Efficiency of a heat engine

As you may know, the ideal thermodynamic efficiency of a heat engine is given by... 

An estimate of the efficiency of a heat engine working between two temperatures T and T - can be obtained by assuming the Carnot cycle is used. By combining the results from applying the first and second laws to the Carnot cycle, the Carnot efficiency e, may be written ... 

Efficiency of a Heat Engine.—The efficiency (N) of a heat engine is measured by the fraction of the quantity of heat received from the source which is converted into work, both heat and work being measured in the same units. 

Note that the coefficient of performance of a heat pump of a refrigerator, unlike the efficiency of a heat engine, can be greater than unity. 

The efficiency of a heat engine is defined as what we want from the engine (work) divided by what we pay for (heat from the hot reservoir) ... 

Students are reminded of the upper thermodynamic limit set on the efficiency of a heat engine, for example the internal combustion and gas-turbine engines. The ideal and totally unrealistic engine would operate on the so-called Carnot cycle where the working substance (e.g. the gas) is taken in at the high temperature (Th) and pressure and after doing external work is exhausted at the lower temperature (Tc) and lower pressure. The Carnot efficiency, /, is given by... 

For proper comparison with the efficiency of a heat engine, the efficiency of a fuel cell must be calculated on the basis of the heat content of the fuel (AHI2F = 1.48 VO, not on the basis of the free energy change (AGI2F = J.23 VO-... 

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 ... 

Thus, the problem of finding the efficiency of a heat engine modeled as a Curzon-Ahlbom cycle, maximizing power output or maximizing ecological function, becomes the problem of finding a function z=z(i ). Substituting z=z(e) in Equation (6), one has... 

By definition, the efficiency of a heat engine is equal to the ratio of the total work W done in the cycle to the heat Qi taken in at the upper temperature hence, by equations (18.2) and (18.7), the efficiency of the hypothetical Carnot engine is... 

Calculate the thermodynamic efficiency of a heat engine operating between the temperatures 600 K and 400 K,... 

Thus the efficiency of a heat engine is given by the difference in temperatures between the heat reservoir and the heat sink (both in kelvins), divided by the temperature of the heat reservoir. In practice we can make (Th — TJ as large as possible, but since cannot be zero and cannot be infinite, the efficiency of a heat engine can therefore never be 100 percent. 

What is the maximum possible efficiency of a heat engine that has a hot reservoir of water boiling under pressure at 125 °C and a cold reservoir at 25 °C ... 

Sadi Carnot established the fact that the maximum efficiency of a heat engine is governed by the difference of temperature of steam entering from the boiler and... 

Thus, based on first-law considerations, the efficiency of a heat engine is reduced according to the amount of heat energy transferred to the low temperature heat sink. However, nothing in the first law prevents cfrom being zero giving an efficiency of 1 (or 100 percent efficiency). To understand the restrictions on the efficiency of a heat engine, we must turn to the second law. 

The thermal efficiency measures the efficiency of a heat engine in converting a heat input into shaft work. 

Carnot (1824) concluded that in an irreversible process, the efficiency of a heat engine is always less than unity, which gives the second part of the Second law. That is, in the irreversible process the rate of absorption of heat AQi from the high temperature source that is converted to work becomes smaller than in a reversible process, and the heat output increases therefore, from (D.4) we have... 

The variation in efficiency for the reactions of carbon and hydrogen with oxygen as a function of temperature, in comparison to the maximum efficiency of a heat engine obeying the theoretical Carnot limitation. 

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