Maximum work output

In general, we shall not subsequently consider these extraction and delivery work terms here, but use [ —AGq] as an approximation to the maximum work output obtainable from a chemical reaction, since the work extraction and delivery quantities are usually small. Their relative importance is discussed in detail by Horlock et al. [4]. 

Many industrial processes require electrical power and heat. This heat is often provided from large quantities of low-pressure steam. In this section, it is demonstrated that a thermal power station gives up very large quantities of heat to the cooling water in the condenser. For this purpose, the steam pressure in the condenser is usually at the lowest practical pressure (around 0.05 bar-absolute) to achieve maximum work output from the turbine. 

The second law of thermodynamics determines how much work can be extracted from a process for maximum work output there is an associated minimum heat output ... 

The maximum work output of any thermodynamic system or process can be obtained, if the material in the system or the working fluid in the process is brought into equilibrium with the environment reversibly. The actual work output of a technical process with combustion is much smaller because the combustion is highly irreversible. The work losses in a continuous combustion can be evaluated if the exergy (or available energy) before and after the reaction is calculated. This exergy is described by the equation ... 

To obtain the maximum work output that can be obtained from a process, the following conditions should be met ... 

Exergy Ex is the maximum amount of work theoretically available (availability A = H — TgS) by bringing a resource into equilibrium with its surrounding through a reversible process. Therefore, exergy is a fuuction of both the physical properties of a resource and its environment. The maximum work output of auy process occurs if the process proceeds reversibly toward equilibrium with the environment (dead state or reference state). The actual work output is much smaller due to process irreversibility. The work loss in a continuous process is the difference in the exergy before and after the process. 

The maximum woric from an electric battery in a finite time interval derived by Bejan and Dan [37] is considered unreasonable by Yan [42]. Indeed, they calculated a maximum work output that can be written in a more compact form as... 

The value of the load resistance providing the maximum work output of the battery is obtaiued by replaciug by t iu Equation 9.72, which gives... 

Combustion. The primary reaction carried out in the gas turbine combustion chamber is oxidation of a fuel to release its heat content at constant pressure. Atomized fuel mixed with enough air to form a close-to-stoichiometric mixture is continuously fed into a primary zone. There its heat of formation is released at flame temperatures deterruined by the pressure. The heat content of the fuel is therefore a primary measure of the attainable efficiency of the overall system in terms of fuel consumed per unit of work output. Table 6 fists the net heat content of a number of typical gas turbine fuels. Net rather than gross heat content is a more significant measure because heat of vaporization of the water formed in combustion cannot be recovered in aircraft exhaust. The most desirable gas turbine fuels for use in aircraft, after hydrogen, are hydrocarbons. Fuels that are liquid at normal atmospheric pressure and temperature are the most practical and widely used aircraft fuels kerosene, with a distillation range from 150 to 300 °C, is the best compromise to combine maximum mass —heat content with other desirable properties. For ground turbines, a wide variety of gaseous and heavy fuels are acceptable. 

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. 

This cycle produces an increase of 30% in work output, but the overall efficiency is slightly decreased as seen in Figure 2-15. An intercooling regenerative cycle can increase the power output and the thermal efficiency. This combination provides an increase in efficiency of about 12% and an increase in power output of about 30%, as indicated in Figure 2-16. Maximum efficiency, however, occurs at lower pressure ratios, as compared with the simple or reheat cycles. 

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 Figure 2-19. 

For an open circuit (non-cyclic) gas turbine plant (Fig. 1.3) a different criterion of performance is sometimes used—the rational efficiency (tjr). This is defined as the ratio of the actual work output to the maximum (reversible) work output that can be achieved between the reactants, each at pressure (po) and temperature (To) of the environment, and products each at the same po. Tq. Thus... 

This equation, as illustrated in the (T, s) chart of Fig. 2.8 for an open circuit gas turbine, shows how the maximum possible work output from the ideal combustion process splits into the various terms on the right-hand side ... 

The rational efficiency may be defined as the ratio of the actual work output [Wcvlx to the maximum possible work output, approximately [—AGq],... 

The thermal efficiency, the work output as a fraction of the fuel exergy (the maximum reversible work), is shown as no. 1 in the figure and is 0.368. The internal irreversibility terms, are shown as nos. 2, 3, and 4 in the diagram, for the combustion... 

A reversible recuperative a/s cycle, with the maximum possible heat transfer from the exhaust gas, qj = Cp(74 — 7y), is illustrated in the T,s diagram of Fig. 3.2, where 7y = 72. This heat is transferred to the compressor delivery air, raising its temperature to 7x = 74, before entering the heater. The net specific work output is the same as that... 

It can be seen from Fig. 7.10 that the eurve for wcv lies above that for wh. As for the gas turbine eyele the pressure ratio for maximum effieiency in the eombined plant may be obtained by drawing a tangent to the work output curve from a point on the x-axis where x= 1 +7 (.(0— 1), i.e. X = 4.6 in the example. The optimum pressure ratio for the eombined plant (r = 18) is less than that for the gas turbine alone (r = 30) although it is still greater than the pres.sure ratio which gives maximum speeific work in the higher plant (r = 11). However, the efficieney tjcp varies little with r about the optimum point. 

Diesel engines, however, operate on an unrestricted air flow at all speeds and loads to provide the cylinders with an excess air charge. This results in a very lean air/fuel ratio of approximately 90 1 to 100 1 or higher at an idle speed. At the engine s rated speed (full load maximum power output) the air/fucl ratio will drop to 20 1 to 25 1 but still provide an excess air factor here of 10 to 20 percent. This excess air supply lowers the average specific heat of the cylinder gases, which in turn increases the indicated work obtained... 

In twin-flue design, these figures are approximately double. Normal working pressures of 10-17 bar are available with a maximum working pressure for a shell boiler at 27 bar. The outputs of larger boilers will be limited if high pressures are required. 

In any process such as the cycle of material the conversion of energy is to work, useful constructs is limited by thermodynamic reasoning to a maximum amount (not 100%). This maximum thermodynamic efficiency cannot be achieved by any machine working at a real speed and which operates under constraints. The resultant work output, we shall refer to as optimal insofar that waste is avoided. As the constraints in the ecosystem are often ill-defined the reader will observe a certain looseness in the use of the words efficiency and effectiveness (fitness) throughout this book (see Section 4.7 and Appendix 4C). 

For human data, volunteers performed one-legged knee extension during which power output is produced mainly from quadriceps muscle, and maximum work rate was performed for at least one minute (Blomstrand et al. (1997))... 

A Diesel engine receives air at 27°C and 100 kPa. The compression ratio is 18. The amount of heat addition is 500kJ/kg. The mass of air contained in the cylinder is 0.0113 kg. Determine (1) the maximum cycle pressure and maximum cycle temperature, (2) the efficiency and work output, and (3) the MEP. Plot the sensitivity diagram of cycle efficiency versus compression ratio. 

Referring to Problem 1 and with fixed heat source and heat sink temperatures, determine the maximum power output of the cycle. Find the working fluid temperatures in the isothermal heat addition and heat... 

UGS represents the most effective means. In 2000, there were 602 underground storage sites world-wide, with a working gas volume capacity of 310 bcm2 and a maximum daily output around 4.46 bcm/d. The two other alternatives offer limited capacities ... 

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