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Hiroyuki KOIZUMI
1. Principle
Seebeck effect
Peltier effect
Thomson effect
Thermoelectric effect
ฮ๐
๐ผ
ฮ๐
๐
๐ผ ๐Heattransfer
Current
Voltagedifference
Temperaturedifference
Seebeck effect
Peltier effect
Thomson effect
ฮ๐ = โ๐ฮ๐
๐ = ฮ ๐ด โ ฮ ๐ต ๐ผ
๐ = โ๐ ๐ผฮ๐
Thermoelectric effect
Peltier effect
Thomson effect
๐ = ฮ ๐ด โ ฮ ๐ต ๐ผ
๐ = โ๐ ๐ผฮ๐
Electricity Heat
Joule heating ๐ = ๐ ๐ผ2Generation
Transfer (Q>0 = output)
Transfer
Peltier effect
Thomson effect
๐ = ฮ ๐ต โ ฮ ๐ด ๐ผ
๐ = ๐ ๐ผฮ๐
Electricity Heat
Joule heating ๐ = ๐ ๐ผ2Irreversible
Reversible
Reversible
Thermoelectric EMF(็ฑ่ตท้ปๅ)
Seebeck coefficient or Thermopower (็ฑ้ป่ฝ)
Found by T.J. Seebeck
Seebeck effect (1821)ใผใผใใใฏๅนๆ
๐ ๐ + ฮ๐
ฮ๐
ฮ๐ = โ๐ ฮT
๐๐ด ๐๐ต
๐๐ด๐ต
๐๐ด๐ต = โ ๐ด
๐ต
๐ ๐ ๐๐
Seebeck effect (1821)ใผใผใใใฏๅนๆ
8
Thermal equilibrium condition with Electron diffusion
No temperature gradient case
With temperature gradient case
heating
Same temperatures
Charge is carried by electron flow
MaterialSeebeck
coefficient/(ฮผV/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 ๐
P-type semiconductor
Carrier: positive hole
ฮ๐ = โ๐ ฮ๐
High ๐
Lower hole density(stochastically, by random walk)
Negative potential
Low ๐
๐ > 0
N-type semiconductor
Carrier: negative electron
ฮ๐ = โ๐ ฮ๐
High ๐
Lower electron density(stochastically, by random walk)
Positive potential
Low ๐
๐ < 0
P-N junctionPCarrier: positive hole
NCarrier: negative electron
Found by J.C.A. Peltier
Peltier effect (1844)ใใซใใงๅนๆ
Q = ฮ ๐ผ
A
ฮ A๐ผ ฮ ๐ต๐ผ
BQAB = (ฮ ๐ด โ ฮ ๐ต)๐ผ
QAB
ฮ : Peltier coefficient
Metal N-type P-typeEnergy
Electron energy state in solids
Metal AEnergy
Electron energy state in solids
Metal Bcurrent
Energy gap
Metal AEnergyMetal Bcurrent
Energy gap
HeatHeating
Metal AEnergyMetal Bcurrent
Energy gap
HeatCooling
N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy release
N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy injection
20
๐ : Thomson coefficient
(electric specific heat)
Predicted by William Thomson (Lord Kelvin)
Thomson effect (1854๏ผใใ ใฝใณๅนๆ
๐ ๐ + ฮ๐
Q = โ๐ ๐ผฮ๐
๐ผ
Current
Energy
๐ ๐ + ฮ๐
Low energycarrier
High energycarrier
Heat
Current
Energy
๐ ๐ + ฮ๐
Low energycarrier
High energycarrier
Heat
Seebeck effect
Peltier effect
Thomson effect
ฮ๐ = ๐ฮ๐
๐ = ฮ ๐ต โ ฮ ๐ด ๐ผ
๐ = ๐ ๐ผฮ๐
Thermoelectric effectAll the phenomena are caused by the current carriers
They should be related each other
๐ ๐ + ฮ๐
ฮ๐
๐in ๐out
๐ex
๐J
๐in = ฮ ๐ ๐ผ
Current๐ผ
๐out = ฮ ๐ + ฮ๐ ๐ผ
๐J = โ๐ผฮ๐
Peltier effect
๐J + ๐in โ ๐out โ ๐ex = 0 Energy balance
Note, voltage drop with current is โฮ๐
ฮ๐
๐in ๐out
๐ex
๐J
Current๐ผ
ฮ๐ = โ๐ฮ๐ฅ
๐ด๐ผ โ ๐ฮ๐
Resistance effect+Seebeck effect
๐ : resistivity
๐ด : cross section
๐ ๐ + ฮ๐
๐ex = ๐ฮ๐ฅ
๐ด๐ผ2 โ
dฮ
๐๐โ ๐ ฮ๐๐ผ
๐ex = ๐ฮ๐ฅ
๐ด๐ผ2 โ
dฮ
๐๐โ ๐ ฮ๐๐ผ
Thomson effect
๐ = โ๐ ๐ผฮ๐
Joule heating
๐ = ๐ ๐ผ2
๐ =dฮ
๐๐โ ๐
The first Thomson relation
Current๐ผ
Two different materials
Temperature difference
Voltage differenceand current flow
Adjusting voltage to neglect ๐ผ2 term
Voltage supply
to ๐ผ2 โ 0
B A
๐H
๐C๐
Voltage supply
to ๐ผ2 โ 0
B A
๐ + ฮ๐
๐
๐ = ๐๐ตฮ๐ โ ๐๐ดฮ๐ + ๐ฟ๐
๐
to flow a little current
to compensate the thermoelectric EMF
๐T,๐ต ๐T,๐ต
๐P,๐ต๐ด
๐P,๐ด๐ต
๐P,๐ต๐ด = ฮ ๐ต๐ด ๐ + ฮ๐ ๐ผ
๐P,๐ด๐ต = ฮ ๐ด๐ต ๐ ๐ผ
๐T,๐ต = โ๐ ๐ตฮ๐๐ผ
๐T,๐ด = ๐ ๐ดฮ๐๐ผ
ฮ ๐ด๐ต = ฮ ๐ด โ ฮ ๐ต
๐ โ โ๐๐ด๐ตฮ๐
๐๐ผ = ๐P,๐ต๐ด + ๐P,๐ด๐ต + ๐T,๐ต + ๐P,๐ด
๐ฮ ๐ด๐ต๐๐
โ ๐๐ด๐ต = ๐ ๐ด๐ต
๐๐ด๐ต = ๐๐ด โ ๐๐ต
๐ ๐ด๐ต = ๐ ๐ด โ ๐ ๐ต
(The first Thomson relation)
Energy balance
Entropy balanceIrreversible process, Joule heating, is neglected by ๐ผ2 โ 0
๐P,๐ต๐ด๐ + ฮ๐
+๐P,๐ด๐ต๐
+๐T,๐ต
๐ + ฮ๐/2+
๐T,๐ด๐ + ฮ๐/2
= 0
ฮ ๐ต๐ด ๐ + ฮ๐
๐ + ฮ๐+ฮ ๐ด๐ต ๐
๐+
๐ ๐ด๐ตฮ๐
๐ + ฮ๐/2= 0
๐ฮ ๐ด๐ต๐๐
โฮ ๐ด๐ต๐= ๐ ๐ด๐ต
ฮ ๐ต๐ด ๐ + ฮ๐
๐ + ฮ๐=ฮ ๐ต๐ด๐+dฮ ๐ต๐ดd๐
ฮ๐
๐โฮ ๐ต๐ด๐2ฮ๐ + ๐ ฮ๐2
ฮ๐ โ 0
๐ฮ ๐ด๐ต๐๐
โฮ ๐ด๐ต๐= ๐ ๐ด๐ต
๐ฮ ๐ด๐ต๐๐
โ ๐๐ด๐ต = ๐ ๐ด๐ต
Energy balance(The first Thomson relation)Entropy balance
ฮ ๐ด๐ต๐= ๐๐ด๐ต
The second Thomson relation
๐ฮ
๐๐โ ๐ = ๐
ฮ
๐= ๐
Seebeck coefficient: ๐
Peltier coefficient: ฮ
Thomson coefficient: ๐
Three coefficients
Two relations
One of three coefficientsgives the other two coefficients
The only one directly measurable for individual materials
Onsager reciprocal relationsin Non-equilibrium thermodynamicsCheck it for more exact and more universal deviation.
Potential: ๐
Its conjugate: ๐
Its flow: ๐ฝ
๐ฝ1๐ฝ2โฎ๐ฝ๐
=๐ฟ11 โฏ ๐ฟ1๐โฎ โฑ โฎ๐ฟ๐1 โฏ ๐ฟ๐๐
โ๐1๐ป๐2โฎ๐ป๐๐
๐ฟ๐๐ = ๐ฟ๐๐ Onsager reciprocal relations
๐, ๐๐ , ๐, ๐,โฏ
๐ , ๐, ๐,๐,โฏ
(๐๐ has the unit of energy)
Intensive variables
Extensive variables
2. Thermocouple
Thermocouple thermometer
Thermocoupleโvery basicโ temperature measurement way.Using Seebeck effect
๐
๐๐ด๐ต = โ ๐ต
๐ด
๐ ๐ ๐๐
Thermocoupleโvery basicโ temperature measurement way.Using Seebeck effect
Unknown
๐๐ด
Known
๐๐ต
Unknown
๐๐ด
Known
๐๐ต
Thermocoupleโvery basicโ temperature measurement way.Using Seebeck effect
๐ Meter
Wire
Connection is (usually) necessary
Thermocouple
๐ Meter
๐๐๐ด = โ ๐
๐ด
๐w ๐ ๐๐
๐๐ต๐ = โ ๐ต
๐
๐w ๐ ๐๐
Unknown
๐๐ด
Known
๐๐ต
What you measure is ๐๐ต๐ด โ ๐๐๐ด โ ๐๐ต๐
Thermocouple
๐
๐ = ๐ต
๐ด
๐+ ๐ โ ๐โ ๐ ๐๐
Unknown
๐๐ด
Known
๐๐ต
What you measure is
Uniform temperature
Material-
Material+
๐
Use two materials(no other way)
Thermocouple
๐ = ๐ต
๐ด
๐+ ๐ โ ๐โ ๐ ๐๐
Coupled propertiesare important
Type Materials๐ยฑ/
(๐๐/โ)
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
Thermocouple
T Range/โ Remarks
-200 +1350High sensitivityHigh linearity
-40 +750High sensitivityEasily rusting
-270 +1300Wide range
stability
0 +1600High temperature
Expensive
-200 350Low temperature
Thermal noise
-110 +140Highest
sensitivity
Type Materials๐ยฑ/
(๐๐/โ)
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
Thermocouple
Type Materials๐ยฑ/
(๐๐/โ)
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
Color code
IEC BS
3. ThermoelectricPower Generation
44
Semiconductor thermoelectric circuit
Small heat engines Non-mechanical engine(Radioisotope generators) Recovery of waste heat (Energy Harvesting)
Thermoelectric power generation
Load
resistance: ๐
Heat input
๐๐H
๐C
Ptype
Ntype
45
Thermoelectric power generation
Load
resistance: ๐
Heat input
๐๐H
๐C
Generated power W
Excited current IPtype
Ntype
Current๐ผ
๐ผ =๐
๐ + ๐=๐ ๐๐ป โ ๐๐ถ๐ ๐ + 1
๐ =๐
๐
๐ = ๐ผ2๐ =๐2 ๐๐ป โ ๐๐ถ
2
๐ ๐ + 1 2
h : hightA : cross section ฯ : resistivity ฮป : thermal conductance
๐ =โp๐p
๐ดp+โn๐n๐ดn
Thermoelectric power generation
Load
resistance: ๐
Heat input
๐๐H
๐C
Ptype
Ntype
Current๐ผ
Ohmic heating
Heat conduction
Peltier heat
h : hightA : cross section ฯ : resistivity ฮป : thermal conductance
๐๐ = ๐๐ผ2 ๐ =
โp๐p
๐ดp+โn๐n๐ดn
๐๐ป = ฮ(๐๐ป โ ๐๐ถ)ฮ =
๐p๐ดp
โp+๐n๐ดnโn
๐๐ = ๐๐๐ป๐ผ
Thermoelectric power generation
Load
resistance: ๐
Heat input
๐๐H
๐C
Ptype
Ntype
Current๐ผ
Heat balance on hot side
๐ +1
2๐๐ โ ๐๐ป โ ๐๐ = 0
๐ = ๐๐๐ป๐ผ + ฮ ๐๐ป โ ๐๐ถ โ1
2๐๐ผ2
Thermoelectric power generation
Theoretical thermal efficiency
๐opt = 1 +๐
2๐๐ป โ ๐๐ถ
๐ =๐๐ป โ ๐๐ถ๐๐ป
๐opt โ 1
๐opt + ๐๐ถ/๐๐ป
๐ =๐
๐= ๐(๐๐ป , ๐๐ถ , ๐, ๐)
Maximum efficiency (impedance matching)
๐opt = S2 ๐๐๐๐ + ๐๐๐๐
โ2
๐ =๐2
ฮ๐Figure-of-merit (็ฑ้ป็ด ๅญๅฏพใฎๆง่ฝๆๆฐ )
Thermoelectric materials
49
Temperature dependence of ZT (dimensionless parameter)
p-type (left) and n-type (right) semiconductors
Design example
50
Specifications
p n
e [mV/K] 210 โ170
r [mWm] 18 14
l [W/mK] 1.1 1.5
h [cm] 1.0 1.0
S [cm2] 1.3 1.0
TH=1,000K and TC=400K๏ผS has been optimized๏ผ
Thermal efficiency
Output =4.5[W]
6
p n 380 10 [V/K]e e e
2
2 -1
max p p n n 0.00177[K ]Z e l r l r
opt 1.5m R r
max
1000 400 1.5 10.6 0.26 0.16
1000 1.5 400 1000
2 2
opt opt
opt
0.2280.004127
0.006886
TW R
R r
e
2.8mr W
=
Radioisotope Generator: RTG ๅๅญๅ้ปๆฑ
Energy from the decay of a radioactive isotope to generate electricity๏ผdifferent from nuclear reactor๏ผ
Nuclear ReactorUse of nuclear chain reaction
Natural decay Chain reaction
Control the rateby the material and environment
Chain reactionUse of nuclear chain reaction
Electron
Nucleus
= Protons+ neutrons
Atom
Chemical energyUse of electron energy states
Electron
Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
540 W/kg
RTG๏ฝ5 W/kg
SAP๏ฝ50 W/kg(1 AU)
59
Radioisotope-Thermoelectric Generator
Electric output 290W/250W
Thermal Output 4,234Wt
TH 1000โ
Total mass 55kg
Pu mass 7.561kg
size 114cmรf42cm
Galileo RTG
Radioisotope Generator: RTG ๅๅญๅ้ปๆฑ
Energy from the decay of a radioactive isotope to generate electricity๏ผdifferent from nuclear reactor๏ผ
VoyagerRTG was located with a distance from the main body.Power would be 73% of BOL after 39 years.
CuriosityRTG on the back (hip)
CassiniThree RTGswith a cover for each
New HorizonsThe latest RTG
Thank you
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