Carnot efficiencies

Because batteries direcdy convert chemical energy to electrical energy ia an isothermal process, they are not limited by the Carnot efficiency. The thermodynamic efficiency S for electrochemical processes is given by ... 

The industrial economy depends heavily on electrochemical processes. Electrochemical systems have inherent advantages such as ambient temperature operation, easily controlled reaction rates, and minimal environmental impact (qv). Electrosynthesis is used in a number of commercial processes. Batteries and fuel cells, used for the interconversion and storage of energy, are not limited by the Carnot efficiency of thermal devices. Corrosion, another electrochemical process, is estimated to cost hundreds of millions of dollars aimuaUy in the United States alone (see Corrosion and CORROSION control). Electrochemical systems can be described using the fundamental principles of thermodynamics, kinetics, and transport phenomena. 

The process illustrates the use of mechanical refrigeration in its high-efficiency temperature range the maximum use of compression energy because of its high efficiency and the use of turboexpansion at a low temperature—its Carnot efficiency is best at low temperatures, especially because it permits large use of the efficient pressure effect. 

For any process converting heat energy to mechanical efficiency, the Carnot efficiency is the theoretical maximum. It is calculated as... 

Clearly raising 7 ,ax and lowering 7 ,in will lead to higher Carnot efficiency. 

Conventional gas turbine cycles do not achieve Carnot efficiency because they do not match these features, and there exist... 

The overall effect of these failures to achieve Carnot efficiency is then encompassed in a new parameter, where... 

Plots of thermal efficiency for the [CHTJr and [CHTXJr cycles against the isentropic temperature ratio x are shown in Fig. 3.3, for 6 = Ty/Tf = 4, 6.25. The efficiency of the [CHTJr cycle increases continuously with x independent of 6, but that of the [CHTXJr cycle increases with 6 for a given x. For a given 6 = Ty/T, the efficiency of the [CHTXJr cycle is equal to the Carnot efficiency at j = 1 and then decreases with x until it meets the... 

The maximum possible efficiency at which a heat engine can work is defined by the Carnot efficiency equation E = (T2—Tl)/T2, where E is the efficiency of the heat engine, T1 is the temperature of the cold... 

Stirling engines also have the maximum theoretical possible efficiency because their power cycle (their theoretical pressure volume diagram) matches the Carnot cycle. The Carnot cycle, first described by the French physicist Sadi Carnot, determines the maximum theoretical efficiency of any heat engine operating between a hot and a cold reservoir. The Carnot efficiency formula is... 

These delicate engines provide value as educational tools, but they immediately inspire curiosity into the possibility of generating power from one of the many sources of low temperature waste heat (less than 100°C) that are available. A quick look at the Carnot formula shows that an engine operating with a hot side at 100°C and a cold side at 23°C will have a maximum Carnot efficiency of [((373 K—296 K)/373 K) X 100] about 21 percent. If an engine could be built that achieved 25 percent of the possible 21 percent Carnot efficiency it would have about 5 percent overall Carnot efficiency. 

That figure seems quite low until one realizes that calculating Carnot efficiency for an engine that uses a free heat source might not make much sense. For this type of engine it would probably be more worthwhile to first consider what types of engines can be built, then use dollars per watt as the appropriate figure of merit. 

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 ... 

This remarkable result shows that the efficiency of a Carnot engine is simply related to the ratio of the two absolute temperatures used in the cycle. In normal applications in a power plant, the cold temperature is around room temperature T = 300 K while the hot temperature in a power plant is around T = fiOO K, and thus has an efficiency of 0.5, or 50 percent. This is approximately the maximum efficiency of a typical power plant. The heated steam in a power plant is used to drive a turbine and some such arrangement is used in most heat engines. A Carnot engine operating between 600 K and 300 K must be inefficient, only approximately 50 percent of the heat being converted to work, or the second law of thermodynamics would be violated. The actual efficiency of heat engines must be lower than the Carnot efficiency because they use different thermodynamic cycles and the processes are not reversible. 

Here Tc is the temperature of the cooling reservoir, i.e. the surroundings, while Th is the temperature of the process, i.e. the temperature of combustion. The Carnot efficiency is applicable for conventional heat pump engines. Efficiencies of more than 100 % correspond to converting heat from the surroundings into electricity and is only of academic interest, as is the high efficiency listed in Tab. 8.10. 

In practice the situation is less favorable due to losses associated with overpotentials in the cell and the resistance of the membrane. Overpotential is an electrochemical term that, basically, can be seen as the usual potential energy barriers for the various steps of the reactions. Therefore, the practical efficiency of a fuel cell is around 40-60 %. For comparison, the Carnot efficiency of a modern turbine used to generate electricity is of order of 50 %. It is important to realize, though, that the efficiency of Carnot engines is in practice limited by thermodynamics, while that of fuel cells is largely set by material properties, which may be improved. 

Carnot efficiency of, 24 654 thermodynamics of, 24 653-654, 655 Heaters, feedwater, 23 218 Heat exchange, 10 144 Heat exchanger design equation, 13 189 Heat-exchanger effectiveness method,... 

Liquid hydrogen is preferred in combination with internal combustion engines, as the low temperature of the hydrogen yields a higher efficiency (Carnot efficiency). 

Their efficiency is not limited by Carnot efficiency like thermal cycles. 

A bottle of champagne at a temperature of 280 K is placed in a refrigerator that releases its heat into a room at a constant temperature of 300 K the efficiency of the refrigerator is 0.5 times the corresponding Carnot efficiency. How many joules of electric energy are required to cool the bottle to a temperature of 276 K (Assume that the heat capacity of the filled bottle is equal to that of 1 kg of water and independent of temperature.)... 

Installation of b will require 200,000 more than installation of a, which is an amount that must be borrowed at an interest rate of 6% per year. The principal must be repaid from the operational savings of the heat pump. Assume that the heat pump releases heat into the building at a temperature of 40°C and that the heat pump operates at 40% of the ideal Carnot efficiency. How many years will be required to repay the borrowed money ... 

Carnot efficiency is one of the cornerstones of thermodynamics. This concept was derived by Carnot from the impossibility of a perpetuum mobile of the second kind [ 1]. It was used by Clausius to define the most basic state function of thermodynamics, namely the entropy [2]. The Carnot cycle deals with the extraction, during one full cycle, of an amount of work W from an amount of heat Q, flowing from a hot reservoir (temperature Ti) into a cold reservoir (temperature T2 < T ). The efficiency r] for doing so obeys the following inequality ... 

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