Direct Energy, 2018a

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12 RELATING ENERGY CONVERSION PROCESSES 281 The last rows of Tables 12.4 and12.5 list the relationship that results when an energy conversion device is described in the language of calculus of variations, the Euler-Lagrange equation is set up, andthe Euler- Lagrange equation is solvedfor the equation of motion. The laws that result, Newton's secondlaw, conservation of momentum, conservation of angular momentum, and conservation of torque, are fundamental ideas of mechanics.
282 12.4 Thermodynamic Energy Conversion 12.4 Thermodynamic Energy Conversion Four fundamental thermodynamic properties were introduced in Section 8.2: volume V,pressure P,temperature T ,and entropy S. Many devices convert between some form of energy and either energy stored in a conned volume,energy stored in a material under pressure,energy in a temperature dierence,or energy of a disordered system. We can describe energy conversion processes in these devices using the language of calculus of variations with one of these parameters, V, P, T ,or S,as the generalized path and another as the generalized potential. Table 12.7 summarizes the results. Many sensors convert energy between electrical energy and energy stored in a volume,pressure,or temperature dierence. A capacitive gauge can measure the volume of liquid fuel versus vapor in the tank of an aircraft. Strain gauges and Piranhi hot wire gauges (Sec. 10.5),for example,are sensors that can measure pressure on solids or in gases. Pyroelectric detectors (Sec. 3.2),thermoelectric detectors (Sec. 8.8),thermionic devices (Sec. 10.2),and resistance temperature devices (Sec. 10.5) can be used to sense temperature changes. Many other energy conversion devices convert between energy stored in a conned volume,energy stored in a material under pressure,or energy in a temperature dierence and another form of energy without involving electricity. For example,if you tie a balloon to a toy car then release the air in the balloon,the toy car will move forward. Energy stored in the conned volume of the balloon,as well as in the stretched rubber of the balloon,is converted to kinetic energy of the toy car. An aerator or squirt bottle converts energy of a pressure dierence to kinetic energy of a liquid. An eye dropper converts energy of a pressure dierence to gravitational potential energy. An airfoil converts a pressure dierence to kinetic energy in the form of lift. A piston converts energy of a gas under pressure to kinetic energy. As discussed in Sec. 10.6,a constricted pipe,or a weir, converts energy of a pressure dierence in a owing liquid to kinetic energy of the liquid. A baseball thrown as a curve ball converts the rotational energy of the rotating ball into a pressure dierential to deect the ball's path [162,p. 350]. A Sterling engine converts a temperature dierence to kinetic energy. Calculus of variations can be used to gain insights into thermodynamic energy conversion processes in these devices. The rst step in applying the ideas of calculus of variations is to identify an initial and nal form of energy. The Lagrangian is the dierence between these forms of energy as a function of time. Some authors choose the Lagrangian as an entropy
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Direct Energy Conversion by Andrea
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CONTENTS i Contents Contents i 1 In
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CONTENTS iii 6.3.2 Energy Levels in
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CONTENTS v 9.6 Fuel Cells . . . . .
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Acknowledgements I would like to th
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2 1.2 Preview of Topics to connect
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4 1.2 Preview of Topics Math throug
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6 1.2 Preview of Topics Process Spo
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8 1.2 Preview of Topics drodynamic
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10 1.4 Measures of Power and Energy
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12 1.5 Properties of Materials 1.5
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14 1.5 Properties of Materials most
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16 1.6 Electromagnetic Waves −→
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18 1.6 Electromagnetic Waves Relate
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20 1.6 Electromagnetic Waves A unif
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22 1.7 Problems
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24 2.2 Capacitors 2.2 Capacitors 2.
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26 2.2 Capacitors 2.2.3 Permittivit
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28 2.2 Capacitors â z â y â x No
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30 2.2 Capacitors Figure 2.3: Natur
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32 2.3 Piezoelectric Devices Piezoe
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34 2.3 Piezoelectric Devices Lattic
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36 2.3 Piezoelectric Devices Herman
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38 2.3 Piezoelectric Devices Figure
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40 2.3 Piezoelectric Devices c a β
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42 2.3 Piezoelectric Devices In cer
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44 2.3 Piezoelectric Devices made m
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46 2.3 Piezoelectric Devices tions.
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48 2.4 Problems 2.5. A piezoelectri
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50 2.4 Problems 2.13. Consider a pi
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52 2.4 Problems 2.16. The gure belo
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54 3.2 Pyroelectricity Material Che
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56 3.3 Electro-Optics KH 2 PO 4 [25
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58 3.3 Electro-Optics The rst two t
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60 3.3 Electro-Optics used as an el
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62 3.4 Notation Quagmire Notation i
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64 3.5 Problems 3.5 Problems 3.1. F
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66 3.5 Problems −→ DinC/m 2 unp
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68 4.1 Introduction Center-fed half
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70 4.2 Electromagnetic Radiation In
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72 4.2 Electromagnetic Radiation ar
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74 4.3 Antenna Components and Denit
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76 4.4 Antenna Characteristics ante
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78 4.4 Antenna Characteristics Impe
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80 4.4 Antenna Characteristics Azim
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82 4.4 Antenna Characteristics 4.4.
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84 4.4 Antenna Characteristics 5 Li
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86 4.5 Problems Figure 4.6: A snow
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88 4.5 Problems 4.5. Match the foll
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90 4.5 Problems 4.8. Radiation patt
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92 5.2 Physics of the Hall Eect The
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94 5.2 Physics of the Hall Eect The
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96 5.3 Magnetohydrodynamics This am
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98 5.5 Applications of Hall Eect De
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100 5.6 Problems 5.6 Problems 5.1.
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102 6.2 The Wave and Particle Natur
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104 6.3 Semiconductors and Energy L
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120 6.4 Crystallography Revisited L
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122 6.5 Pn Junctions E Indirect Sem
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124 6.5 Pn Junctions an excess of n
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126 6.5 Pn Junctions V x - + Energy
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128 6.6 Solar Cells to day and loca
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130 6.6 Solar Cells dot based mater
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132 6.7 Photodetectors Solar Panel
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134 6.7 Photodetectors 6.7.2 Measur
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6 PHOTOVOLTAICS 137 6.3. The gure i
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7 LAMPS, LEDS, AND LASERS 139 7 Lam
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7 LAMPS, LEDS, AND LASERS 141 Photo
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7 LAMPS, LEDS, AND LASERS 143 Absor
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7 LAMPS, LEDS, AND LASERS 145 We ca
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7 LAMPS, LEDS, AND LASERS 147 If we
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7 LAMPS, LEDS, AND LASERS 149 tube
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7 LAMPS, LEDS, AND LASERS 151 easil
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7 LAMPS, LEDS, AND LASERS 153 Power
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7 LAMPS, LEDS, AND LASERS 155 Two L
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7 LAMPS, LEDS, AND LASERS 157 but n
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7 LAMPS, LEDS, AND LASERS 159 of ec
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7 LAMPS, LEDS, AND LASERS 161 the o
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7 LAMPS, LEDS, AND LASERS 163 Ti:Sa
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7 LAMPS, LEDS, AND LASERS 165 the b
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7 LAMPS, LEDS, AND LASERS 167 Gas D
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7 LAMPS, LEDS, AND LASERS 169 categ
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7 LAMPS, LEDS, AND LASERS 171 7.8.
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8 THERMOELECTRICS 173 8 Thermoelect
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8 THERMOELECTRICS 175 Symbol Name V
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8 THERMOELECTRICS 177 per unit volu
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8 THERMOELECTRICS 179 kPa, and the
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8 THERMOELECTRICS 181 Seebeck Effec
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8 THERMOELECTRICS 183 gradient acro
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8 THERMOELECTRICS 185 thermocouples
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8 THERMOELECTRICS 187 The gure of m
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8 THERMOELECTRICS 189 or mass invol
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8 THERMOELECTRICS 191 temperatures?
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8 THERMOELECTRICS 193 Figure 8.4: L
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8 THERMOELECTRICS 195 8.9 Problems
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8 THERMOELECTRICS 197 8.8. A thermo
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8 THERMOELECTRICS 199 Figure 8.5 8.
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202 9.2 Measures of the Ability of
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212 9.3 Charge Flow in Batteries an
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214 9.3 Charge Flow in Batteries an
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216 9.4 Measures of Batteries and F
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224 9.5 Battery Types specic energi
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226 9.5 Battery Types at the anode
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228 9.5 Battery Types Figure 9.8: T
Page 241 and 242: 230 9.6 Fuel Cells Fuel cell compon
Page 243 and 244: 232 9.6 Fuel Cells 9.6.3 Practical
Page 245 and 246: 234 9.7 Problems 9.7 Problems 9.1.
Page 247 and 248: 236 9.7 Problems A E - + I B D H 2
Page 249 and 250: 238 10.3 Radiation Detectors high e
Page 251 and 252: 240 10.5 Resistive Sensors capacito
Page 253 and 254: 242 10.6 Electrouidics However, ene
Page 255 and 256: 244 10.6 Electrouidics
Page 257 and 258: 246 11.2 Lagrangian and Hamiltonian
Page 259 and 260: 248 11.3 Principle of Least Action
Page 261 and 262: 250 11.4 Derivation of the Euler-La
Page 263 and 264: 252 11.5 Mass Spring Example not in
Page 265 and 266: 254 11.5 Mass Spring Example Path 1
Page 267 and 268: 256 11.5 Mass Spring Example We can
Page 269 and 270: 258 11.6 Capacitor Inductor Example
Page 271 and 272: 260 11.6 Capacitor Inductor Example
Page 273 and 274: 262 11.7 Schrödinger's Equation 11
Page 275 and 276: 264 11.8 Problems 11.4. Figure 11.2
Page 277 and 278: 266 11.8 Problems a famous result k
Page 279 and 280: 268 11.8 Problems (c) Find the gene
Page 281 and 282: 270 12.2 Electrical Energy Conversi
Page 287 and 288: 276 12.3 Mechanical Energy Conversi
Page 289 and 290: 278 12.3 Mechanical Energy Conversi
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Page 295 and 296: 284 12.4 Thermodynamic Energy Conve
Page 297 and 298: 286 12.5 Chemical Energy Conversion
Page 299 and 300: 288 12.6 Problems 12.6 Problems 12.
Page 301 and 302: 290 12.6 Problems 12.6. Match the d
Page 303 and 304: 292 13.1 Introduction • Describe
Page 305 and 306: 294 13.2 Preliminary Ideas Assuming
Page 307 and 308: 296 13.3 Derivation of the Lagrangi
Page 317 and 318: 306 13.4 Deriving the Thomas Fermi
Page 319 and 320: 308 13.5 From Thomas Fermi Theory t
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Page 323 and 324: 312 14.1 Introduction damental equa
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Page 333 and 334: 322 14.4 Derivation of the Innitesi
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332 14.5 Invariants in the limit ε
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334 14.5 Invariants Next use Eq. 14
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336 14.6 Summary 14.6 Summary In th
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338 14.7 Problems 14.6. The equatio
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340 14.7 Problems
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342 Appendices Symbol Quantity Unit
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350 Appendices Prex name Symbol Val
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352 Appendices for voltage. (As an
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354 Appendices Material or Device S
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356 REFERENCES [15] E. C. Jordan an
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358 REFERENCES [45] V. K. Tikhomiro
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360 REFERENCES [73] M. G. Thomas, H
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362 REFERENCES [100] A. Ishibashi,
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364 REFERENCES [125] D. Wright, Req
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366 REFERENCES [150] J. P. Owejan,
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368 REFERENCES [175] G. K. Woodgate
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Index Absorption, 139 Action, 247 A
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372 INDEX Nernst equation, 220 Neur
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About the Book Direct Energy Conver
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Direct Energy, 2018a

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