The Maximum Thermal Efficiency

We conclude, thus, that as the cycle approaches reversible operation, its thermal efficiency approaches its maximum value. We will demonstrate next that, of all heat engines operating between two specified tempera-tures, the reversible one has the maximum thermal efficiency. 

If B is more efficient, and both engines produce the same amount of work, then from the definition of thermal efficiency (Eq.3.5.1)  

We have, therefore, a process - the combination of the two cycles -whereby the only effect is the transfer of an amount of heat = kil  

1021 fro lower to a higher temperature. This, of course, violates statement B of the second law and, consequently, the irreversible engine cannot be more efficient than the reversible one. 

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A limit on the efficiency of the electrical energy conduction can be obtained by applying the second law of thermodynamics to the secondary loop. The maximum thermal efficiency, s,, is given in terms of the input and output heats ... 

Not all of the heat produced in a nuclear reactor can be used for woilc, i.e. for turning the turbine blades connected to the rotor of an electric generator. According to the second law of thermodynamics, the maximum thermal efficiency (tf) is... 

Use eqn. (19.33) to estimate the maximum thermal efficiency for the Creys-Malville plant. 

Using Eq. (2.8) for the reversible work, one can calculate the maximum thermal efficiency (maximum work for given energy input) of a fuel cell or fuel cell hybrid (fuel cell and heat engine) systan for the H2 oxidation reaction, where AH" is... 

Determine the maximum thermal efficiency 77 of a reversible heat engine which is supplied with heat at 650 °C and releases heat at 10 °C ... 

Thus, a heat engine is limited in thermal efficiency by the Carnot cycle, and an electrochemical reaction engine is not. The thermal efficiency of a Carnot cycle, which is the measure of the maximum thermal efficiency of a chemical reaction heat engine, is... 

The maximum thermal efficiency is established by the Carnot cycle, Eq.3.5.3, which indicates that complete conversion of thermal energy into mechanical is not possible. 

Since Qi=vRTyn V2/Vi), the maximum thermal efficiency of the ideal thermal engine is... 

Employing wood chips, Cowan s drying studies indicated that the volumetric heat-transfer coefficient obtainable in a spouted bed is at least twice that in a direct-heat rotaiy diyer. By using 20- to 30-mesh Ottawa sand, fluidized and spouted beds were compared. The volumetric coefficients in the fluid bed were 4 times those obtained in a spouted bed. Mathur dried wheat continuously in a 12-in-diameter spouted bed, followed by a 9-in-diameter spouted-bed cooler. A diy-ing rate of roughly 100 Ib/h of water was obtained by using 450 K inlet air. Six hundred pounds per hour of wheat was reduced from 16 to 26 percent to 4 percent moisture. Evaporation occurred also in the cooler by using sensible heat present in the wheat. The maximum diy-ing-bed temperature was 118°F, and the overall thermal efficiency of the system was roughly 65 percent. Some aspec ts of the spouted-bed technique are covered by patent (U.S. Patent 2,786,280). 

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. 

To obtain a more accurate relationship between the overall thermal efficiency and the inlet turbine temperatures, overall pressure ratios, and output work, consider the following relationships. For maximum overall thermal cycle efficiency, the following equation gives the optimum pressure ratio for fixed inlet temperatures and efficiencies to the compressor and turbine ... 

By differentiating Eq. (3.13) with respect to x and equating the differential to zero, it may be shown that the isentropic temperature ratio for maximum thermal efficiency (jCe) is given by the equation... 

The [CBT]ig efficiency is replotted in Fig. 3.14, against (Tt,ITx) with pressure ratio as a parameter. There is an indication in Fig. 3.14 that there may be a limiting maximum temperature for the highest thermal efficiency, and this was observed earlier by Horlock et al. [8] and Guha [9]. It is argued by the latter and by Wilcock et al. [10] that this is a real gas effect not apparent in the a/s calculations such as those shown in Fig. 3.9. This point will be dealt with later in Chapter 4 while discussing the turbine cooling effects. 

In this chapter, cycle calculations are made with assumed but realistic estimates of the probable turbine cooling air requirements which include some changes from the uncooled thermal efficiencies. Indeed it is suggested that for modern gas turbines there may be a limit on the combustion temperature for maximum thermal efficiency [2,3]. 

The pressure and temperature at the start of compression in an air Diesel cycle are 101 kPa and 300 K. The compression ratio is 15, and the amount of heat addition is 2000kJ/kg of air. Determine (a) the maximum cycle pressure and maximum temperature of the cycle, and (b) the cycle thermal efficiency. 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

A conventional power plant fired by fossil fuels converts the chemical energy of combustion of the fuel first to heat, which is used to raise steam, which in turn is used to drive the turbines that turn the electrical generators. Quite apart from the mechanical and thermal energy losses in this sequence, the maximum thermodynamic efficiency e for any heat engine is limited by the relative temperatures of the heat source (That) and heat sink (Tcoid) ... 

The output temperature is given by the ambient temperature of the waste-heat loop and can be taken to be 30°C for purposes of estimation. The input temperature of the steam is limited by physical constraints on the reactor primary cooling loop to be about 300°C. Therefore, the maximum Carnot efficiency is approximately carnot = (573 K-303 K)/573 K = 0.47, whereas the actual efficiency is typically 8dec = 0.35 when measured as electrical power outside the plant to total thermal power in the core. For comparison, a coal-powered plant might have values of carnot = 0.65, 8eiec = 0.5 due to higher steam temperatures... 

Performance of a heater is characterized by the average heat flux in the radiant zone and the overall thermal efficiency. Heat fluxes of representative processes are listed in Table 8.15. Higher fluxes make for a less expensive heater but can generate high skin temperatures inside and out. Thermal sensitivity of the process fluid, the strength of the metal and its resistance to corrosion at elevated temperatures are factors to be taken into accoimt in limiting the peak flnx. Because of the refractory nature of water, however, allowable fluxes in steam boilers may reach 130,000 Btu/ (hr)(sqft), in comparison with a maximum of about 20,000 in hydrocarbon service. Example 8.13 is a study of the effect of tube spacing on inside film peak temperatures. 

The heating value of a typical biomass is sufficient to produce steam in excess of that required by the activated process if the system has been designed for maximum thermal efficiency. This can be especially important to developing countries who have large supplies of biomass such as rice hulls or coconut shells and who are currently contemplating the manufacture of activated carbon for export or local water treatment. 

Based upon the analysis developed in this paper, the indirectly heated system can obtain approximately 45% PSU with mole percent H20 equal to 40% as shown in Fig. 10. From Fig. 13 we see that this PSU brings the process into the range of minimum energy requirements and therefore maximum thermal efficiency. On this basis we have recommended further research and development of indirectly heated reactors for the production of activated carbon from municipal solid waste and biomass. 

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