Direct Energy, 2018a

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12 RELATING ENERGY CONVERSION PROCESSES 275 Energy storage device Generalized Path Generalized Potential Generalized Capacity Constitutive relationship Energy Law for potential Dielectric Material, ɛ>ɛ 0 Displacement Flux Density −→ D in m C 2 Electric eld Intensity −→ E in Vm = C·m J Permittivity ɛ in F Dielectric Material, ɛ>ɛ 0 Electric Field Intensity −→ E in Vm = C·m J Displacement Flux Density −→ D in m C 2 1 ɛ m = J·m C2 −→ −→ −→ D = ɛE E = 1 ɛ ´ V Magnetic Material, μ>μ 0 Magnetic Flux Density −→ B in Wb m 2 Magnetic Field Intensity −→ H in Am = Wb·m J Permeability μ in H Magnetic Material, μ>μ 0 Magnetic Field Intensity −→ H in Am = Wb·m J Magnetic Flux Density −→ B in Wb m 2 1 μ m = Wb2 −→ −→ J·m −→ −→ D B = μH H = 1 μ−→ B 1 ɛ|−→ E | 2 dV ´V 1 1 |−→ D| 2 dV ´V 1 μ|−→ H | 2 dV ´V 1 1 |−→ B | 2 dV 2 2 ɛ 2 2 μ Gauss's Law for Elec. −→ ∇·−→ D = ρch Gauss's Law for Elec. −→ ∇·−→ E = Gauss's Law for Mag. −→ ∇·−→ B =0 Gauss's Law for Mag. −→ ∇·−→ H =0 ɛρ ch Table 12.3: Describing electromagnetic systems in the language of calculus of variations.
276 12.3 Mechanical Energy Conversion 12.3 Mechanical Energy Conversion The previous section summarized how the language of calculus of variations can be applied to electrical and electromagnetic energy conversion devices. Similarly, this language can be used to describe energy conversion processes occurring in linear springs, torsion springs, moving masses, and ywheels. We can convert energy to and from spring potential energy by compressing and releasing a spring. Similarly, we can store or release energy from a moving mass by changing its velocity. A ywheel is a device that stores energy in a spinning mass. Flywheels are used, in addition to batteries, in some electric and hybrid vehicles because storing rotational kinetic energy in a ywheel requires fewer energy conversion processes than storing energy in a battery. All of these energy conversion devices can be described in the language of calculus of variations with some parameter chosen as the generalized path. Tables 12.4 and 12.5 summarize the parameters resulting from describing mechanical energy conversion processes in the language of calculus of variations. While electromagnetic systems are described by four vector elds, mechanical systems are described by eight possible vector elds, and they are listed along with their units in Table 12.6. Each column of Tables 12.4 and 12.5 describes the case of choosing a dierent vector eld from Table 12.6 as the generalized path. By comparing across the rows of these tables as well as the electrical tables, comparisons can be made between the dierent energy conversion processes. In Sec. 11.5, energy conversion in a linear spring was discussed in the language of calculus of variations. That example considered the displacement of a point mass m in kg where the generalized path was chosen to be displacement x in m. The resulting Euler-Lagrange equation was Newton's second law. Section 11.5 concluded with Table 11.1 summarizing the resulting parameters. The third column of the Table 12.4 repeats that information. Circuit devices are often assumed to be point-like while electromagnetic properties of materials, like permittivity and permeability, are specied as functions of position. Similarly, mechanical devices can be treated as pointlike or as functions of position. For example, mass is used to describe a point-like device while density is used to describe a device that varies with position. Researchers studying aerodynamics and uid dynamics typically prefer the latter description. However, in Tables 12.4 and 12.5, point-like devices of mass m are assumed. Ideas in these tables can be generalized to situations where energy conversion devices are not treated as point-like and instead mass and other material properties vary with position.
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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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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.
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Page 249 and 250: 238 10.3 Radiation Detectors high e
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Page 253 and 254: 242 10.6 Electrouidics However, ene
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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
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Page 269 and 270: 258 11.6 Capacitor Inductor Example
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Page 273 and 274: 262 11.7 Schrödinger's Equation 11
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Page 277 and 278: 266 11.8 Problems a famous result k
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Page 281 and 282: 270 12.2 Electrical Energy Conversi
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Page 289 and 290: 278 12.3 Mechanical Energy Conversi
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Page 297 and 298: 286 12.5 Chemical Energy Conversion
Page 299 and 300: 288 12.6 Problems 12.6 Problems 12.
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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
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Page 323 and 324: 312 14.1 Introduction damental equa
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326 14.4 Derivation of the Innitesi
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328 14.4 Derivation of the Innitesi
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330 14.5 Invariants and we end up w
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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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