is equal to the work performed The efficiency is defined to be: where is the work done by the system (energy exiting the system as work), < 0 is the heat taken from the system (heat energy leaving the system), > 0 is the heat put into the system (heat energy entering the system), is the absolute temperature of the cold reservoir, and is the absolute temperature of the hot reservoir. is the maximum system entropy is the minimum system entropy The expression with the temperature can be derived from the expressions above with the entropy: and . Since , a minus sign appears in the final expression for . This is the Carnot heat engine working efficiency definition as the fraction of the work done by the system to the thermal energy received by the system from the hot reservoir per cycle. This thermal energy is the cycle initiator. Reversed Carnot cycle A Carnot heat-engine cycle described is a totally reversible cycle. That is, all the processes that compose it can be reversed, in which case it becomes the Carnot heat pump and refrigeration cycle. This time, the cycle remains exactly the same except that the directions of any heat and work interactions are reversed. Heat is absorbed from the low-temperature reservoir, heat is rejected to a high-temperature reservoir, and a work input is required to accomplish all this. The P–V diagram of the reversed Carnot cycle is the same as for the Carnot heat-engine cycle except that the directions of the processes are reversed. Carnot's theorem It can be seen from the above diagram that for any cycle operating between temperatures and , none can exceed the efficiency of a Carnot cycle. Carnot's theorem is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirs. Thus, Equation gives the maximum efficiency possible for any engine using the corresponding temperatures. A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient. Rearranging the right side of the equation gives what may be a more easily understood form of the equation, namely that the theoretical maximum efficiency of a heat engine equals the difference in temperature between the hot and cold reservoir divided by the absolute temperature of the hot reservoir. Looking at this formula an