Carnot cycle limitation

It is commonly expressed that a fuel cell is more efficient than a heat engine because it is not subject to Carnot Cycle limitations, or a fuel cell is more efficient because it is not subject to the second law of thermodynamics. These statements are misleading. A more suitable statement for... 

This conversion is not subject to the Carnot cycle limitations and is thus theoretically more efficient than a heat-based process. 

In 1894, the German physical chemist Wilhelm Ostwald formulated the idea that an electrochemical mechanism can be used instead of combustion (chemical oxidation) of natural kinds of fuel, such as those used in thermal power plants. Because in this case the reaction will bypass the intermediate stage of heat generation, this would be cold combustion, the direct conversion of chemical energy of a fuel to electrical energy not being subject to Carnot-cycle limitations. A device to perform this direct energy conversion was named fuel cell. 

Two objectives are immediately clear. If the top temperature can be raised and the bottom temperature lowered, then the ratio t= (Tjnin/Tjnax) decreased and, as with a Carnot cycle, thermal efficiency will be increased (for given /a,). The limit on top temperature is likely to be metallurgical while that on the bottom temperature is of the surrounding atmosphere. 

The exergy equation (2.26) enables useful information on the irreversibilities and lost work to be obtained, in comparison with a Carnot cycle operating within the same temperature limits (T ,ax = Ey and T in = To). Note first that if the heat supplied is the same to each of the two cycles (Carnot and IJB), then the work output from the Carnot engine (Wcar) is greater than that of the IJB cycle (Wijg), and the heat rejected from the former is less than that rejected by the latter. 

We now take the system round a reversible Carnot cycle, the reversibility for such a system, in the limit, having been previously demonstrated. 

This approximation improves as we take more and more, smaller and smaller, Carnot cycles, until in the limit of an infinite number of infinitesimal cycles, the agreement is exact. When this occurs, the sum in equation (2.36) is replaced by an integral over the cycle. That is,... 

For every pair of sections, BA and DN, of the actual path we have corresponding (isothermal) pairs, BC and DE, which are parts of an approximate Carnot cycle. In the limit of an infinite mrmber of infinitesimally small cycles, sections BA and DN can be considered isothermal at temperatures T equal to the respective temperatures T for sections BC and DE. Hence we can write... 

A Diesel cycle has a compression ratio of 18. Air-intake conditions (prior to compression) are 72°F and 14.7 psia, and the highest temperature in the cycle is limited to 2500° F to avoid damaging the engine block. Calculate (a) thermal efficiency, (b) net work, and (c) mean effective pressure (d) compare engine efficiency with that of a Carnot cycle engine operating between the same temperatures. 

The Ericsson, Wicks, and ice cycles are modified Brayton cycles with many stages of intercooling and reheat. It has the same efficiency of the Carnot cycle operating between the same temperature limits. The Feher cycle is a cycle operating above the critical point of the working fluid. 

The recuperated Brayton cycle approaches Carnot efficiency in the ideal limit. As compressor and turbine work are reduced, the average temperatures for heat addition and rejection approach the cycle limit temperature. The limit is reached as compressor and turbine work (and cycle pressure ratio) approach zero and fluid mass flow per unit power output approaches infinity. It can be expected from this that practical recuperated Brayton cycles would operate at relatively low pressure ratios, but be very sensitive to pressure drop. With tire assumption of constant gas specific heat over the cycle temperature range, a good assumption for helium, the cycle efficiency of a recuperated Brayton cycle may be expressed ... 

Note that the output heat is the waste heat. In the limit that the machine operates in a Carnot cycle, which can be characterized by constant temperatures at the input and output, then the maximum efficiency is... 

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... 

Electrochemical cells are devices that convert chemical energy directly into electrical energy thus circumventing the fundamental efficiency limit set by the Carnot cycle. This is the case whether the device is the familiar battery or the less familiar fuel cell. 

The thermodynamic efficiency of a fuel cell is defined as the ratio between AG° and the enthalpy of reaction, AH°, p = AG°IAH°, and is not, unlike thermal external or internal combustion engines, limited by the ideal Carnot cycle. 

The reaction that gives chemical energy to heat engines in cars (hydrocarbon oxidation) has to obey the Carnot cycle efficiency limitation (I - 7 , y7),igh).With around body temperature (37 °C), the metabolic would have to be 337 °C to explain this metabolic efficiency in terms of a heat engine. Thus, the body energy conversion mechanism cannot use this means to get the energy by which it works. 

The Carnot cycle forms the basis for a thermodynamic scale of temperature. Because e = 1 — Ti/Tf, the Carnot efficiencies determine temperature ratios and thereby establish a temperature scale. The difficulty of operating real engines close to the reversible limit makes this procedure impractical. Instead, real gases at low pressures are used to define and determine temperatures (see Section 9.2). 

The existence of a finite heat transfer in the isothermal processes is affected with the assumption of a non-endoreversible cycle with ideal gas as working substance. Power output and ecological function have also an issue that shows direct dependence on the temperature of the working substance. Expressions obtained with the changes of variables have the virtue of leading directly to the shape of the efficiency through Z, function. Thus, in classical equilibrium thermodynamics, the Stirling cycle has its efficiency like the Carnot cycle efficiency in finite time thermodynamics, this cycle has an efficiency in their limit cases as the Curzon-Ahlborn cycle efficiency. 

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