Direct Energy, 2018a

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8 THERMOELECTRICS 197 8.8. A thermoelectric device has a gure of merit of Z =0.7 K −1 . A second device is made out of the same semiconducting materials, but it has been doped so that the electrical conductivity is 20% higher. Find the gure of merit of the second device. 8.9. A thermoelectric device is made from a material with resistivity 5 · 10 −8 Ω·m and Seebeck coecient 8.5 · 10 −5 K V . A cube, 1 cm on each side, was used to determine the thermal conductivity. One side of the cube was heated. At a steady state, the rate of energy transfer by conduction through the cube is 1.8 W. The temperature distribution through the material is linear, and a temperature dierence across is measured to be 20 K across the cube. Find the thermal conductivity κ, and nd the gure of merit Z for the material. 8.10. As shown in Fig. 8.3, a heater supplies heat to one side of an iron rod. The rod is cylindrical with length 30 cm and radius 2 cm. The heater supplies 2 W of power to the edge of the rod. Iron has a thermal conductivity of κ =80 m·K W . Two thermocouples are are spaced 15 cm apart as shown in the gure. What is the dierence in temperature (in degrees Celsius) measured between the two thermocouples? 8.11. A thermoelectric device is used to build a small refrigerator that can hold two pop cans. When the device is operating, the cold side of the device is at T =10 ◦ C while the hot side of the device, outside the refrigerator, is at T =42 ◦ C. What is the maximum possible eciency of this device? 8.12. The cold side of a thermoelectric device, used to generate electricity, is at a temperature of 100 ◦ C. What is the minimum temperature of the hot side of the device needed to achieve an eciency of η eff = 15%? 8.13. The Carnot eciency describes the limit of the eciency for some devices. Does it apply to the following types of devices? (Answer yes or no.) • Hall eect device • Semiconductor laser • Photovoltaic device • Piezoelectric device • Pyroelectric device • Thermoelectric device used as a temperature sensor
198 8.9 Problems • Thermoelectric device used as a refrigerator • Thermoelectric device used to generate electricity for a sensor system 8.14. The gures show Seebeck coecient $(T ),electrical resistivity ρ(T )= 1 , and thermal conductivity κ(T ) plotted versus temperature T for σ(T ) a family of materials known as skutterudites. These materials have the composition Tl x Co 4−y Fe y Sb 12 and Tl x Co 4 Sb 12−y Sn y where x and y range from zero to 1. The gures used with permission from reference [121]. Recently,scientists have been studying the possibility of making thermoelectric devices from these materials. Using the data in the gures,approximate the thermoelectric gure of merit Z in units K −1 at a temperature of T = 200 K for the material with x =0.1.
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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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Page 204 and 205: 8 THERMOELECTRICS 193 Figure 8.4: L
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Page 241 and 242: 230 9.6 Fuel Cells Fuel cell compon
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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
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Page 257 and 258: 246 11.2 Lagrangian and Hamiltonian
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248 11.3 Principle of Least Action
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250 11.4 Derivation of the Euler-La
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252 11.5 Mass Spring Example not in
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254 11.5 Mass Spring Example Path 1
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256 11.5 Mass Spring Example We can
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258 11.6 Capacitor Inductor Example
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260 11.6 Capacitor Inductor Example
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262 11.7 Schrödinger's Equation 11
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264 11.8 Problems 11.4. Figure 11.2
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266 11.8 Problems a famous result k
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268 11.8 Problems (c) Find the gene
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270 12.2 Electrical Energy Conversi
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276 12.3 Mechanical Energy Conversi
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282 12.4 Thermodynamic Energy Conve
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284 12.4 Thermodynamic Energy Conve
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286 12.5 Chemical Energy Conversion
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288 12.6 Problems 12.6 Problems 12.
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290 12.6 Problems 12.6. Match the d
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292 13.1 Introduction • Describe
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294 13.2 Preliminary Ideas Assuming
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296 13.3 Derivation of the Lagrangi
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306 13.4 Deriving the Thomas Fermi
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308 13.5 From Thomas Fermi Theory t
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310 13.6 Problems (a) Write the Ham
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312 14.1 Introduction damental equa
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314 14.2 Types of Symmetries be wri
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316 14.3 Continuous Symmetries and
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322 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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