The proof of the Carnot theorem is a proof by contradiction or reductio ad absurdum (a method to prove a statement by assuming its falsity and logically deriving a false or contradictory statement from this assumption), based on a situation like the right figure where two heat engines with different efficiencies are operating between two thermal reservoirs at different temperature. The relatively hotter reservoir is called the hot reservoir and the other reservoir is called the cold reservoir. A (not necessarily reversible) heat engine M with a greater efficiency \eta_{_M} is driving a reversible heat engine L with a less efficiency \eta_{_L}, causing the latter to act as a heat pump. The requirement for the engine L to be reversible is necessary to explain work W and heat Q associated with it by using its known efficiency. However, since \eta_{_M}>\eta_{_L}, the net heat flow would be backwards, i.e., into the hot reservoir:
