Hiroyuki KOIZUMI
1. Principle
Thermoelectric effect Seebeck effect Temperature difference ΔT Voltage difference ΔV Peltier effect I Q Thomson effect I Current Q Heat transfer
Thermoelectric effect Seebeck effect ΔV = SΔT Peltier effect Q = Π A Π B I Thomson effect Q = κiδt
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
Electricity Heat Irreversible Joule heating Q = RI 2 Peltier effect Thomson effect Reversible Q = Π B Π A I Reversible Q = κiδt
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
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
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
P-type semiconductor Carrier: positive hole ΔV = S ΔT S > 0 Low T High T Lower hole density (stochastically, by random walk) Negative potential
N-type semiconductor Carrier: negative electron ΔV = S ΔT S < 0 Low T High T Lower electron density (stochastically, by random walk) Positive potential
P Carrier: positive hole P-N junction N Carrier: negative electron
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
Electron energy state in solids Energy Metal N-type P-type
Electron energy state in solids Energy Metal A current Metal B Energy gap
Heating Energy Metal A Heat current Metal B Energy gap
Cooling Heat Energy Metal A current Metal B Energy gap
N-type carrier: electron Heat current P-type carrier: hole Energy release
N-type carrier: electron Heat current P-type carrier: hole Energy injection
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
Heat Low energy carrier Energy Current High energy carrier T T + ΔT
Heat Low energy carrier Energy Current High energy carrier T T + ΔT
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
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
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
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
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
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
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)
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
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
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
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
2. Thermocouple
Thermocouple very basic temperature measurement way. Using Seebeck effect Thermocouple thermometer
Thermocouple very basic temperature measurement way. Using Seebeck effect A Unknown V AB = B S T dt T A V Known T B
Thermocouple very basic temperature measurement way. Using Seebeck effect Unknown Connection is (usually) necessary T A V Meter Known Wire T B
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
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
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
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/ -200 +1350-40 +750-270 +1300 0 +1600-200 350-110 +140 Remarks High sensitivity High linearity High sensitivity Easily rusting Wide range stability High temperature Expensive Low temperature Thermal noise Highest sensitivity
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
3. Thermoelectric Power Generation
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
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 + 1 2 45
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
Thermoelectric power generation Heat input Q T H Heat balance on hot side Q + 1 2 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
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
Thermoelectric materials Temperature dependence of ZT (dimensionless parameter) p-type (left) and n-type (right) semiconductors 49
Design example Specifications p n e [mv/k] 210 170 r [mwm] 18 14 l [W/mK] 1.1 1.5 h [cm] 1.0 1.0 S [cm 2 ] 1.3 1.0 T H =1,000K and T C =400K(S has been optimized) Thermal efficiency Output e e e 6 p n 380 10 [V/K] 2 Z e l r l r m 2-1 max p p n n 0.00177[K ] opt R r 1.5 max r 2.8mW 1000 400 1.5 1 0.6 0.26 = 0.16 1000 1.5 400 1000 2 e T 0.228 Wopt Ropt 0.004127 Ropt r 0.006886 2 =4.5[W] 50
Radioisotope Generator: RTG 原子力電池 Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)
Nuclear Reactor Use of nuclear chain reaction Natural decay Chain reaction
Chain reaction Use of nuclear chain reaction Control the rate by the material and environment
Electron Atom Nucleus = Protons+ neutrons
Chemical energy Use of electron energy states Electron
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
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 94 540 W/kg x 92 x 142 x 92
RTG ~5 W/kg SAP ~50 W/kg (1 AU)
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
Voyager RTG was located with a distance from the main body. Power would be 73% of BOL after 39 years.
Curiosity RTG on the back (hip)
Cassini Three RTGs with a cover for each
New Horizons The latest RTG
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