Heat engine temperature dependence

Hence all periodic reversible heat engines working between the same two temperatures must convert the same fraction of the heat absorbed at the higher temperature into work. The maximum efficiency of a heat engine therefore depends only on the temperatures between which it works. In order to calculate this function of the temperature it is sufficient to determine the work done in an arbitrary reversible cycle, which we may perform with any arbitrarily chosen working substance. For simplicity we shall choose a perfect gas as working substance, as its equation of condition is accurately known. The reversible cycle which we shall suppose it to perform is known as CamoFs cycle. It is as follows ... 

Carnot s cycle A hypothetical scheme for an ideal heat machine. Shows that the maximum efficiency for the conversion of heat into work depends only on the two temperatures between which the heat engine works, and not at all on the nature of the substance employed. 

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

Although fuel cells are not heat engines, heat is still produced and must be removed in a fuel cell power system. Depending upon the size of the system, the temperature of the available heat, and the requirements of the particular site, this thermal energy can be either rejected, used to produce steam or hot water, or converted to electricity via a gas turbine or steam bottoming cycle or some combination thereof... 

The temperature scales that have been discussed earlier are quite arbitrary and depend upon the properties of a particular substance. Kelvin was the first to observe that the efficiency of a reversible heat engine operating between two temperatures is dependent only upon the two temperatures and not at all upon the working substance. Therefore, a temperature scale could be defined that is independent of the properties of any substance. 

We prove the identity of the Kelvin scale and the ideal gas scale by using an ideal gas as the fluid in a reversible heat engine operating in a Carnot cycle between the temperatures T2 and 7. An ideal gas has been defined by Equations (2.36) and (2.37). Then the energy of an ideal gas depends upon the temperature alone, and is independent of the volume. 

We now discuss the efficiency of a reversible heat engine operating in a Carnot cycle. The efficiency depends upon the difference between the two temperatures. The greater the difference for a fixed T2 is, the greater the... 

Equation (1.56) implies that the efficiency depends on the two operating temperatures of the engine. The smaller the numerator (temperature difference), the less heat absorbed is converted to work. If the lower temperature is at absolute zero, the efficiency becomes 100%. The engine described is not of interest to pharmaceutical scientists but important to engineers and others who deal with heat engines or refrigerators. However, this heat engine is of interest to all disciplines of science from the viewpoint of the development of absolute zero temperature. 

Since all reversible heat engines working between the same two temperatures will have the same efficiencies, we can conclude that their efficiencies depend only upon the two temperatures between which they work. For further thermodynamic consideration it is, therefore, sufficient that we consider that type of reversible machine, which will lend itself to simple thermodynamic treatment. A machine employing Carnot s cycle is of such a type. 

Thus, the efficiency of reversible heat engine depends only on the temperatures between which the heat engine operates. The lower the temperature of sink where the lower quality of heat is discarded the higher is the efficiency of the heat engine. 

Hae most effective cyclical conversion of heat into work is produced by the hypothetical Carnot engine and depends upon the temperature difference of the two reservoirs. The further apart the temperatures of the two reservoirs, the more effective the conversion. The fraction of heat that can be converted to work with a Carnot engine is called the efficiency e, and is given by ... 

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