Carnot ratio

In using equation (6) work flux is taken as equal to exergic flux. Heat flux is multiplied by the Carnot ratio to obtain its exergic flux, i.e. 

The Intercooled Regenerative Reheat Cycle The Carnot cycle is the optimum cycle between two temperatures, and all cycles try to approach this optimum. Maximum thermal efficiency is achieved by approaching the isothermal compression and expansion of the Carnot cycle or by intercoohng in compression and reheating in the expansion process. The intercooled regenerative reheat cycle approaches this optimum cycle in a practical fashion. This cycle achieves the maximum efficiency and work output of any of the cycles described to this point. With the insertion of an intercooler in the compressor, the pressure ratio for maximum efficiency moves to a much higher ratio, as indicated in Fig. 29-36. 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

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. 

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... 

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. 

Since the vapour compression cycle uses energy to move energy, the ratio of these two quantities can be used directly as a measure of the performance of the system. This ratio, the coefficient of performance, was first expressed by Sadi Carnot in 1824 for an... 

Evaporator Condenser Compression ratio Reversed Carnot COP... 

It is an immediate consequence of Carnot s theorem that the ratio of the quantities of heat absorbed and rejected by a perfectly reversible engine working in a complete cycle, depends only on the temperatures of the bodies which serve as source and refrigerator. 

The simple Rankine cycle is inherently efficient. Heat is added and rejected isothermally and, therefore, the ideal Rankine cycle can achieve a high percentage of Carnot cycle efficiency between the same temperatures. Pressure rise in the cycle is accomplished by pumping a liquid, which is an efficient process requiring small work input. The back-work ratio is large. 

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 working of the cell under reversible thermodynamic conditions does not follow Carnot s theorem, so that the theoretical energy efficiency, deflned as the ratio between the electrical energy produced (—AG°) and the heat of combustion (—AH°) at constant pressure, is... 

The temperature gap (AT) between the two flows is chosen as the controlling parameter it determines both the enthalpy feed and the Carnot efficiency of the thermoelectric element. The value of AT is related to the heat exchanger efficiency Tiexc or e-NTU (normal thermal unit), the ratio of the heat exchanged to the total exchangeable heat. This relationship comes from the definition of e-NTU for the exchanger efficiency and, in this specific case, it has the following form [16] ... 

Note that Carnot s efficiency (4.9) is definitely more restrictive than the first-law efficiency (4.2b), constrained by the ratio of heat expelled (at tc) to heat absorbed (at th). 

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 ... 

An absolute scale of temperature can be designed by reference to the Second Law of Thermodynamics, viz. the thermodynamic temperature scale, and is independent of any material property. This is based on the Carnot cycle and defines a temperature ratio as ... 

The resultis given inFigure 13.7 for an assumed ratio of T0/T, = 0.5, that is, an ordinary power station. For a renewable fuel / is close to 0 and the optimal efficiency is 0.3 as opposed to the Carnot value of 0.5. For a costly nonrenewable fuel such as natural gas with/ = 0.5 (i.e., 50% of all costs are spent on fuel), the optimal efficiency is 0.35, so around 15% better, although possible environmental costs related to the emission of waste have been ignored (although we should not exclude environmental costs for renewable fuel beforehand). Figure 13.8 depicts how the situation improves when Tu the temperature of the heat source, increases. Nevertheless, the trend that nonrenewable fuels are more favorable appears to persist, however, under the same restriction as just mentioned. By the way, this optimum, which we call the economic optimum, is also known as the thermoeconomic optimum and the analysis with which it was obtained is known as thermoeconomic analysis. 

Define r as the ratio of the actual work, WI + WII, to the Carnot work ... 

According to this definition, the quality of mechanical or electrical energy is equal to unity and that of thermal energy at a temperature, T, is equal to the Carnot factor, 1 - TQ/T. For chemical reactions, the exergy ratio (a-) represents that fraction of the delivered energy that could be converted to thermodynamic work by a reversible process and has a value most often (but not always) between zero and unity. 

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. 

We may define the right side of Eq. (5.4) as the ratio of two thermodynamic temperatures they are to each other as the absolute values of the heats absorbed and rejected by Carnot engines operating between reservoirs at these temperatures, quite independent of the properties of any substance. However, Eq. (5.4) still leaves us arbitrary choice of the empirical temperature represented by 9 once this choice is made, we must determine the function ifi. If 6 is chosen as the Kelvin temperature T, then Eq. (5.4) becomes... 

The above equation is a generalization of the Carnot relation. The ratio between the exergy and the heat Ex/q is called the exergy factor. When T < T0, there is a lack of energy in the system the value of Ex/q greatly increases for... 

AQ = Carnot cycle power, kW ACf = Circulator power, kW AG = Fuel cell power, kW y = Specific heat ratio = C /C, ... 

For a single reversible process between two sets of fixed conditions, the work is independent of the reversible path. However, in a network of reversible processes, such as Figure A.l, alteration of the pressure and temperature of the isothermal enclosure alters the pressure ratio of, for example, the fuel isothermal expander. The power output of Figure A.l is therefore variable and not a constant, merely because it is reversible. The maximum power, the fuel chemical exergy, is obtained from an electrochemical reaction at standard temperature, Tq, and sum of reactant and product pressures, Pg, with isothermal expanders only and without a Carnot cycle. 

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