In molecular terms,
the random thermal motion of the hot reservoir has been converted into ordered
motion characteristic of work. Because the conclusion is contrary to experience, the
initial assumption that engines A and B can have different efficiencies must be false.
It follows that the relation between the heat transfers and the temperatures must also
be independent of the working material, and therefore that eqn 3.10 is always true for
any substance involved in a Carnot cycle.