It is generally believed that the laws of thermodynamics govern superconductivity as an equilibrium state of matter. Here we point out that within the conventional BCS-London description of the normal-superconductor transition in the presence of a magnetic field, the transition cannot be reversible, in contradiction with the thermodynamic description and with experiments. This indicates that the conventional theory of superconductivity is internally inconsistent. We argue that to describe a reversible transition it is necessary to assume that charge transfer occurs across the normal-superconductor phase boundary, as proposed in the theory of hole superconductiviy. This provides also a solution to the angular momentum puzzle pointed out in previous work. Our explanation can only apply if the current carriers in the normal state are holes. An experimental test of these ideas is proposed.