A heat engine performs the conversion of heat energy to work by exploiting the temperature gradient between a hot "source" and a cold "sink". Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. The theoretical maximum efficiency of any heat engine is defined by the Carnot Cycle. The carnot heat engine (the ideal imaginary heat engine) has an efficency equal to (T1 - T2)/T1 where T1 is the temperature of the hot source and T2 is the temperature of the cold sink.

Examples of everyday heat engines include: the steam engine, the diesel engine, and the gasoline (petrol) engine in an automobile. All of these familiar heat engines are powered by the expansion of heated gases. The general surroundings are the heat sink, providing relatively cool gases which when heated, expand rapidly to drive the mechanical motion of the engine.

Examples of heat engines:

(A refrigerator is effectively a heat pump, a heat engine in reverse, which does work to create a heat differential.)

From the laws of thermodynamics, we conclude that:

H = C - W

where H is the energy exchanged with the high temperature system, C is the energy exchanged with the cold system, and W is the work done by the engine.

The efficiency of a heat engine is defined by:

e = W / H = (C / H) - 1

The efficiency of any real engine can not be 1. In fact, the most efficient a heat engine operating between two temperatures (Th [h for hot] and Tc [c for cold]) can possibly be is determined by how efficiently a Carnot Engine would work; given by:

ecarnot = 1 - Tc / Th

The reasoning behind the proof of this theorem relates to the laws of thermodynamics. It is first assumed that if a more efficient heat engine than a Carnot engine is possible, then it could be driven in reverse as a heat pump. Mathematical analysis is used to show that this assumed combination would result in a net decrease in entropy. Since no exceptions have ever been found to the Laws of Thermodynamics, which require that entropy increases, it is concluded that it is not possible to build a heat engine more efficient than a Carnot Cycle engine.

Empirically, no engine has ever been scientifically shown to run at a greater efficiency than a Carnot Cycle heat engine.

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