained by diffusive motion at room temperature, absolute zero and the behavior of the heat capacity can only be understood on the basis of quantum mechanics.