In the years after Joule's experiment on the equivalence of heat and work, it was taken for granted that heat and work could be independently defined and that the change in energy for a change of state is the sum of the heat and the work. Only with the work of Caratheodory and Born did it become clear that heat cannot be measured independently, that the change in energy is equal to the adiabatic work, and that heat is equal to the difference between energy change and work for a nonadiabatic process for the same change of state. (Contains 3 notes.)