Carnot efficiency calculation

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

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. 

Much more would have to be done in the laboratory to investigate the possibility of a practical Faradaic reformer choice of electrode and electrolyte the possibility of irreversible electrode reactions the need for an electrocatalyst. It can be concluded safely that a basis for fuel chemical exergy efficiency calculations exists, namely the Faradaic reformer, fuel cell combination at standard conditions. The reduced performance of the reformer fuel cell combination, at temperature and pressure, can be left as a major exercise for the reader by adding isentropic circulators and a Carnot cycle to Figure A.2. 

The thermodynamic basis of the calculation of the maximum possible work potential or chemical exergy of reversible and irreversible chemical reactions is explained and discussed. Combustion is asserted to be fundamentally irreversible. It is a nonequilibrium uncontrollable chain reaction with hot branches, in a cool milieu, and a limited work output proportional to Carnot efficiency x calorific value (Barclay, 2002). 

Also, one should note that the efficiency calculated above is somewhat less than the Carnot efficiency, " . ... 

The efficiency, ijcarnot, of the Carnot engine is the work done on the surroundings divided by the heat input from the hot reservoir. The heat exhausted at the cold reservoir is wasted and is not included in the efficiency calculation. 

A fascinating point, especially to physical chemists, is the potential theoretical efficiency of fuel cells. Conventional combustion machines principally transfer energy from hot parts to cold parts of the machine and, thus, convert some of the energy to mechanical work. The theoretical efficiency is given by the so-called Carnot cycle and depends strongly on the temperature difference, see Fig. 13.3. In fuel cells, the maximum efficiency is given by the relation of the useable free reaction enthalpy G to the enthalpy H (AG = AH - T AS). For hydrogen-fuelled cells the reaction takes place as shown in Eq. (13.1a). With A//R = 241.8 kJ/mol and AGr = 228.5 under standard conditions (0 °C andp = 100 kPa) there is a theoretical efficiency of 95%. If the reaction results in condensed H20, the thermodynamic values are A//R = 285.8 kJ/ mol and AGR = 237.1 and the efficiency can then be calculated as 83%. 

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. 

For the ideal gas Carnot cycle, the efficiency is easily calculated ... 

A fluid undergoes the Carnot cycle in Figure 4-r with Tl = 300 °C, Th = 500 °C. Calculate the amounts of heat and work for each step, as well as the thermod5mamic efficiency of the cycle (net amount of work produced over amount of heat absorbed) assuming the fluid is in the ideal-gas state. 

Steam undergoes a Carnot cycle between temperatures 500 °C and 300 °C. During the isothermal heating step, the steam expands from pressure 50 bar to 30 bar. Determine the states in each of the four corners A, B, C, and D of the cycle (see Figure 4-f ). calculate the thermodynamic energy balances and determine the thermodynamic efficiency of the cycle. 

Problem 4.21 A Carnot cycle using steam in a closed system operates between 700 "C and 500 "C. During the isothermal step the steam expands from 20 bar to 10 bar. Perform the energy and entropy balances, calculate the efficiency, and compare to the theoretical value. 

The efficiency of any energy conversion device is defined as the ratio between useful energy output and energy input. The efficiency limit for heat engines, such as steam and gas turbines, is known as the Carnot limit. If the maximum temperature of the heat engine is Tj, and flie heated fluid is released at temperature T2, which is never likely to be smaller flian room temperature (about 290 K), then the Carnot limit of the efficiency can be calculated by... 

Carnot did not derive a mathematical expression for the maximum efficiency attained by a reversible heat engine in terms of the temperatures between which it operated. This was done later by others who realized the importance of his conclusion. Carnot did, however, find a way of calculating the maximum work that can be generated. (For example, he concluded that 1000 units of heat passing from a body maintained at the temperature of 1 degree to another body maintained at zero would produce, in acting upon the air, 1.395 units of motive power [1, p. 42].)... 

Given that fuel cells generate electrical potential difference directly from Gibb s potential rather than by heat exchange cycles between two focuses at different temperatures i.e. fuel cells are not limited by Carnot heat cycle, the reversible energy efficiency of a DEFC, calculated as the ratio between the free energy and enthalpy at the equihbiium potential ... 

Calculate the efficiency of a Carnot heat engine that represents a steam engine with its boiler at 600.0 K and its exhanst at 373.15 K. 

A steam engine has an efficiency that is 55% as large as that of a Carnot engine. If its boiler is at 250°C and its exhaust is at 100°C, calculate the height to which it can lift a 1000 kg mass near the earth s surface if it bums 5.00 kg of coal. Pretend that the coal is pure graphite and that its enthalpy change of combustion is equal to that at 25°C. 

In other studies, another simple calculation method for thermal efficiency has also been used. First, thermal efficiencies of Carnot and Rankine cycles were calculated with the given steam conditions. Second, an averaged value between these efficiencies was obtained and a factor was calculated so that the thermal efficiency of the current BWR was correctly estimated by this method. If the core outlet temperature is given as 400°C, the thermal efficiencies obtained by the... 

Turning to the heat rejection step, we notice that the temperature at which the condenser operates is determined, as with case of the boiler, by the operating pressure. The effect on the cycle efficiency is presented in Figure 3.9. Here we keep the boiler pressure and steam temperature constant (35 bar and 475°C). Again as predicted by the Carnot cycle, low operating pressures and, thus, temperatures, lead to higher efficiencies. Note Calculations of efficiencies are based on a reversible and adiabatic turbine. 

If we compare Clapeyron s efficiency of the Carnot cycle, Eq.4.8.1, with the one we developed in Chapter 3, Eq.3.5.3, it follows that C = J, i.e. the absolute temperature. (This, of course, was not doneimtil later.) And this is why the calculated values of C are, within the accuracy of evaluating the slope (dP /dt)y equal to the absolute temperature in Kelvin. 

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