Importance of Heat
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Courtesy of Lawrence Livermore National Laboratory. Used with permission.
Vehicle Systems
T
I
M
,
n o
e
t
h
l
C
a
g
losses
9kJMechanical
m
r
n
Exhaust
a
10kJ
9kJ he
n
G
T
o
Driving
Gasoline
/
6kJ
10kJ
i
r
©
s
a
r
t
100 kJ
l
e
Gasoline h
6kJ
o
v
g
Auxiliary
S
30kJ n
35kJ
100kJri10kJ
30kJ
t
o
y
35kJ
c
p
C
10kJ ire
o
C DParasiticrgy
e
Coolant
Exhaust
7
7
heat n
losses
9
9
Parasitic
9
9
E
Exhaust
Coolant
.
.
heat
losses
l
2 r 2 ca
i
o
r
t
• FIn US,ctransportation
uses ~26% of total energy.
e
l
E
Photo from Wikimedia Commons, http://commons.wikimedia.org
Co-Generation in Residential Buildings
T
I
M
,
In US, residential
n and
e
o
t
h
commercial
buildings
l
C
a
consume
~35%
energy
g
m
r
n
e
a
supply h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
Entropy
e
o
r
Oil or
i
y
C
Thermal
Power
Heating
g
D
Nat’l Gas
r
e
7
7
9
9
TE Recoveryn
9
9
E
.
.
&
&
l
2 r 2 ca Electrical PowerRefrigeration
Appliances
Appliances
i
o
r
F ctPV
Electricity
e
l
E
Photo by bunchofpants on Flickr.
Image removed due to copyright restrictions.
Please see any photo of the Honda freewatt
Micro-CHP system, such as http://www.hondanews.
com/thumbnails/2007/4/3/13644_preview.jpg
Industrial Waste
Heat
T
I
Photos by arbyreed and toennesen on Flickr.
7
9
9
.
2 r 2.
o
F
e
l
E
M
,
n o
e
t
h
l
C
a
g
m
r
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g tS n
i
r
o
y
c
p ire
C
o
C D rg y
7 ne
9
9 lE
a
c
i
r
ct
Fig. ES.1 in Hemrick, James G., et al. "Refractories for Industrial Processing:
Opportunities for Improved Energy Efficiency." DOE-EERE Industrial Technologies
Program, January 2005.
Renewable Heat Sources
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Photos by Jon Sullivan at http://pdphoto.org/ and NASA.
Solar Thermal
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
E
Photos of solar hot water tubes removed due to
copyright restrictions. Please see, for example,
http://image.made-in-china.com/2f0j00KeoavBGJycbN/
Unpressurized-Solar-Water-Heater-VERIOUS-.jpg
http://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpg
http://www.treehugger.com/Solar-Thermal-Plant-photo.jpg
Images by Sandia National Laboratories and NREL.
http://media.photobucket.com/
Direct Energy Conversion
T
I
M
,
n o
e
t
h
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
t
e
Thermoelectrics h
o
v
g
i
S
n
r
t
o
y
c
p
C
e
o
r
C D i rg y
e
7
7
n
9
9
9
9
E
2. r 2. cal
i
o
r
F ct
e
l
Photovoltaics
E
COLD SIDE
Image removed due to copyright restrictions.
Please see http://web.archive.org/web/20071011185223
/www.eneco.com/images/science-new.jpg
HOT SIDE
http://www.solareis.anl.gov/images/photos/Nrel_flatPV15539.jpg
Image by Nadine Y. Barclay, USAF.
Thermophotovoltaics
http://www.keelynet.com/tpvcell.jpg
Courtesy of John Kassakian. Used with permission.
Solar Spectrum
T
I
M
,
1600
AM1.5 Solar Spectrumn
e
o
t
h
Energy
Usable
for
Silicon
PV
Cells
l
1400
C
a
g
m
r
n
1200
e
a
h
n
G
T
o
1000
/
i
r
©
s
a
r
t
l
e
h
o
800
v
g
i
S
n
r
t
Bandgap
of Silicon
o
y
c
p
600
C
e
(1.1
μm)
o
r
i
y
C D rg
400
e
7
7
n
9
9
9
9
E
.
l
2. 200
2
a
r 0 ric
o
F 0ct 0.5 1 1.5 2 2.5 3
e
Wavelength (μm)
l
E
Terrestrial Solar Spectrum (W/m2μm)
1800
Solar
1500
1000
500
0
0
0.5
1.0
1.5
2.0
2.5
3.0
Power (W/m2μm)
(a)
1.5E4
1.0E4
0.5E4
0
0
2
4
6
(d)
•
•
8
10
12
Emissivity Absorptance
Power (W/m2μm)
Solar Thermophotovoltaics
T
I
M
,
Insolation
n o
e
t
h
l
Optical ConcentratorC
a
g rm
n
e
a
Selective
Wavelength (μm)
h
n
G
T
o
i
Absorber r/
©
s
a
r
t Emitter
l
Irradiance
e
h
o
v
From Emitterig
S
n
r
t
Selective
y
TPV Cell o
c
p
C
e
o
r
i
y
C
g
Wavelength (μm) D
r
e
Thermal
Management
7
7
n
9
9
Wavelength (μm)
9
9
E
.
.
l
2Theoretical
2
maximum
efficiency: 85.4%; comparable to that of infinite
a
r
c
i
o
number
of multi-junction
cells, but with only a single junction PV cell.
r
t
F
c
Key Challenges:
Selective surfaces absorbing solar radiation but ree
lonly in a narrow spectrum near the bandgap of photovoltaic
emitting
E
cells, working at high temperatures.
1.5
Absorber
1.0
0.5
(b)
0
0
1.5
5
10
(c)
15
Emitter
1.0
0.5
0
0
2
4
6
8
10
12
Solar Thermoelectrics
T
I
30.0
M
,
T =30 C
n o
e
25.0
h
700l Ct
C
a
600
C
g
m
20.0
n er 500 C
a
h
400
C
n
G
T
o
15.0
/
i
250 C
r
©
s
a
r
t
l ve 200 C
h
o
g10.0 t S n
i
r
150 C
o
y
c
p ir5.0
e yC
o
C D rg
e
7
7
0.0
n
9
9
0.5
1.0
1.5
2.0
2.5
9
9
E
.
.
AVERAGE FIGURE OF MERIT ZT
2 r 2 cal
Lowomaterialsricost and low capital cost, potentially high efficiency.
t Develop materials with high thermoelectric figure of
F Challenges:
Key
c
e
l
merit; and
E selective surfaces that absorb solar radiation but do not
T -T
hot
cold
EFFICIENCY (%)
cold
(b)
•
•
re-radiative heat.
1st Law of Thermodynamics
T
I
Closed:
E2 − E1 = Q,12M− W12
Environment
n o
e
t
dE =Cδh
Q − δW
l
a
Q
g
W
m
r
n
dE e& &
System
a
G /T=hQ −ioWn
© ladtr rs
t
Boundary
e
h
o
State
v
g
i
S
n
r
Process
t
Properties:
o
y
c
C
Dependent
Closed Systemop
e
Process
r
Open System
C Di rgy Independent Quantities
e
7
7
n
9
9
9
9
E
2. Er 2=. KEc+alPE + U (Internal Energy) + ...
i
o
r
t
F Specific
du
c
Heat C =
[J/K - kg, or J/K - m ]
e
l
E
dT
3
2nd Law of Thermodynamics
T
I
δQ
M
,
S −S = ∫
+ S (S ≥ 0)n
T
e to
h
l
Entropy
C
a
Entropy
Entropy
Change
g
m
r
n
Transfer
Generation
State
e
a
h
G /T ion
Properties
r rsdS = 0
©
Duringt a cycle:la
e
h
∫
o
Heat Reservoir T
v
g
i
S
n
r
t
Q Q
o
y
c
0
=
−
p
C
No rentropy
generation
e
o
Q
T
T
C D i rg y
e
7
7
Maximum
Efficiency
W Q −Q
n
9
9
η=
=
9
9
E
(Carnot
Efficiency)
.
.
W
Q
Q
2 Qr 2 cal
i
o
r
C, T =23 C, η=40%
F ct TT =223
=5800 K, T =300 K, η=95%
e
l
Heat Reservoir
T
E
2
1
gen
gen
boundary
h
h
h
c
h
c
h
h
c
h
c
h
o
c
c
c
h
Tc
= 1−
Th
o
Thermal power plant η~40%, IC engines η~25%
Microscopic Picture of Entropy
T
I
M
,
n o
•
e
t
h
•
l
C
a
g rm
n
e
a
h
G /T ion 1
r rs P =
© laProbability
Boltzmann Principle
t
Ω
e
h
o
v
g
i
S
n
r
S = k B ln Ωy k =1.38x10
J/K ---Boltzmann constant
t
o
c
p
C
e
o
r
i
y
C
g
D
r
• Constant
Temperature
• Constant Temperature
e
7
7
n
9
9
and
Closed
Systems
But Open Systems
9
9
E
.
.
l
2 r 2 ca− E /( k T )
− ( E − μ ) /(
k T
)
Po( E ) =triAe
P
(
E
)
=
Ae
F c
e
μ --- chemical
potential (driving force for mass diffusion);
l
E
• For Isolated Systems
B
B
•
Microstate: a quantum
mechanically allowed state
A total of Ω microstate
Principle of equal probability:
each microstate is equally
possible to be observed
-23
B
average energy needed to move a particle in/out off a system
Maxwell distribution
T
I
(
) ,M
n o
e
t
h
l
⎡C
m(v + va + v )⎤
P( v , v , v ) = A exp
⎢
⎥
g
m
n ⎢⎣ er2k T ⎥⎦
a
A box of gas
h
n
G
T
o
/
molecules
All Probability
must
normalize
to one
i
r
©
s
t ola er
h
v
g ⎡ m(vt S
i
n
r
⎛ m
⎞
+ v + vo)⎤
y
⎟
A = ⎜⎜
A exp ⎢ec
1 = ∫ dv ∫ dv ∫ dv
⎥
p
C
⎟
2
π
k
T
o
2
k
T
r
⎠
⎝
C Di ⎢⎣ rgy ⎥⎦
e
7
7
⎡ m(v + v + v )⎤
n
⎛ m ⎞
9
9
Maxwell
9
9
⎟⎟ exp ⎢
P ( v ,lvE, v ) = ⎜⎜
.
.
⎥
Distribution
2 r 2 ca
k
T
k
T
2
π
2
⎢⎣
⎥
⎝
⎠
⎦
i
Fo ctr
e
l
E
1
E = m v 2x + v 2y + v 2z
2
2
x
x
y
2
y
2
z
z
B
∞
∞
x
−∞
∞
y
−∞
2
x
2
y
3/ 2
2
z
z
−∞
B
B
3/ 2
x
y
2
x
2
y
z
B
B
2
z
One molecule
T
I
⎡ m(v , +M
v + v )⎤
1
E = ∫ dv ∫ dv ∫ dv m(v + v + v )A exp ⎢ n
⎥
e
o
2
2k tT
⎥⎦
⎢⎣
h
l
C
a
g rm
3
n
E = k T
e
a
2
h
G /T ion
© ∫ lar term
s
Equipartition Principle:tevery quardratic
in microscopic
r
e
h
energy contributesig
k T/2. So
v
n
r
t
o
y
c
p
C J/K × 300K = 5.14 ×
10
J
kirTe= 1.38y× 10
How much o
C
g
Is k T at room D
r
e
×10 J
5.14
7
7
temperature
n
9
9
= 26 meV
=
9
9
E
2. r 2. cal 1.6 ×10 J / eV
i
o
r
t
F
3k T
3 ×1.38 ×10 J / K × 300 K
c
= 220 m/s
v
=
=
Oxygen
Atom
at
300
K
e
l
m
16 ×1.67 ×10 kg
E
∞
∞
x
−∞
∞
y
−∞
z
2
x
2
y
2
x
2
z
−∞
2
y
2
z
B
B
E =
B
−23
-21
B
- 21
B
−19
−23
B
− 27
Fermi-Dirac Distribution
T
I
• From quantum mechanics
M
,
• Energy levels are quantized
n
Energy
:
E = htνo = h
ω
e
• Each quantum state can have
h
l
maximum one electron
C
a
Momentum : p = h/λ = hk
g
• Planck-Einstein Relation
m
r
n
h = h /(e2π )
a
• Planck constant h=6.6x10 Js,
G /Th ion
r
© with
s
•
Consider one quantumt state
an energy
E at constant
a
r
l
e
h
temperature T. Thegstate
cano
have zero
electron (n=0) or one
v
Saverage
nnumber of electrons if
ri iscthe
electron (n=1). yWhat
t
o
p observations?
C
one does many
e
o
r
C D i rg y
⎛ μ ⎞⎡
⎛ E ⎞⎤
e
7
7
n
⎟⎟ ⎢1 + exp⎜⎜ −
⎟⎟⎥
9
9
= A exp⎜⎜
1 = ∑ Ae
9
9
E
⎝ k T ⎠⎣
⎝ k T ⎠⎦
2. r 2. cal
i
o
r
t of electrons in the state
• Average
F number
c
e
l
E
-34
− ( E − μ ) /( k BT )
n = 0 ,1
B
B
Fermi-Dirac Distribution
T
I
M
• Average number of electrons in the state
,
n o
e
t
h
1
l
Fermi-Dirac
=
f = ∑ nAe
C
a
Distribution
⎛ E −g
μ⎞
m
exp⎜⎜an ⎟⎟ + 1er
G⎝ k T/T⎠h ion
© lar rs
t
e
h
o
v
g
At T=0K, μ is called
i
S
n
r
t
y ec Co Fermi level, E
p
o
C Dir rgy F=1 for E<μ
e
7
7
n
9
9
F=0 for E>μ
9
9
E
.
.
2 r 2 cal
i
o
r
F ct
e
l
E
− ( E − μ ) /( k BT )
n = 0 ,1
B
FERMI-DIRAC DISTRIBUTION
1
0.8
f
1000 K
0.6
0.4
100 K 300 K
0.2
0
-0.1
-0.05
0
E-μ (eV)
0.05
0.1
Photons and Phonons
T
I
M
,
Energy
: E = hν =
hω
n
e to
h
l : p = h/λ = h
k
Momentum
C
a
g h = 6r.m
n
6 ×10 Js; h = h /(2π )
e
a
h oofna quantum state:
G /TEnergy
i
r
©
s
t ola Ee=r⎛⎜ n + 1 ⎞⎟hω n = 0,1,2...
h
g t S nv ⎝ 2 ⎠
i
r
y ec Co
p
Zero point energy
•
Classical Oscillator
o
r
C Di rgy Natural Frequency
e
7
7
Spring
n
9
9
9
9
E
1
K
2. r 2. cal
ν =
2π M
i
o
r
F ctM
1⎞
⎛
E
=
n
+
e
⎜
⎟hω n = 0,1,2...
Energy of Mode
l
2⎠
⎝
E
•
From quantum mechanics
• EM waves are quantized, basic
energy quanta is called a photon
• Photon has momentum
• Planck-Einstein Relation
• Each quantum state of photon (an
EM wave mode) can have only
integral number of photons
One Photon
−34
Basic vibrational energy quanta hν is called a phonon
Bose-Einstein Distribution
BOSE-EINSTEIN DISTRIBUTION
5
T
I
M state
• Consider one, quantum
n o
in thermal
equilibrium
e
t
h
l
− ( E − μ ) /( k T )
C
a
Pg( En ) =mAe
n er
a
G /Th ion
r rs Distribution
© l•aBose-Einstein
t
e
h
o
v
g
i
S
n
r
Average
number of
t
o
y
c
p
C
photons/phonons in one
e
o
r
C Di rgy mode (quantum state)
e
7
7
1
n
9
9
f =
9
9
E
.
.
l
⎛E−μ ⎞
2 r 2 ca
⎟⎟ − 1
exp⎜⎜
i
o
⎝ k T ⎠
F c tr
e
l
Usually μ=0
E
n
4
5000 K
3
1000 K
2
300 K
1
100 K
0
0
0.1
0.2
0.3
FREQUENCY (X10
14
0.4
0.5
Hz)
B
B
Heat Transfer Modes
T
I
M
Thermal
Radiation
Convection
,
Heat Conduction
n o
e
t
h
l
C
a
T
T
T
g
T
m
r
n
e
a
L
G /Th ion
• Fourier Law
© lawlaofr coolingrs• Stefan-Boltzmann
• Newton’s
t
e
h
o
Law for Blackbody
dT
v
g
&
i
S
& =thA
Q = −kA
[W]
r
(
Q
T −oTn )
dx
y
& = AσT
c
Q
p
C
e
Cross- o
r
y
C Di Convective
Stefan-Boltzmann Constant
Thermal
Sectional
g
Heat
r
Conductivity 7
σ=5.67x10 W/m K
Area
e
Transfer
Coefficient
7
n
9
9
[W/m-K]
[W/m
K]
9
9
E
• Heat transfer
.
.
Materials Property
2 r 2 cal Flow dependent
)
Q& = AF εσ (T − T
i
o
r
• HeatF
Flux ct
• Natural Convection
Emissivity of
View factor
e
l
dT
• Forced Convection
two surfaces
F=1 for two
&
E
Fluid Ta
y
cold
hot
uy
ux
x
cold
hot
Tw
w
4
a
-8
2
4
2
4
hot
q = −k
dx
[
(= -k∇T) W/m 2
]
parallel plates
4
cold
Heat Conduction
T
I
M
Heat Conduction
,
n o
e
t
h
l
C
T
T
a
g rm
n
L
e
a
h
G /T ion
1D, no heat generation
© lar rs
t
e
h
o
T
T
T
T
−
−
v
g
i
S
Q& = kA
=
n
r
t
Ry
L
o
c
p
C
L
e
o
r
Thermal Resistance
C DR i = kA rgy
e
7
7
&
Heat Current
Q
n
9
9
9
9
E
2. r 2. cal
To
T
i
r
R
F ct
e
l
Convection
E R=1
5
10
Diamond
4
10
cold
hot
Silicon
3
hot
cold
hot
Thermal conductivity (W/mK)
10
cold
th
Copper
Quartz single
crystal (// to c-axis)
2
10
Stainless steel
(type 304)
1
10
Ice
th
Fused quartz
0
10
Water
(saturated)
Helium
(1 atm)
10
hot
-1
cold
th
10
th
hA
Air
(1 atm)
Steam
(saturated)
-2
10
1
2
10
Temperature (K)
3
10
Heat Conduction: Kinetic Picture
T
I
M
,
n o
e
t
Hot
q
h
Cold
l
C
a
g rm
n
e
a
h
G /T ion
© lar rs
vτ x
t
e
h
o
v
g
S
1ri
1
n
t
o
y
− (nEv c)
q
= (nEv )
p
C
2 ire
2
o
y
C
g
r
d(Env )
vDτ dUedT
q = -v τ97
=7−
n
9
dx
3
dT
dx
dU J
9
9
E
.
.
[
]
=
C
l
2v τ dT
2
m
K
a
dT
dT
=−
Cor = −kric
3F dx ct dx
C = ρc
e
1
Specific heat El
x
x
x
x
x−vx τ
x
x+vx τ
2
x
x
• Energy per particle: E [J]
• Number of particles per
unit volume: n [1/m3]
• Average random
velocity of particles v
x • Average time between
collision of two particles
τ---relaxation time
• Average distance
travelled between
collision Λ=vτ---Mean
free path
• Volumetric specific heat
x
3
2
Thermal Conductivity
k = CvΛ
3
Density
per unit mass
Thermal Radiaton: Planck’s Law
T
I
M
Perfectly
Basic Relations
,
Reflecting Wall
n
Frequency ν
e
o
at T
t
h
Angular Frequency ω=2πν
l
Inside the Cavity
C
a
Wavelength λ
EM Wave In
g rm
Wavevector
magnitude k=2π/λ
n
Equilibrium at
e
a
Wavevector
k=(k ,k
,k
Temperature T
k
h
G /T ) ion
©c = νλlar ωrs= ck = c k + k + k
t
e
h
o
ω(k): Dispersion relation (linear)
v
g
i
S
n
r ct
o
y
energy in the cavity?
p ire How much
C
o
C D Ur=g2y hωf (ω,T ) =
∑∑∑
e
λ 9λ7
λ 97
n
L = 9,2 ,..., n
,...
9
E
2.2 2π 2r 2. 2 cal 2∫ (2πdk/ 2L ) ∫ (2πdk/ 2L ) ∫ (2πdk/ 2L )hωf (ω,T )
k =n o
i
r
L
2
F ct
dk
dk
dk
e
=
2
hωf (ω , T )
l
∫
∫
∫
(2π / L ) (2π / L ) (2π / L )
Two
E polarization
x
y
z
2
x
∞
x
x
x
∞
n x =1 n y =1 n z =1
x
x
∞
∞
∞
∞
y
x
x
x
x
0
x
∞
y
0
y
x −∞
z
0
∞
∞
x
−∞
z
z
y
−∞
z
2
y
2
z
Thermal Radiaton: Planck’s Law
T
I
• Energy density per
ω interval
M
∫ ∫ ∫ hωf (ω , T )dk dk dk
,
n
u (ω ) = hωf (ω ,e
T )D(ω ) o
2V
t
h
(
)
=
f
T
k
dk
h
,
4
ω
ω
π
l
hω C 1
a
8π ∫
=
Planck’s law
πg
c
⎛ hωm
⎞
n
exp⎜⎜ r ⎟⎟ − 1
2V
⎛ω ⎞ ⎛ω ⎞
e
a
=
hωf (ω , T )4π ⎜ ⎟ d ⎜ ⎟
⎝k T ⎠ n
∫
h
G
8π
⎝c⎠ ⎝c⎠
T
o
/
•
Intensity:
energy
flux per unit
i
r
©
s
ω
U
a angle
r
t olsolid
= ∫ hωf (ω , T )
dω
e
h
V
π c
g t S dAnv cu(ω ) hω
i
r
1
o
y
(
)
=
=
ω
I
c
= ∫ hωf (ω , T )D(ω )dω p
C
e
4π
4π c
⎛ hω ⎞
o
r
⎟⎟ − 1
i
exp⎜⎜
y
C D rg
k
T
⎝
⎠
e
7 n Solid Angle Per unit wavelength interval
= ∫ u (ω )d9
ω7
9
9
9
E
.
.
l
dA
1
I (ω )dω 4πch
2 r 2 ca
dΩ =
I (λ ) =
=
R
i
λ
dλ
⎛ 2πhc ⎞
o
D(ω)-density
of states
per
r
⎜⎜
⎟⎟ −1
exp
t
F
whole
space
c
unit volume per unit
⎝ k Tλ ⎠
e
Planck’s
law
4π
angular frequency
El interval
2V
U= 3
8π
∞ ∞ ∞
x
y
z
− ∞− ∞− ∞
∞
2
3
3
0
2 3
∞
2
B
3
0
∞
2
2 3
0
∞
p
3
3 2
0
∞
B
0
p
2
5
B
Thermal Radiaton: Planck’s Law
T
I
M
Q&
Wien’s displacement law
,
n o
e
t
λ T = 2898 Kμmh
l
C
a
g rm
n
e
a
h
n
G
T
o
/
Emissive Power
i
r
©
s
t ola er
h
g t S nv
i
Q& (λ ) = AπI (λ )
r
o
y
c
p
C
1o
hω
e
r
=A
i
y
4π c
⎛C
hω ⎞
g
r
⎟⎟ − 1 D
exp⎜⎜
e
7 ⎝ k T 9⎠ 7 n
9
9
9
E
.
.
l
2 r 2 ca
Total
i
o
r
Q& = ∫F
Q& (λ )dλ = c
AσtT
e
l
E
2
EMISSIVE POWER (W/cm μm)
max
3
2 2
B
10
4
10
3
10
2
10
1
5600 K
2800 K
1500 K
10
0
∞
800 K
4
0
10
-1
0
2
4
6
WAVELENGTH (μm)
8
10
MIT OpenCourseWare
http://ocw.mit.edu
2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies
Fall 2009
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.