Thermoelectric effect

Transcription

1 Hiroyuki KOIZUMI

2 1. Principle

3 Thermoelectric effect Seebeck effect Temperature difference ΔT Voltage difference ΔV Peltier effect I Q Thomson effect I Current Q Heat transfer

4 Thermoelectric effect Seebeck effect ΔV = SΔT Peltier effect Q = Π A Π B I Thomson effect Q = κiδt

5 Electricity Heat Generation Joule heating Q = RI 2 Peltier effect Thomson effect Transfer (Q>0 = output) Q = Π A Π B I Transfer Q = κiδt

6 Electricity Heat Irreversible Joule heating Q = RI 2 Peltier effect Thomson effect Reversible Q = Π B Π A I Reversible Q = κiδt

7 Found by T.J. Seebeck Seebeck effect (1821) ゼーペック効果 T T A ΔV V AB T + ΔT T B Thermoelectric EMF ( 熱起電力 ) ΔV = S ΔT V AB = Seebeck coefficient or Thermopower ( 熱電能 ) A B S T dt

8 Seebeck effect (1821) ゼーペック効果 No temperature gradient case With temperature gradient case Same temperatures hea ting Thermal equilibrium condition with Electron diffusion Charge is carried by electron flow 8

9 Material Seebeck coefficient/(μv/k) Selenium 895 Tellurium 495 Silicon 435 Germanium 325 Antimony 42 Nichrome 20 Molybdenum 5.0 Cadmium, tungsten 2.5 Gold, silver, copper 1.5 Rhodium 1.0 Tantalum -0.5 Lead -1.0 Aluminium -1.5 Carbon -2.0 Mercury -4.4 Platinum -5.0 Sodium -7.0 Potassium -14 Nickel -20 Constantan -40 Bismuth -77 Wide variety Dependency on T

10 P-type semiconductor Carrier: positive hole ΔV = S ΔT S > 0 Low T High T Lower hole density (stochastically, by random walk) Negative potential

11 N-type semiconductor Carrier: negative electron ΔV = S ΔT S < 0 Low T High T Lower electron density (stochastically, by random walk) Positive potential

12 P Carrier: positive hole P-N junction N Carrier: negative electron

13 Found by J.C.A. Peltier Peltier effect (1844) ペルチェ効果 Q = ΠI Q AB Π: Peltier coefficient Π A I A B Π B I Q AB = (Π A Π B )I

14 Electron energy state in solids Energy Metal N-type P-type

15 Electron energy state in solids Energy Metal A current Metal B Energy gap

16 Heating Energy Metal A Heat current Metal B Energy gap

17 Cooling Heat Energy Metal A current Metal B Energy gap

18 N-type carrier: electron Heat current P-type carrier: hole Energy release

19 N-type carrier: electron Heat current P-type carrier: hole Energy injection

20 Predicted by William Thomson (Lord Kelvin) Thomson effect (1854) トムソン効果 Q = κiδt I T T + ΔT κ: Thomson coefficient (electric specific heat) 20

21 Heat Low energy carrier Energy Current High energy carrier T T + ΔT

22 Heat Low energy carrier Energy Current High energy carrier T T + ΔT

23 Thermoelectric effect All the phenomena are caused by the current carriers They should be related each other Seebeck effect ΔV = SΔT Peltier effect Q = Π B Π A I Thomson effect Q = κiδt

24 Q in ΔV Q J Current I Q out T Q ex T + ΔT Q J + Q in Q out Q ex = 0 Energy balance Q in = Π T I Q out = Π T + ΔT I Peltier effect Q J = IΔV Note, voltage drop with current is ΔV

25 Q in ΔV Q J Current I Q out T ΔV = ρ Δx A I SΔT Resistance ρ : resistivity A : cross section Q ex T + ΔT effect + Seebeck effect Q ex = ρ Δx A I2 dπ dt S ΔTI

26 The first Thomson relation κ = dπ dt S Q = RI 2 Joule heating Q = κiδt Thomson effect Q ex = ρ Δx A I2 dπ dt S ΔTI

27 B A T H Current I Two different materials V T C Temperature difference Voltage supply to I 2 0 Voltage difference and current flow Adjusting voltage to neglect I 2 term

28 Q P,BA T + ΔT Q P,BA = Π BA T + ΔT I Q T,B B A Q T,B Q T,B = κ B ΔTI V T Q T,A = κ A ΔTI Q P,AB = Π AB T I Voltage supply to I 2 0 Q P,AB Π AB = Π A Π B V = S B ΔT S A ΔT + δv to flow a little current to compensate the thermoelectric EMF

29 Energy balance VI = Q P,BA + Q P,AB + Q T,B + Q P,A V S AB ΔT dπ AB dt S AB = κ AB S AB = S A S B κ AB = κ A κ B (The first Thomson relation)

30 Entropy balance Irreversible process, Joule heating, is neglected by I 2 0 Q P,BA T + ΔT + Q P,AB T + Q T,B T + ΔT/2 + Q T,A T + ΔT/2 = 0 Π BA T + ΔT T + ΔT + Π AB T T + κ ABΔT T + ΔT/2 = 0 Π BA T + ΔT T + ΔT = Π BA T + dπ BA dt ΔT T Π BA ΔT + O ΔT2 T2 ΔT 0 dπ AB dt Π AB T = κ AB

31 The second Thomson relation Π AB T = S AB Entropy balance Energy balance (The first Thomson relation) dπ AB dt Π AB T = κ AB dπ AB dt S AB = κ AB

32 Two relations dπ dt S = κ Π T = S Three coefficients Seebeck coefficient: Peltier coefficient: S Π Thomson coefficient: κ One of three coefficients gives the other two coefficients The only one directly measurable for individual materials

33 Onsager reciprocal relations in Non-equilibrium thermodynamics Check it for more exact and more universal deviation. Potential: φ T, φ e, P, μ, Intensive variables Its conjugate: p s, q, V, m, (pφ has the unit of energy) Its flow: J Extensive variables J 1 J 2 J N = L 11 L 1N L N1 L NN φ 1 φ 2 φ N L ij = L ji Onsager reciprocal relations

34 2. Thermocouple

35 Thermocouple very basic temperature measurement way. Using Seebeck effect Thermocouple thermometer

36 Thermocouple very basic temperature measurement way. Using Seebeck effect A Unknown V AB = B S T dt T A V Known T B

37 Thermocouple very basic temperature measurement way. Using Seebeck effect Unknown Connection is (usually) necessary T A V Meter Known Wire T B

38 Thermocouple What you measure is V BA V MA V BM Unknown T A V MA = V Meter A M S w T dt Known T B V BM = B M S w T dt

39 Thermocouple What you measure is V = B A S + T S T dt Unknown T A Material- Material+ Use two materials (no other way) Known T B V V Uniform temperature

40 Thermocouple Type Materials S ± / (μv/ ) K Chromel Alumel 41 J Iron Constantan 50 V = B A S + T S T dt Coupled properties are important N Nicrosil Nisil 39 R 87%Pt/13 %Rh Platinum 10 T Copper Constantan 43 E Chromel Constantan 68

41 Thermocouple Type Materials S ± / (μv/ ) K Chromel Alumel 41 J Iron Constantan 50 N Nicrosil Nisil 39 R 87%Pt/13 %Rh Platinum 10 T Copper Constantan 43 E Chromel Constantan 68 T Range/ Remarks High sensitivity High linearity High sensitivity Easily rusting Wide range stability High temperature Expensive Low temperature Thermal noise Highest sensitivity

42 Thermocouple Type Materials S ± / (μv/ ) IEC Color code BS K Chromel Alumel 41 J Iron Constantan 50 N Nicrosil Nisil 39 R 87%Pt/13 %Rh Platinum 10 T Copper Constantan 43 E Chromel Constantan 68

43 3. Thermoelectric Power Generation

44 Thermoelectric power generation Heat input Q T H Semiconductor thermoelectric circuit P type N type Load resistance: R T C Small heat engines Non-mechanical engine (Radioisotope generators) Recovery of waste heat (Energy Harvesting) 44

45 Thermoelectric power generation Heat input Q T H h : hight A : cross section ρ : resistivity λ : thermal conductance P type N type T C Excited current I I = V R + r = S T H T C r m + 1 r = h pρ p A p + h nρ n A n m = R r Load resistance: R Current I Generated power W W = I 2 R = S2 T H T C 2 r m

46 Thermoelectric power generation Heat input Q T H h : hight A : cross section ρ : resistivity λ : thermal conductance P type N type Load resistance: R T C Current I Ohmic heating Q O = ri 2 Heat conduction Q H = Λ(T H T C ) Peltier heat Q P = ST H I r = h pρ p A p Λ = λ pa p h p + h nρ n A n + λ na n h n

47 Thermoelectric power generation Heat input Q T H Heat balance on hot side Q Q O Q H Q P = 0 P type N type T C Q = ST H I + Λ T H T C 1 2 ri2 Load resistance: R Current I

48 Thermoelectric power generation Theoretical thermal efficiency η = W Q = f(t H, T C, m, Z) Z = S2 Λr Maximum efficiency (impedance matching) Figure-of-merit ( 熱電素子対の性能指数 ) m opt = 1 + Z 2 T H T C Z opt = S 2 λ p ρ p + λ n ρ n 2 η = T H T C T H m opt 1 m opt + T C /T H

49 Thermoelectric materials Temperature dependence of ZT (dimensionless parameter) p-type (left) and n-type (right) semiconductors 49

50 Design example Specifications p n e [mv/k] r [mwm] l [W/mK] h [cm] S [cm 2 ] T H =1,000K and T C =400K(S has been optimized) Thermal efficiency Output e e e 6 p n [V/K] 2 Z e l r l r m 2-1 max p p n n [K ] opt R r 1.5 max r 2.8mW = e T Wopt Ropt Ropt r =4.5[W] 50

51 Radioisotope Generator: RTG 原子力電池 Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)

52 Nuclear Reactor Use of nuclear chain reaction Natural decay Chain reaction

53 Chain reaction Use of nuclear chain reaction Control the rate by the material and environment

54 Electron Atom Nucleus = Protons+ neutrons

55 Chemical energy Use of electron energy states Electron

56 Radioactive decay Use of nucleus energy He Plutonium 238 Half decay by 88 years Uranium 234 x 2 x 2 x 2 x 94 x 144 x 94 x 92 x 142 x 92

57 Radioactive decay Use of nucleus energy He Plutonium 238 Half decay by 88 years Uranium 234 x 2 x 2 x 2 x 94 x 144 x W/kg x 92 x 142 x 92

58 RTG ~5 W/kg SAP ~50 W/kg (1 AU)

59 Radioisotope Generator: RTG 原子力電池 Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor) Radioisotope-Thermoelectric Generator Electric output Thermal Output 290W/250W 4,234Wt T H 1000 Total mass Pu mass size Galileo RTG 55kg 7.561kg 114cm f42cm 59

60 Voyager RTG was located with a distance from the main body. Power would be 73% of BOL after 39 years.

61 Curiosity RTG on the back (hip)

62 Cassini Three RTGs with a cover for each

63 New Horizons The latest RTG

64

65 Thank you