Thermodynamic: efficiency

Since the maximum possible electrical work is equivalent to the change in Gibbs free energy (Agf) considering no losses or irreversibilities, the maximum theoretical limit for the efficiency is 100% in an ideal fuel cell. 

However, this may not be the best representation of fuel cell efficiency since the available chemical energy content of a fuel for power conversion is the enthalpy of formation or the heating values of the fuel. Thus, a more practical definition of fuel cell efficiency is given as the ratio of electrical work produced to the enthalpy of formation of the fuel 

Since the maximum electrical work in a fuel cell is limited by the available Gibbs free energy, the maximum thermodynamic or reversible efficiency of a fuel cell is defined as the ratio of Gibbs free energy change for conversion into electrical energy to the net fuel energy available in the form of enthalpy of formation as 

This also corresponds to the condition of open circuit reversible voltage, with no current flowing through the external circuit. Such a condition leads to the maximum electrical energy conversion and Equation 4.57 for reversible thermodynamic efficiency of a fuel cell can also be expressed as 

Note that Gibbs function decreases with increase in temperature. Thus, the reversible work and thermod5mamic efficiency of a fuel cell decrease wifh increase in temperafure. This is in contrast to the reversible thermodynamic efficiency of a Carnot heat engine where the efficiency or reversible work increases with increase in temperature. 

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Stea.m-Ra.ising Converter. There are a variety of tubular steam-raising converters (Fig. 7d) available, which feature radial or axial flow, with the catalyst on either shell or tube side. The near-isothermal operation of this reactor type is the most thermodynamically efficient of the types used, requiring the least catalyst volume. Lower catalyst peak temperatures also result in reduced by-product formation and longer catalyst life. 

Other Separation Techniques. Under some circumstances, distillation is not the best method of separation. Among these instances are the following when relative volatiHty is <1.05 when <1% of a stream is removed, as in gas drying (adsorption or absorption) or C2H2 removal (reaction or absorption) when thermodynamic efficiency of distillation is <5% and when a high boiling point pushes thermal stabiHty limits. A variety of other... 

Thermodynamic efficiency is hurt by the large ATbetween the temperatures of melting and freezing. In an analogy to distillation, the high a comes at the expense of a big spread in reboiler and condenser temperature. Erom a theoretical standpoint, this penalty is smallest when freezing a high concentration (ca 90%) material. 

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 thermodynamic efficiency of this process as given by Eq. (4-363) is only 3.9 percent. Significant inefficiencies reside with each of the primary units of the process. 

Thermocompression Evaporators Thermocompression-evap-orator calculations [Pridgeon, Chem. Metall. Eng., 28, 1109 (1923) Peter, Chimin Switzerland), 3, II4 (1949) Petzold, Chem. Ing. Tech., 22, 147 (1950) and Weimer, Dolf, and Austin, Chem. Eng. Prog., 76(11), 78 (1980)] are much the same as single-effect calculations with the added comphcation that the heat suppied to the evaporator from compressed vapor and other sources must exactly balance the heat requirements. Some knowledge of compressor efficiency is also required. Large axial-flow machines on the order of 236-mVs (500,000-ftVmin) capacity may have efficiencies of 80 to 85 percent. Efficiency drops to about 75 percent for a I4-mVs (30,000-ftVmin) centrifugal compressor. Steam-jet compressors have thermodynamic efficiencies on the order of only 25 to 30 percent. 

As you may know, the ideal thermodynamic efficiency of a heat engine is given by... 

Fluid Iron Ore Reduction (FIOR) is a process for reducing ore to iron with a reducing gas in a fluid bed. For thermodynamic efficiency, iron ore reduction requires counter current flow of ore and reducing gas. This is achieved in FIOR in a multiple bed reactor. Precautions are necessary to prevent significant back mixing of solids between beds, since this would destroy counter current staging. 

Although the Westinghouse s PWR Shippingport reactor was the first LW R to generate electricity in the U.S., GE s BWR Dresden 1 reactor followed within a year. Operating power reactors range from 600 to 1,200 MWe (million watts of electric power). Since the thermodynamic efficiency is -33%, the thermal heat production is 1,800 to 3,600 MWt. Both types of reactor operate at about the same temperature (-bOOT),... 

If a condenser is employed for a turbine with a condensing section then it is normally chosen to provide the best thermodynamic efficiency consistent with an economical capital expenditure. The condenser exhaust vacuums are usually 0.05 bara or higher. 

Fuel cells such as the one shown on Fig. 3.4a convert H2 to H20 and produce electrical power with no intermediate combustion cycle. Thus their thermodynamic efficiency compares favorably with thermal power generation which is limited by Carnot-type constraints. One important advantage of solid electrolyte fuel cells is that, due to their high operating temperature (typically 700° to 1100°C), they offer the possibility of "internal reforming" which permits the use of fuels such as methane without a separate external reformer.33 36... 

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). 

To conclude this brief note (for details see texts of Biochemistry) we stress that the thermodynamic efficiency of molecular motors can be quite high, approaching 100% but never reaching this thermodynamic limit see Everett and also Neilson and Crawford in References to Appendix. We must always be aware of the heat losses in any real process and this is true all the way from the simplest molecular machines to multi-molecular constructs to man-made machines. 

Figure 5.15(b) shows that the final expansion stage occurs in a turbine, rather than in an isenthalpic Joule-Thomson orifice. It has a higher thermodynamic efficiency than that of the Joule-Thomson but is more complex and expensive. 

De Nevers, N., and Seader, J. D. 1980. Lost work A measure of thermodynamic efficiency. Energy 5 757-69. 

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