How might a heat engine attain the highest possible efficiency? Does a heat-engine’s efficiency depend on its construction? On the type of intermediate substance employed? On the temperature of the boiler? Of the condenser? Carnot argued that all these factors may, in fact, affect the efficiency of a heat-engine. But in principle, there exists a special class of heat-engines which possess the highest possible efficiency. These special heat-engines are the reversible heat-engines—those in which there is (essentially) no useless heat flow between various internal components, and thus in which all of the heat flow from the hot to the cold reservoir provides useful work.
Why must a reversible heat-engine have the highest possible efficiency? Carnot employs a proof by contradiction to demonstrate this point: he supposes, for the sake of argument, that a heat engine exists which is more efficient than a reversible heat engine. He then proves that such a heat-engine could be driven backwards (by a reversible heat engine running forwards) in such a way as to drive heat from a cold to a hot body without expending any work. But this would violate a fundamental principle of nature: its tendency to restore equilibrium in the caloric. Thus, such a more-efficient heat-engine could not be possible. In the following reading selection, Carnot provides a more exact formulation of this argument. He does so by introducing what is now known as the Carnot-cycle—a cycle of operations which are performed on a heat engine in such a way as to accomplish the maximum amount of work.