As he no doubt himself perceived, his idea was quite independent of this hypothesis, since, as we have seen, he was led to surmise that heat could disappear; but his demonstrations needed to be recast and, in some points, modified.
It is to Clausius that was reserved the credit of rediscovering the principle, and of enunciating it in language conformable to the new doctrines, while giving it a much greater generality.

The postulate arrived at by experimental induction, and which must be admitted without demonstration, is, according to Clausius, that in a series of transformations in which the final is identical with the initial stage, it is impossible for heat to pass from a colder to a warmer body unless some other accessory phenomenon occurs at the same time.
Still more correctly, perhaps, an enunciation can be given of the postulate which, in the main, is analogous, by saying: A heat motor, which after a series of transformations returns to its initial state, can only furnish work if there exist at least two sources of heat, and if a certain quantity of heat is given to one of the sources, which can never be the hotter of the two.

By the expression "source of heat," we mean a body exterior to the system and capable of furnishing or withdrawing heat from it.
Starting with this principle, we arrive, as does Clausius, at the demonstration that the output of a reversible machine working between two given temperatures is greater than that of any non-reversible engine, and that it is the same for all reversible machines working between these two temperatures.
This is the very proposition of Carnot; but the proposition thus stated, while very useful for the theory of engines, does not yet present any very general interest.

Clausius, however, drew from it much more important consequences.

First, he showed that the principle conduces to the definition of an absolute scale of temperature; and then he was brought face to face with a new notion which allows a strong light to be thrown on the questions of physical equilibrium.