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Cha
pter
4:T
empe
ratu
re M
easu
rem
ent
1. In
trod
uctio
n
2. E
xpan
sion
Met
hods
for
Mea
surin
g T
empe
ratu
res
3. R
esis
tanc
e th
erm
omet
ers
4. T
herm
ocou
ples
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re S
enso
rs
6. P
yrom
etry
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
90
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
1. In
trod
uctio
n
T
empe
ratu
re, u
nlik
e qu
antit
ies
such
as
leng
th, t
ime
or m
ass
is a
n ab
stra
ct
quan
tity
that
mus
t be
defin
ed in
term
s of
the
beha
vior
of m
ater
ials
as
the
tem
pera
ture
cha
nges
.
•E
xam
ples
of c
hang
e in
Beh
avio
r:
C
hang
e in
vol
ume
of li
quid
,
C
hang
e in
leng
th o
f a b
ar,
C
hang
e in
ele
ctric
al r
esis
tanc
e of
a w
ire,
C
hang
e in
pre
ssur
e of
a g
as a
t con
stan
t vol
ume,
C
hang
e in
col
or o
f a la
mp
filam
ent,
etc.
S
ever
al te
mpe
ratu
re s
cale
s ha
ve b
een
deve
lope
d ov
er ti
me
to
prov
ide
a su
itabl
e re
fere
nce
for
the
leve
l of t
herm
odyn
amic
ac
tivity
ass
ocia
ted
with
tem
pera
ture
cha
nges
.
91
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
1. In
trod
uctio
n
Sev
eral
tem
pera
ture
sca
les
have
bee
n de
velo
ped
over
tim
e to
pro
vide
a
suita
ble
refe
renc
e fo
r th
e le
vel o
f the
rmod
ynam
ic a
ctiv
ity a
ssoc
iate
d w
ith
tem
pera
ture
cha
nges
.
T
he F
ahre
nhei
t sca
le (
intr
oduc
ed in
171
5)W
ith 1
80 d
ivis
ions
bet
wee
n th
e fr
eezi
ng p
oint
(+
32°F
) an
d th
e bo
iling
poin
t of
wat
er (
212°
F).
T
he C
elsi
us s
cale
(in
trod
uced
in 1
742
by A
nder
s C
elsi
us)
Div
ides
the
inte
rval
bet
wee
n fr
eezi
ng p
oint
and
boi
ling
poin
t ofw
ater
into
100
di
visi
ons.
T
he z
ero
valu
e of
this
sca
le c
orre
spon
ds to
the
free
zing
poi
nt o
f wat
er
(acc
ordi
ng to
Lin
naeu
s).
T
wo
othe
r sc
ales
are
use
d to
des
crib
e ab
solu
te te
mp
erat
ures
: (a
bsol
ute
zero
is e
quiv
alen
t to
ther
mod
ynam
ic m
inim
um):
The
Ran
kine
Sca
le:T
R=
θF
+ 4
65,7
9T
he K
elvi
n S
cale
:TK
= θ
c+
273
,15
92
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
1. In
trod
uctio
n
P V
= R
T
P =
is th
e ab
solu
te p
ress
ure
V
= is
the
spec
ific
volu
me
R
= is
the
univ
ersa
l gas
con
stan
t
T =
is th
e ab
solu
te te
mpe
ratu
re
T
he in
tern
atio
nal t
empe
ratu
re s
cale
has
bee
n de
fined
in te
rms
ofth
e be
havi
or o
f a n
umbe
r of
mat
eria
ls a
t the
rmod
ynam
ic fi
xed
poin
ts.
T
he in
tern
atio
nal t
empe
ratu
re s
cale
is b
ased
on
17 fi
xed
poin
ts w
hich
cov
er
the
tem
pera
ture
ran
ge fr
om -
270.
15°C
to 1
084.
62°C
.
M
ost o
f the
se 1
7 po
ints
cor
resp
ond
to a
n eq
uilib
rium
sta
te d
urin
g a
phas
e tr
ansf
orm
atio
n of
a p
artic
ular
mat
eria
l.
The
idea
l gas
law
usi
ng th
e ab
solu
te te
mpe
ratu
res
93
T
he fi
xed
poin
ts a
ssoc
iate
d w
ith e
ither
mel
ting
or fr
eezi
ng o
f am
ater
ial a
re
dete
rmin
ed a
t pre
ssur
e of
one
sta
ndar
d at
mos
pher
e (1
atm
).
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
1. In
trod
uctio
n
Fix
ed P
oint
N°
Mat
eria
lS
tate
Tem
pera
ture
He
Vap
or-2
70.1
5--2
68.1
5T
riple
Poi
nt-2
59.3
467
e-H
2V
apor
-256
.16
e-H
2V
apor
-252
.85
Ne
Vap
or-2
48.5
939
O2
Trip
le P
oint
-218
.791
6A
rT
riple
Poi
nt-1
89.3
442
Hg
Trip
le P
oint
-38.
8344
H2O
Trip
le P
oint
0.01
Ga
Trip
le P
oint
27.7
646
InM
eltin
g15
6.59
85S
nF
reez
ing
231.
928
Zn
Fre
ezin
g41
9.52
7A
lF
reez
ing
660.
327
Ag
Fre
ezin
g96
1.78
Au
Fre
ezin
g10
64.1
8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
e–
Ha 2
Cu
Fre
ezin
g10
84.6
2
T
riple
poi
nt is
the
tem
pera
ture
at w
hich
the
solid
, liq
uid
and
vapo
r ph
ases
are
in e
quili
briu
m.
94
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
1. In
trod
uctio
n
B
etw
een
the
trip
le p
oint
of e
-H2
(-25
9.34
67°C
= 1
3.80
33K
) an
d th
e fr
eezi
ng
poin
t of A
g (9
61.7
8°C
= 1
234.
94K
), th
e te
mpe
ratu
re i
s de
fined
with
a
plat
inum
res
ista
nce
ther
mom
eter
.
A
bove
the
free
zing
poi
nt o
f Ag,
the
tem
pera
ture
is d
efin
ed u
sing
an o
ptic
al
pyro
met
er
95
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
2. E
xpan
sion
Met
hods
For
Mea
surin
g T
empe
ratu
res
W
hen
mat
eria
ls a
re s
ubje
cted
to te
mpe
ratu
re c
hang
es (
∆T =
T-T
o), t
hey
expe
nd o
r co
ntra
ct a
ccor
ding
to :
∆l
= th
e ch
ange
in le
ngth
α
= th
e te
mpe
ratu
re c
oeffi
cien
t of e
xpan
sion
for
the
mat
eria
ll 0
= th
e le
ngth
at t
he r
efer
ence
tem
pera
ture
T0
∆l=
αl 0
∆T
T
he te
mpe
ratu
re c
oeffi
cien
t of e
xpan
sion
αis
ver
y sm
all f
or m
ost
mat
eria
l (α
is o
f ord
er o
f 20.
10-6
/°C).
T
hus
the
tem
pera
ture
cha
nge
can
not b
e kn
own
dire
ctly
from
the
leng
th c
hang
e ∆l
mea
sure
men
ts
96
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
2.1
The
liqu
id-in
-gla
ss th
erm
omet
ers
2. E
xpan
sion
Met
hods
For
Mea
surin
g T
empe
ratu
res
A
gla
ss c
apill
ary
tube
with
a b
ulb
cont
aini
ng a
vol
ume
of li
quid
(the
mos
t
used
is H
g).
W
hen
the
tem
pera
ture
cha
nges
, the
liqu
id v
olum
e ex
pand
s m
uch
mor
e
then
the
glas
s ca
pilla
ry a
nd b
ulb
beca
use
of th
e di
ffere
nce
in α
betw
een
the
fluid
and
the
glas
s.
A
sca
le e
tche
d on
the
glas
s is
use
d to
con
vert
the
exte
nsio
n of
the
fluid
in
the
capi
llary
to th
e te
mpe
ratu
re o
f the
ther
mom
eter
.
A
dvan
tage
s:H
igh
prec
isio
n ±
0,2°
C to
±2°
C
D
isad
vant
ages
:D
irect
rea
ding
, hig
h tim
e re
spon
se
97
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
2.2
The
Bi-M
etal
lic-S
trip
-The
rmom
eter
s
2. E
xpan
sion
Met
hods
For
Mea
surin
g T
empe
ratu
res
r h=
h2
h1
Thi
ckne
ss R
atio
:
Mod
ulus
of
elas
ticity
Rat
io :
r e=
E2
E1
Tem
pera
ture
D
iffer
ence
:
∆ T=
T w–
T
h
Sw
itch
ρ ρρρ
α ααα 1 >
α > α
> α
> α 2
Sw
itch
cont
act
Tw
Met
al 1
; α ααα 1
Met
al 2
;α ααα2
Th 1 h 2
ρ=
31
+r h
2+
1+
r hr e
r e2–
1r h
r eh
6α
1–
α2
1+
r h∆ T
98
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
∆TR
esis
tanc
e S
enso
r∆R
TW
O K
inds
of R
esis
tanc
e T
herm
omet
ers
Res
ista
nce
Tem
pera
ture
D
etec
tors
(R
TD
’s)
The
rmis
tors
R
esis
tanc
e te
mpe
ratu
re d
etec
tors
are
sim
ply
resi
stiv
e el
emen
ts fo
rmed
of
such
mat
eria
l as
plat
inum
, nic
kel o
r a
nick
el-c
oppe
r al
loy
know
n co
mm
erci
ally
as
Bal
co.
T
hese
mat
eria
ls e
xhib
it a
posi
tive
coef
ficie
nt o
f res
istiv
ity a
nd a
re u
sed
in
RT
D’s
bec
ause
they
are
sta
ble
and
prov
ide
a re
prod
ucib
le r
espo
nse
tote
mpe
ratu
re o
ver
a lo
ng p
erio
d of
tim
e.
99
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.1
Res
ista
nce
Tem
pera
ture
Det
ecto
rs (
RT
D’s
)
A
typi
cal R
TD
con
sist
s of
a w
ire c
oil s
enso
r w
ith a
fram
ewor
k fo
r su
ppor
t, a
shea
th fo
r pr
otec
tion,
a li
near
izin
g ci
rcui
t, a
whe
atst
one
brid
ge, a
nd a
volta
ge d
ispl
ay in
stru
men
t.
T
he s
enso
r is
a r
esis
tive
elem
ent t
hat e
xhib
its a
res
ista
nce-
tem
pera
ture
rela
tions
hip
give
n by
the
expr
essi
on :
R =
R0
(1+
γ 1T
+γ 2
T2 +
…+
γ nT
n )
γ 1
,γ2…
γ n: T
empe
ratu
re c
oeffi
cien
ts o
f res
istiv
ity
R0
: The
res
ista
nce
of th
e se
nsor
at a
ref
eren
ce te
mpe
ratu
reT
0.
T
he r
efer
ence
tem
pera
ture
is u
sual
ly s
peci
fied
as T
0=
0°C
T
he n
umbe
r of
term
s re
tain
ed fo
r an
y ap
plic
atio
n de
pend
s on
the
mat
eria
l
used
in th
e se
nsor
, the
ran
ge o
f tem
pera
ture
, and
the
accu
racy
req
uire
d in
the
mea
sure
men
t.
100
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
-200
020
040
060
080
010
00
2468
Nic
kel
Cop
per
Pla
tiniu
m
Tem
pera
ture
(°C
)
Resistance Ration R/R0
11
3. R
esis
tanc
e T
herm
omet
ers
3.1
Res
ista
nce
Tem
pera
ture
Det
ecto
rs (
RT
D’s
)
Res
ista
nce-
Tem
pera
ture
cur
ves
for
Nic
kel,
Cop
per
and
Pla
tinum
101
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.1
Res
ista
nce
Tem
pera
ture
Det
ecto
rs (
RT
D’s
)
T
he m
ost c
omm
on R
TD
is c
ompo
sed
of h
igh
purit
y (9
9.99
%)
plat
inum
wire
w
ound
abo
ut a
cer
amic
cor
e an
d he
rmet
ical
ly s
eale
d in
a c
eram
ic c
apsu
le.
P
latin
um is
the
supe
rior
mat
eria
l for
pre
cisi
on th
erm
omet
ry:
It
resi
sts
cont
amin
atio
n an
d co
rros
ion
its
mec
hani
cal a
nd e
lect
rical
pro
pert
ies
are
stab
le o
ver
long
per
iod
of ti
me.
T
he p
latin
um w
ire c
oils
are
str
ess
relie
ved
afte
r w
indi
ng, i
mm
obili
zed
agai
nst s
trai
n, a
nd a
rtifi
cial
ity a
ged
afte
r fa
bric
atio
n to
pro
vide
for
long
-ter
m s
tabi
lity.
D
rift i
s us
ually
less
then
0.1
°C w
hen
such
sen
sor
is u
sed
at it
s up
per
tem
pera
ture
lim
it.
P
latin
um R
TD
’s a
re a
lso
cons
truc
ted
usin
gei
ther
thic
k or
thin
-film
tech
nolo
gies
.
With
bot
h of
thes
e ap
proa
ches
, a fi
lm o
f pla
tinum
is p
lace
d on
ath
in fl
at
cera
mic
sub
stra
te a
nd e
ncap
sula
ted
with
a g
lass
or
cera
mic
coa
ting.
102
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
Tim
e af
ter
imm
ersi
on (
s)
00.
20.
40.
60.
81
255075
Pla
tiniu
m (
thic
k 1m
m)
on a
1 m
m th
ick
cera
mic
flat
Pla
tiniu
m (
wire
)
wou
ng o
n a
3 m
m
diam
eter
cor
e
3. R
esis
tanc
e T
herm
omet
ers
3.1
Res
ista
nce
Tem
pera
ture
Det
ecto
rs (
RT
D’s
)
103
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
v s
RT
D
Sen
sor
Wire
1
Wire
2
Wire
3D
ecad
ere
sist
or b
ox
R R
Matched pair ofprecision resistors
Lead
-wire
-
syst
em
1000
Wm
axim
um in
0.0
1 W
step
s
Nul
lIn
dica
tor
3. R
esis
tanc
e T
herm
omet
ers
3.1.
1 R
TD
s an
d th
e W
heat
ston
e B
ridge
:
104
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
AB
C
D
R1 i d
v m
Equ
ilibr
ium
R4
R2
R3
Rc
AB
C
D
wire
1
wire
2
wire
3
R4
R1
R2
R3
3. R
esis
tanc
e T
herm
omet
ers
3.1.
1 R
TD
s an
d th
e W
heat
ston
e B
ridge
:
R1.
R4
= R
2.R
3(R
1+r 1
).R
4=
R2.
(R3+
r 3)
r 1=
r 3
105
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
S
el h
eatin
g of
the
sens
or :
p T=
RT.i2
T
he p
ower
pT
is d
issi
pate
d by
an
RT
D p
lace
d in
a W
heat
ston
e br
idge
with
equa
l res
ista
nces
RT
in e
ach
of th
e fo
ur a
rms
and
supp
lied
with
a v
olta
ge
p T=
V s2
4R
T
T
he in
crea
se in
tem
pera
ture
from
sel
f hea
ting
DT
sh r
equi
red
to d
issi
pate
pT
is:
∆ Tsh
=F s
hpT
F
sh: t
he s
elf h
eatin
g fa
ctor
(°C
/mW
)
T
he m
agni
tude
of
Fsh
is p
rovi
ded
by th
e m
anuf
actu
rer
of th
e se
nsin
g el
emen
t
E
xam
ple
:S
enso
r : R
T=
100
Ω; W
.B :
1V D
C s
uppl
y vo
ltage
,
Fsh
= 0
.5°C
/mW
. pT=
2.5
mW
,
∆Tsh
= 1
,25°
C
106
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
i
Wire
4
Wire
2
Wire
3
Wire
1
DV
MC
onst
ant
curr
ent
pow
er
supp
ly
Mea
d w
ire s
yste
mR
TD
S
enso
r
i
3. R
esis
tanc
e T
herm
omet
ers
3.1.
1 R
TD
s an
d th
e W
heat
ston
e B
ridge
:
A
noth
er c
ircui
t tha
t can
be
empl
oyed
for
auto
mat
ic r
eado
ut is
the
cons
tant
-cu
rren
t pot
entio
met
er c
ircui
t :
C
onst
ant-
curr
ent p
oten
tiom
eter
circ
uit w
ith le
ad-w
ire c
ompe
nsat
ion
and
auto
mat
ic r
eadi
ng o
f the
out
put f
rom
an
RT
D s
enso
r.
T
he o
utpu
t vol
tage
is V
0=R
T. I
It c
an b
e m
onito
red
with
a d
igita
l vol
tmet
er10
7
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.1.
2. C
omm
on E
rror
s:
Ano
ther
circ
uit t
hat c
an b
e em
ploy
ed fo
r au
tom
atic
rea
dout
is th
e co
nsta
nt-c
urre
nt
pote
ntio
met
er c
ircui
t :
lead
-wire
s ef
fect
s
Can
be
min
imiz
ed b
y m
akin
g th
e le
ad w
ires
as s
hort
as
poss
ible
.
The
tota
lres
ista
nce
of th
e le
ads
shou
ld b
e al
way
s le
ss th
an 1
% o
f the
sen
sor
resi
stan
ce
S
tabi
lity
Sta
bilit
y of
the
sens
or is
usu
ally
ass
ured
by
agin
g. T
he e
lem
ents
dur
ing
the
man
ufac
turin
g pr
oces
s. S
tabi
lity
may
bec
ome
a so
urce
of e
rror
ifth
e te
mpe
ratu
re
limit
of a
sen
sor
is e
xcee
ded
eith
er b
y de
sign
or
by a
ccid
ent.
S
elf-
heat
ing
Sel
f hea
ting
erro
rs a
re p
rodu
ced
whe
n ex
cita
tion
volta
ges
or c
urre
nts
are
used
in th
e si
gnal
con
ditio
ning
circ
uit.
Usu
ally
ther
e is
no
need
for
larg
e ex
cita
tion
sign
als
sinc
e an
RT
D is
a h
igh-
outp
ut s
enso
r. S
elf h
eatin
g ca
n be
red
uced
by
limiti
ng th
e po
wer
diss
ipat
ion
in th
e R
TD
to le
ss th
en 2
mW
.
sens
itivi
ty o
f the
RT
D t
o st
rain
Bou
nded
RT
D s
enso
rs r
esem
ble
to s
trai
n ga
ges
and
in fa
ct, t
hey
resp
ond
to s
trai
n
108
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.2.
The
rmis
tors
T
herm
isto
rs a
re te
mpe
ratu
re-s
ensi
tive
resi
stor
s fa
bric
ated
from
sem
i-co
nduc
ting
mat
eria
ls, s
uch
oxid
es o
f nic
kel,
coba
lt or
man
gane
sean
d su
lfide
s
of ir
on, a
lum
inum
or
copp
er.
T
herm
isto
rs w
ith im
prov
ed s
tabi
lity
are
obta
ined
whe
n ox
ide
syst
ems
of
man
gane
se-n
icke
l, m
anga
nese
-nic
kel-c
obal
t, or
man
gane
se-n
icke
l-iro
n ar
e
obta
ined
.
C
ondu
ctio
n is
con
trol
led
by th
e co
ncen
trat
ion
of o
xyge
n in
the
oxid
e
sem
icon
duct
ors.
A
n ex
cess
or
defic
ienc
y of
oxy
gen
from
exa
ct s
toec
hiom
etric
req
uire
men
ts
resu
lts in
latti
ce im
perf
ectio
ns k
now
n as
Sch
ottk
y de
fect
s an
d F
rank
el d
efec
ts.
109
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.2.
The
rmis
tors
T
he r
esis
tanc
e-te
mpe
ratu
re r
elat
ions
hips
for
ther
mis
tor
can
be e
xpre
ssed
as
:
R=
R0e
β1 T
–1 T 0
LnR R
0=
β1 T
–1 T 0
W
here
:
R
: the
res
ista
nce
of th
e th
erm
isto
r at
the
tem
pera
ture
T
R
0: th
e re
sist
ance
of t
he th
erm
isto
r at
the
refe
renc
e te
mpe
ratu
re T
0
β:
a m
ater
ial c
onst
ant t
hat r
ange
s fr
om 3
000
to 5
000K
T a
nd T
0ar
e ab
solu
te te
mpe
ratu
res
in K
T
he S
ensi
tivity
S=
∆ R ∆ T=
–β
T2
R
110
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.2.
The
rmis
tors
A
ther
mis
tor
with
R0
= 2
000
Ωan
d S
= -
0.04
/K e
xhib
its a
res
pons
e
∆R/∆
T =
80Ω
/K
Thi
s la
rge
resi
stan
ce c
hang
e ca
n be
con
vert
ed to
a v
olta
ge w
ith a
sim
ple
two-
wire
pote
ntio
met
ric c
ircui
t.
The
vol
tage
cha
nge
asso
ciat
ed w
ith a
tem
pera
ture
cha
nge
as s
mal
las
0.00
05K
ca
n be
eas
ily a
nd a
ccur
atel
y m
onito
red.
T
herm
isto
rs a
re p
rodu
ced
in th
e fo
rm o
f dis
ks, w
afer
s, fl
akes
, rod
s, w
ashe
rs a
nd
bead
s to
pro
vide
sen
sor
of th
e si
ze a
nd s
hape
req
uire
d fo
r a
wid
e va
riety
of
appl
icat
ions
.
T
he m
ost c
omm
on a
re B
eads
, the
ir di
amet
er r
ange
from
0.1
25 to
1.5
mm
.
The
rmis
tors
can
be
used
to m
easu
re te
mpe
ratu
res
from
a fe
w d
egre
es a
bove
abso
lute
zer
o to
abo
ut 3
15°C
. The
y ca
n be
use
d at
hig
her
tem
pera
ture
s, h
owev
er
stab
ility
beg
ins
to d
ecre
ase
sign
ifica
ntly
abo
ve th
is li
mit.
The
ran
ge o
f a th
erm
isto
r is
usu
ally
lim
ited
to a
bout
100
°C, p
artic
ular
ly w
hen
it
is c
onne
cted
to a
rea
dout
dev
ice
that
has
bee
n co
mpe
nsat
ed to
pro
vide
nea
rly
linea
r ou
tput
. 11
1
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.2.
The
rmis
tors
T
he a
ccur
acy
of a
ther
mis
tor
depe
nds
on th
e te
chni
ques
em
ploy
ed to
mea
sure
∆R/R
and
to c
alib
rate
the
sens
or.
W
ith p
rope
r te
chni
ques
and
gla
ss-e
ncap
sula
ted
ther
mis
tors
, tem
pera
ture
of
125°
C c
an b
e m
easu
red
with
an
accu
racy
of 0
.01°
C.
S
ince
the
chan
ge in
res
ista
nce
is s
o la
rge
(∆R
/R =
80
Ω/K
), a
com
mon
mul
ti-
met
er (
4 or
4 1
/2 d
igits
) ca
n be
em
ploy
ed to
mea
sure
R w
ithin
±1
Ω, N
o br
idge
or
pote
ntio
met
er c
ircui
ts a
re r
equi
red
mai
nly
if re
adin
gs o
f res
ista
nce
are
proc
esse
d in
a d
ata
acqu
isiti
on s
yste
m w
ith a
com
putin
g m
icro
proc
esso
r.
In
suc
h ca
se th
e te
mpe
ratu
re c
an b
e ap
prox
imat
ed b
y th
e eq
uatio
n:
1 T=
A+
B.L
nR
T+
CLn
RT
3
T
= is
the
abso
lute
tem
pera
ture
in K
A
, B, C
are
coe
ffici
ents
det
erm
ined
from
cal
ibra
tion
curv
es
112
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
3.2.
The
rmis
tors
: C
omm
on E
rror
s
le
ad-w
ires
effe
cts
-ar
e us
ually
sm
all e
noug
h to
be
negl
ecte
d fo
r re
lativ
ely
long
lead
-wire
s.
-T
he s
ensi
tivity
of a
ther
mis
tor
is h
igh;
ther
efor
e, th
e ch
ange
in r
esis
tanc
e D
RT
resu
lting
from
a te
mpe
ratu
re c
hang
e is
muc
h gr
ater
then
the
smal
l cha
nge
in
resi
stan
ce o
f the
lead
wire
s re
sulti
ng fr
om th
e te
mpe
ratu
re v
aria
tion.
-A
lso,
the
resi
stan
ce o
f the
ther
mis
tor
is la
rge
rela
tivel
y to
the
resi
stan
ce o
f the
lead
wire
s (R
T/R
L 1
000)
; con
sequ
ently
, any
red
uctio
n in
sen
sitiv
ity o
f the
se
nsor
bec
ause
of l
ead-
wire
res
ista
nce
is n
eglig
ible
.
se
lf he
atin
g -
sinc
e th
e po
wer
(p T
=R
T.i2
) di
ssip
ated
in th
e th
erm
isto
r w
ill h
eat i
t abo
ve it
s am
bien
t tem
pera
ture
.
-It
is r
ecom
men
ded
to u
se a
lim
ited
curr
ent f
low
thro
ugh
the
ther
mis
tor,
that
the
tem
pera
ture
ris
e re
sulti
ng fr
om th
e p
ower
dis
sipa
tion
is s
mal
ler
then
the
reci
sion
to w
hich
the
tem
pera
ture
is to
be
mea
sure
d.
113
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4. T
herm
ocou
ples
A
ther
moc
oupl
e co
nsis
ts o
f tw
o di
ssim
ilar
mat
eria
ls in
ther
mal
con
tact
.
The
ther
mal
con
tact
is c
alle
d Ju
nctio
n.
It
can
be m
ade
by tw
istin
g w
ires
toge
ther
or
by w
eldi
ng, s
olde
ring
or b
razi
ng tw
o
mat
eria
ls to
geth
er.
T
Mat
eria
l A
Mat
eria
l B
T1
Mat
eria
l B
Mat
eria
l A
T2
Mat
eria
l BM
N
J 1J 2
V 0=
C1
T 1–T
2+
C2
T 12
–T22
C
1an
d C
2ar
e th
erm
oele
ctric
con
stan
ts th
at d
epen
d on
the
mat
eria
ls
used
to fo
rm th
e ju
nctio
n
V0
114
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
3. R
esis
tanc
e T
herm
omet
ers
4.1.
SE
EB
EC
K E
FF
EC
T
T
he O
hm la
w c
an b
e m
odifi
ed :
T1
> T
2
T1
T2
e -
e -
e -
T1
> T
2
T1
T2
e -
e -
e -
J=
1 qρ
grad
µ+
S*
grad
T
J
= th
e cu
rren
t den
sity
ρ
= th
e re
sist
ivity
of t
he m
ater
ial
µ
= th
e el
ectr
o-ch
emic
al p
oten
tial w
hich
is r
elat
ed to
the
emf b
y th
e ex
pres
sion
:
q =
the
elec
tric
al c
harg
e of
one
ele
ctro
n.
S
* =
is th
e en
trop
y of
tran
spor
t by
elec
tron
s. It
dep
ends
of t
he ty
pe o
f
cond
ucto
r an
d it'
s te
mpe
ratu
re.
S*
is
posi
tive
grad
µ=
–q
grad
V
115
4. T
herm
ocou
ples
T
he P
eltie
r ef
fect
occ
urs
whe
n a
curr
ent f
low
s in
the
ther
moc
oupl
e ci
rcui
t.
The
Pel
tier
heat
tran
sfer
is in
add
ition
to th
e Jo
ule
heat
ing
effe
ct.
4.2.
PE
LTIE
R
EF
FE
CT
: q p=
ΠA
Bi
q p
= is
the
heat
tran
sfer
due
to th
e
Pel
tier
effe
ct in
wat
ts.
Π
AB=
is th
e P
eltie
r co
effic
ient
for
the
A to
B c
oupl
e.
It
shou
ld b
e no
ted
that
:
Π
AB=
-Π
BA
Mat
eria
lB
Mat
eria
lA v 0
(qp)o
ut(q
p)in
i
Mat
eria
lB
J 1J 2
T1
T2
Mat
eria
lB
Mat
eria
lA v 0
(qp)o
ut(q
p)in
i
Mat
eria
lB
J 1J 2
T1
T2
App
lied
Vol
tage
T
he P
eltie
r co
effic
ient
dep
ends
on
the
dire
ctio
n of
cur
rent
flow
thro
ugh
the
Junc
tion.
T
his
fact
impl
ies
that
hea
t will
tran
sfer
from
the
junc
tion
to th
e en
viro
nmen
t at
junc
tion
J 1an
d fr
om th
e en
viro
nmen
t to
the
junc
tion
at J
2
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
116
4. T
herm
ocou
ples
T
he T
hom
pson
effe
ct is
ano
ther
ther
moe
lect
ric in
tera
ctio
n th
at e
ffect
s th
e be
havi
our
of a
ther
moc
oupl
e ci
rcui
t.
T
his
effe
ct in
volv
es th
e ge
nera
tion
or a
bsor
ptio
n of
hea
t qT
whe
neve
r a
tem
pera
ture
gra
dien
t and
a c
urre
nt e
xist
in a
con
duct
or.
T
he q
uant
ity o
f hea
t qT
bei
ng tr
ansf
erre
d is
giv
en b
y :
4.3.
TH
OM
PS
ON
EF
FE
CT
:
q T=
σi
T 1–
T 2
σ:
the
Tho
mps
on c
oeffi
cien
t th
at d
epen
ds o
n th
e co
nduc
tor
mat
eria
l.
q i
q T
T1
T2
v 1v 2
i=V
1–V
2
R
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
117
V 0=
e B/A
T 1+
e A/B
T 2
4. T
herm
ocou
ples
T
he p
ract
ical
use
of t
herm
ocou
ples
is b
ased
on
the
follo
win
g si
x op
erat
ing
prin
cipl
es:
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
A
ther
moc
oupl
e ci
rcui
t mus
t con
tain
at l
east
two
diss
imila
r m
ater
ials
and
at
leas
t tw
o ju
nctio
ns.
v 0i
Mat
eria
l B
Mat
eria
l A
Mat
eria
l B
J 1J 2
T1
T2
e B/A
=–
e A/B
V 0=
e B/A
T 1–
T 2
1
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
118
4. T
herm
ocou
ples
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
e B
/A: T
he ju
nctio
n po
tent
ial p
er u
nit t
empe
ratu
re a
t a ju
nctio
n as
the
curr
ent
flow
s fr
om m
ater
ial B
to m
ater
ial A
.
e A
/B: T
he ju
nctio
n po
tent
ial p
er u
nit t
empe
ratu
re a
t a ju
nctio
n as
the
curr
ent
flow
s fr
om m
ater
ial A
to m
ater
ial B
.
The
rel
atio
nshi
p be
twee
n V
0an
d (T
1-T
2) is
non
-line
ar s
ince
eB
/Ais
not
a
cons
tant
with
res
pect
to te
mpe
ratu
re
1
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
119
4. T
herm
ocou
ples
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
T
he o
utpu
t vol
tage
V0
of a
ther
moc
oupl
e ci
rcui
t dep
ends
onl
y on
the
diffe
renc
e be
twee
n ju
nctio
n te
mpe
ratu
res
(T1-
T2)
and
is in
depe
nden
t fro
m th
e
tem
pera
ture
s el
sew
here
in th
e ci
rcui
t if n
o cu
rren
t flo
ws
in th
eci
rcui
t.
2
v 0i
Mat
eria
l B
Mat
eria
l A
Mat
eria
l B
T1
T2
T3
T4
T5
T6 T7
T8
T9
T10
V
0is
inde
pend
ent f
rom
the
lead
wire
s an
d th
e te
mpe
ratu
re d
istr
ibut
ion
alon
g th
eir
leng
th.
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
120
4. T
herm
ocou
ples
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
If
a th
ird m
etal
C is
inse
rted
into
eith
er le
g (A
or
B)
of a
ther
moc
oupl
e ci
rcui
t,
the
outp
ut v
olta
ge V
0is
not
effe
cted
, pro
vide
d th
at th
e tw
o ju
nctio
ns (
A/C
and
C/A
) ar
e m
aint
aine
d at
the
sam
e te
mpe
ratu
re, f
or e
xam
ple
: Tj=
T1=
T3
3
T1
Mat
eria
l BMat
eria
l A
T2
Mat
eria
l Bv 0i
Mat
eria
l A
Mat
eria
l C
Ti
Tj
V 0=
e B/A
T 1+
e A/C
T i+
e C/A
T j+
e A/B
T 2S
ince
e B/A
=–
e A/B
and
e A/C
=–
e C/A
We
can
Writ
e
V 0=
e B/A
T 1–
T 2+
e A/C
T i–
T jT
he e
ffect
of t
he A
/C ju
nctio
n is
el
imin
ated
if T
i=
Tj.
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
121
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4. T
herm
ocou
ples
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
T
he in
sert
ion
of a
n in
term
edia
te m
etal
C in
to ju
nctio
n 1
does
not
effe
ct th
e
outp
ut v
olta
ge V
0pr
ovid
ed th
at th
e tw
o ju
nctio
ns fo
rmed
by
inse
rtio
n of
the
inte
rmed
iate
met
al (
A/C
and
C/B
) ar
e m
aint
aine
d at
the
sam
e te
mpe
ratu
re T
1
4
V 0=
e B/C
T 1+
e C/A
T i+
e C/B
T 2
Sin
cee C
/A=
eC
/B+
e B/A
and
e B/C
+e C
/A=
e B/A
V 0=
e B/A
T 1–
T 2T 1 M
ater
ial B
Mat
eria
l A
T 2
Mat
eria
l Bv 0i
Mat
eria
l A
Mat
eria
l C
T 1
T 3
S
uch
situ
atio
n oc
curs
whe
n ju
nctio
ns a
re fo
rmed
by
twis
ting
the
two
ther
moc
oupl
e m
ater
ials
A a
nd B
toge
ther
and
sol
derin
g or
bra
zing
the
conn
ectio
n w
ith a
n in
term
edia
te m
etal
C.
122
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4. T
herm
ocou
ples
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
A
ther
moc
oupl
e ci
rcui
t with
tem
pera
ture
T1
and
T2
prod
uces
an
outp
ut
volta
ge (
V0)
1-2
= f
(T1-
T2)
and
one
exp
osed
to te
mpe
ratu
re T
2an
d T
3
prod
uces
an
outp
ut (
V0)
2-3=
f(T
2-T
3) )
.
If th
e sa
me
circ
uit i
s ex
pose
d to
tem
pera
ture
s T
1 an
d T
3 th
e ou
tput
vol
tage
5
(V0)
1-3
= f(
T1
-T
3) =
(V
0)1-
2+
(V0)
2-3
Mat
eria
l B
Mat
eria
l A Mat
eria
l B
(v0)
1-3
i=
+
Mat
eria
l BMat
eria
l A Mat
eria
l B
(v0)
1-2
i
Mat
eria
l B
Mat
eria
l A Mat
eria
l B
(v0)
2-3
iT
1T
2T
1T
2T
2T
3
123
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
A
ther
moc
oupl
e ci
rcui
t fab
ricat
ed fr
om m
ater
ial A
and
C g
ener
ates
an
outp
ut
volta
ge (
V0)
A-C
whe
n ex
pose
d to
tem
pera
ture
s T
1 an
d T
2 an
d a
sim
ilar
circ
uit f
abric
ated
from
mat
eria
l C a
nd B
gen
erat
es a
n ou
tput
vol
tage
(V
0)C
-B
F
urth
erm
ore,
a th
erm
ocou
ple
fabr
icat
ed fr
om m
ater
ials
A a
nd B
gen
erat
es a
n
outp
ut v
olta
ge
6
4. T
herm
ocou
ples
(V0)
A/B
= (V
0)A
/C+
(V0)
C/B
Mat
eria
l B
Mat
eria
l A Mat
eria
l B
(v0)
A/B
i=
+
Mat
eria
l C
Mat
eria
l A Mat
eria
l C
(v0)
A/C
i
Mat
eria
l BMat
eria
l C Mat
eria
l B
(v0)
C/B
iT
1T
2T
1T
2T
1T
2
124
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4.4
The
rmoc
oupl
es :
Prin
cipl
es o
f Beh
avio
ur
by
em
ploy
ing
this
prin
cipl
e, c
alib
ratio
n ta
bles
can
be
deve
lope
dfo
r an
y pa
ir
of m
ater
ials
if th
e ca
libra
tion
of in
divi
dual
mat
eria
ls a
re p
aire
d w
ith a
sta
ndar
d
ther
moc
oupl
e m
ater
ial,
such
as
plat
inum
.
4. T
herm
ocou
ples
125
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
T
he th
erm
oele
ctric
effe
ct o
ccur
s w
hene
ver
a th
erm
ocou
ple
circ
uiti
s
fabr
icat
ed fr
om a
ny tw
o di
ssim
ilar
mat
eria
ls; i
n m
ost i
nsta
nces
mat
eria
ls a
re
sele
cted
to :
1-P
rovi
de lo
ng-t
erm
sta
bilit
y at
upp
er te
mpe
ratu
re le
vel.
2-E
nsur
e co
mpa
tibili
ty w
ith a
vaila
ble
inst
rum
enta
tion.
3-M
inim
ize
cost
. 4-
Max
imiz
e se
nsiti
vity
ove
r th
e ra
nge
of o
pera
tion.
The
sen
sitiv
ities
of s
ever
al m
ater
ials
is g
iven
in
com
bina
tion
with
pla
tinum
at
0°C
.
Exa
mpl
e:
The
sen
sitiv
ity o
f a c
hrom
el-A
lum
el th
erm
ocou
ple
is g
iven
by
: S
chro
mel
/Alu
mel
= S
chr
omel
/PT
-S
Alu
mel
/PT
Sch
rom
el/A
lum
el =
25.
8 -
(-13
.6)
= 3
9.4
µV
/°C
4.5
The
rmoe
lect
ric M
ater
ial
4. T
herm
ocou
ples
126
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
T
he s
ensi
tivity
of a
ther
moc
oupl
e is
not
con
stan
t, it'
s ou
tput
vol
tage
is n
on
linea
r of
the
diffe
renc
e in
junc
tions
tem
pera
ture
s.
T
he m
ost c
omm
only
use
d th
erm
ocou
ples
are
des
igna
ted
by th
e A
mer
ican
N
atio
nal S
tand
ard
Inst
itute
(A
NS
I) a
s fo
llow
s:
Typ
eP
ositi
ve M
ater
ial
Neg
ativ
e M
ater
ial
E J K N R S T
Chr
omel
Con
stan
tan
Iron
Con
stan
tan
Chr
omel
Alu
mel
N
icro
sil
Nis
il P
latin
um 1
3% R
hodi
umP
latin
um
Pla
tinum
10%
Rho
dium
Pla
tinum
C
oppe
rC
onst
anta
n
4.5
The
rmoe
lect
ric M
ater
ial
4. T
herm
ocou
ples
127
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
The
out
put v
olta
ge V
0ve
rsus
tem
pera
ture
T1
whe
n th
e re
fere
nce
junc
tion
tem
pera
ture
is T
2=
0°C
for
seve
ral t
ypes
of t
herm
ocou
ples
050
010
0015
0020
0025
0030
00
20406080T
ype
E (
Chr
omel
-con
stan
tan)
Typ
e K
(C
hrom
el-A
lum
el)
Typ
e N
(N
icke
l-Nis
il)
Typ
e G
(tu
ngst
en-
tung
sten
26%
rh
eniu
m)
Typ
e S
(P
latin
um-
Pla
tinum
10%
rh
odiu
m)
4.5
The
rmoe
lect
ric M
ater
ial
4. T
herm
ocou
ples
128
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
A th
erm
ocou
ple
circ
uit
resp
onds
to a
tem
pera
ture
di
ffere
nce
(T1-
T2)
4.6
Ref
eren
ce T
empe
ratu
re J
unct
ion
4. T
herm
ocou
ples
It is
ess
entia
l tha
t the
ref
eren
ce
junc
tion
be m
aint
aine
d at
a c
onst
ant
accu
rate
ly k
now
n te
mpe
ratu
re T
2
Fou
r co
mm
on m
etho
ds a
re u
sed
to m
aint
ain
the
refe
renc
e te
mpe
ratu
re :
129
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4.6
Ref
eren
ce T
empe
ratu
re J
unct
ion
4. T
herm
ocou
ples
Met
hod
1: T
he ic
e an
d w
ater
bat
h:
MA
TE
RIA
L A
MA
TE
RIA
L B
The
rmos
bot
tle a
nd c
ap
Cop
per
Cop
per
Mea
surin
g ju
nctio
n
130
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4.6
Ref
eren
ce T
empe
ratu
re J
unct
ion
4. T
herm
ocou
ples
Met
hod
2: T
herm
oele
ctric
ref
riger
atio
n:
T
he c
old
junc
tion
of th
e th
erm
ocou
ple
is p
lace
d in
a c
onta
iner
fille
d of
di
still
ed d
eion
ized
wat
er m
aint
aine
d at
pre
cise
ly 0
°C.
T
he o
uter
wal
ls o
f the
con
tain
er a
re c
oole
d by
ther
moe
lect
ric r
efrig
erat
ion
elem
ents
(P
eltie
r co
olin
g ef
fect
).
T
he in
crea
se in
vol
ume
of w
ater
as
it be
gins
to fr
eeze
on
the
wal
ls o
f the
cont
aine
r ex
pand
s a
bello
ws
(un
souf
flet)
, whi
ch c
onta
cts
a m
icro
sw
itch
and
deac
tivat
es th
e re
frig
erat
ion
elem
ents
.
The
cyc
lic fr
eezi
ng a
nd th
awin
g of
the
ice
on th
e w
alls
of t
he c
onta
iner
accu
rate
ly m
aint
ains
the
tem
pera
ture
of t
he c
onta
iner
at 0
°C.
131
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
4.6
Ref
eren
ce T
empe
ratu
re J
unct
ion
4. T
herm
ocou
ples
Met
hod
3:
The
ele
ctric
al b
ridge
met
hod:
R4
R3R2
R1
(RT
D)
Mea
surin
g ju
nctio
nT
1
Mat
eria
l A
Mat
eria
l B
Ref
eren
ce b
lock
at
ambi
ent t
empe
ratu
re
Tem
pera
ture
rec
orde
r
v s
132
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
E
ach
of th
e tw
o ju
nctio
ns (
chro
mel
-Alu
mel
) in
the
first
ove
n pr
oduc
es a
vol
tage
of
2.66
mV
at a
n ov
en te
mpe
ratu
re o
f 65.
5°C
;
T
he to
tal v
olta
ge o
f 5.3
2 m
V is
can
celle
d by
the
doub
le ju
nctio
nof
Alu
mel
-
Cop
per
and
Cop
per-
Chr
omel
in th
e se
cond
ove
n at
a te
mpe
ratu
re o
f 130
°C.
T
he n
et e
ffect
of t
he fo
ur ju
nctio
ns is
to o
btai
n th
e th
erm
oele
ctric
equ
ival
ent o
f a
sing
le r
efer
ence
junc
tion
at a
tem
pera
ture
of 0
°C.
4.6
Ref
eren
ce T
empe
ratu
re J
unct
ion
4. T
herm
ocou
ples
Met
hod
4: T
he d
oubl
e-ov
en m
etho
d:
Cop
per
Mea
surin
g
junc
tionT
1
Chr
omel
Alu
mel
Chr
omel
Alu
mel
Cop
per
Ove
n at
65
.5°C
Ove
n at
13
0°C
Rea
dout
133
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
A
ll th
e in
trod
uced
sen
sors
(bi
-met
allic
str
ip, R
TD
'S, t
herm
isto
rs,
ther
moc
oupl
es ..
.) a
re in
tend
ed to
mea
sure
tem
pera
ture
ove
r a
rela
tivel
y
smal
l reg
ion
of a
muc
h la
rge
body
.
T
hey
have
diff
eren
t ope
ratin
g pr
inci
ple
but e
xhib
it se
vera
l com
mon
char
acte
ristic
s w
hich
incl
ude
dyna
mic
res
pons
e an
d so
urce
s of
err
or.
T
empe
ratu
re s
enso
rs a
re c
lass
ified
as
first
-ord
er s
yste
ms,
sin
ce th
eir
dyna
mic
res
pons
e is
con
trol
led
by a
firs
t-or
der
diffe
rent
ial e
quat
ion
that
desc
ribes
the
rate
of h
eat t
rans
fer
betw
een
the
sens
or a
nd th
e su
rrou
ndin
g m
ediu
m.
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
134
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
q=
hA
T m–
T=
mC
dT dt
Sur
face
A
rea
Sen
sor
m, T
, C
q
T ∞
Whe
re :
•q
= th
e ra
te o
f hea
t tra
nsfe
r to
the
sens
or
•h
= th
e co
nvec
tion
heat
tran
sfer
coe
ffici
ent
•A
= th
e su
rfac
e ar
ea th
roug
h w
hich
hea
t pas
ses
•m
= th
e m
ass
of th
e se
nsor
•C
= th
e sp
ecifi
c he
at c
apac
ity o
f the
sen
sor.
dT dt
+h
Am
C=
hA
mC
T m
S
olvi
ng th
e eq
uatio
n fo
r th
e ho
mog
eneo
us p
art y
ield
s to
:
W
here
:
C
1=
a c
onst
ant o
f int
egra
tion
β
= ti
me
cons
tant
of t
he s
enso
r gi
ven
by:
T=
C1
e–t ββ
β=
mC
hA
135
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
T
he r
espo
nse
of a
tem
pera
ture
sen
sor
to a
ste
p-fu
nctio
n in
put c
orre
spon
ds to
the
resp
onse
of a
sen
sor
sudd
enly
imm
erse
d in
a fl
uid
med
ium
mai
ntai
ned
at
cons
tant
tem
pera
ture
Tm
In
this
exa
mpl
e, th
e pa
rtic
ular
sol
utio
n is
: T
= T
m.
T
here
fore
, the
gen
eral
sol
utio
n is
T =
C1.
e-t/β
+ T
m
F
or th
e in
itial
con
ditio
n T
(0)=
0, t
he in
tegr
atio
n co
nsta
nt C
1=
-T
m
T
he fi
nal e
xpre
ssio
n fo
r te
mpe
ratu
re T
as
a fu
nctio
n of
tim
e t,
for
the
step
-fu
nctio
n in
put i
s: T
= T
m(1
-e-
t/β)
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
5.1
Ste
p F
unct
ion
Inpu
t
136
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
Temperatureratio T/Tm
0.5
1.0
12
34
00
Nor
mal
ized
tim
e t/β
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
5.1
Ste
p F
unct
ion
Inpu
t
−
=
−
t βm
TT
1e
t β1
mT
Ce
T−
=+
137
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
5.2.
Ram
p F
unct
ion
inpu
t
T
he s
enso
r an
d th
e su
rrou
ndin
g m
ediu
m a
re a
t the
sam
e te
mpe
ratu
re.
T
here
afte
r, th
e te
mpe
ratu
re o
f the
med
ium
incr
ease
s lin
early
with
tim
e so
that
:
Tm
= k
. t
T
he p
artic
ular
sol
utio
n gi
ves
: T =
b (
t -β βββ )
b
is th
e sl
ope
of th
e te
mpe
ratu
re-t
ime
ram
p fu
nctio
n th
e ge
nera
l sol
utio
n fo
r
the
ram
p-fu
nctio
n in
put i
s : T =
C1
e-t/
β βββ+
b (
t -β βββ)
for
t =
0,
*T
(0)
= T
m(0
) =
0
*C
1=
b .
βT
= b
. t -
b. β βββ
. (1
-e-
t/β βββ
)
138
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
5. D
ynam
ic R
espo
nse
of T
empe
ratu
re
Sen
sors
5.2.
Ram
p F
unct
ion
inpu
tTemperature 0
0T
ime
Ram
p -
func
tion
inpu
t
βT
ime
lag
b1
b
1
Sen
sor
Res
pons
e T
T
he in
itial
res
pons
e of
the
sens
or is
slu
ggis
h
A
fter
a sh
ort i
nitia
l int
erva
l, th
e se
nsor
trac
ks th
e ris
e in
tem
pera
ture
of t
he m
ediu
m
surr
ound
ing
the
sens
or w
ith
the
corr
ect s
lope
but
with
a
time
lag
equa
l to
β
T
he e
xpon
entia
l ter
m is
impo
rtan
t dur
ing
the
initi
al r
espo
nse
and
the
linea
r te
rm d
omin
ates
the
long
-ter
m r
espo
nse
(t>
3β)
Acc
urat
e te
mpe
ratu
re m
easu
rem
ent c
an b
e m
ade
for
times
grea
ter
than
3β
139
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.1
Intr
oduc
tion
A
s th
e te
mpe
ratu
re o
f a b
ody
incr
ease
s, it
bec
omes
incr
easi
ngly
diff
icul
t to
mea
sure
it’s
tem
pera
ture
with
res
ista
nce
tem
pera
ture
det
ecto
rs, t
herm
isto
rs
or th
erm
ocou
ples
Lack
of s
tabi
lity,
bre
ak d
own
of in
sula
tion,
sec
urity
of t
he
oper
ator
Pro
blem
s:
Dev
elop
men
ts o
f pyr
omet
ry
By
empl
oyin
g th
e pr
inci
ples
of r
adia
tion,
met
hods
hav
e be
en
deve
lope
d to
mea
sure
sur
face
tem
pera
ture
with
out c
onta
ctin
g th
e bo
dy
Prin
cipl
es:
140
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.1
Intr
oduc
tion
Tw
o di
ffere
nt r
adia
tion
met
hods
are
wid
ely
empl
oyed
O
ptic
al P
yrom
etry
:C
ompa
re th
e br
ight
ness
of t
he li
ght r
adia
ting
from
a b
ody
with
a k
now
n
stan
dard
P
hoto
n de
tect
or:
Use
of p
hoto
n de
tect
or to
mea
sure
the
phot
on fl
ux d
ensi
ty th
at v
arie
s w
ith
the
tem
pera
ture
of t
he s
urfa
ce
141
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.2
Prin
cipl
es o
f rad
iatio
n
The
rmal
rad
iatio
n is
an
elec
trom
agne
tic r
adia
tion
emitt
ed b
y a
body
as
a re
sult
of it
s te
mpe
ratu
re
•M
any
kind
s of
rad
iatio
n
•T
herm
al r
adia
tion
is o
nly
one
kind
•P
ropa
gatio
n at
the
spee
d of
ligh
t (c
= 3
.108
m/s
)
6.2.
1 P
hysi
cal M
echa
nism c
=λ
×ν
Spe
ed o
f lig
ht
(m/s
)W
avel
engt
h (m
)
Fre
quen
cy (
Hz,
s-1
)
142
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
The
pro
paga
tion
of th
erm
al r
adia
tion
take
s pl
ace
in th
e fo
rm o
f di
scre
te q
uant
a, e
ach
quan
tum
hav
ing
an e
nerg
y of
:
6.2.
1 P
hysi
cal M
echa
nism
Eh
=×
ν
h : P
lank
’s c
onst
ant,
h =
6.6
25 1
0-34
J.s
Ass
umpt
ion:
qu
antu
m =
par
ticle
hav
ing
ener
gy, m
ass
and
mom
entu
m (
mol
ecul
e of
gas)
143
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.2.
1 P
hysi
cal M
echa
nism
By
cons
ider
ing
the
radi
atio
n as
suc
h a
gas,
the
prin
cipl
es o
f qua
ntum
-st
atis
tical
ther
mod
ynam
ics
can
be a
pplie
d to
der
ive
an e
xpre
ssio
n fo
r th
e
ener
gy d
ensi
ty o
f rad
iatio
n pe
r un
it vo
lum
e an
d un
it w
avel
engt
h as
:
2
25
25
0hc
/K
Tc
/T
2hc
2hc
Me
1e
1
−−
λλ
λπ
λπ
λ=
=−
−
K: T
he B
oltz
man
’s c
onst
ant,
K=
1.3
8066
10-
23J/
mol
/K
C2:
Con
stan
t, C
2=
1,4
4 10
-2m
.K
144
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.2.
1 P
hysi
cal M
echa
nism
Spe
ctra
l pow
er e
mis
sion
from
a b
lack
bod
y at
diff
eren
t tem
pera
ture
s
145
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.2.
1 P
hysi
cal M
echa
nism
00
40
EM
dT
∞λ
=λ
=σ
∫
The
Ste
phan
Bol
tzm
an la
w:
E0 :
ene
rgy
radi
ated
per
uni
t tim
e pe
r un
it su
rfac
e by
the
idea
l rad
iato
r (b
lack
bod
y)
σ: t
he S
teph
an-B
oltz
man
n co
nsta
nt =
5.6
69 1
0-8
W/m
2 /K
4
The
spe
ctra
l rad
iatio
n in
tens
ity:
: am
ount
of p
ower
em
itted
by
radi
atio
n of
the
wav
elen
gth
λfr
om a
flat
su
rfac
e at
tem
pera
ture
T.
0M
λ
146
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er•
Use
d in
the
rang
e [7
00 C
–40
00 C
]
•T
he r
adia
nt e
nerg
y em
itted
by
the
body
is c
olle
cted
with
an
obje
ctiv
e le
ns a
nd
focu
sed
onto
a c
alib
rate
d p
yrom
eter
lam
p.
•A
n ab
sorp
tion
filte
r is
inse
rted
in th
e op
tical
sys
tem
bet
wee
n th
e ob
ject
ive
lens
and
the
pyro
met
er la
mp
whe
n th
e te
mpe
ratu
re o
f the
bod
y ex
ceed
s 13
00 C
•T
he r
adia
nt e
nerg
y fr
om b
oth
the
hot b
ody
and
the
filam
ent o
f the
pyr
omet
er la
mp
is th
en p
asse
d th
roug
h a
red
filte
r w
ith a
sha
rp c
ut-o
ff be
low
λ=
0.6
3 µm
.
•T
he li
ght
tran
smitt
ed th
roug
h th
is fi
lter
is c
olle
cted
by
an o
bjec
tive
lens
and
focu
sed
for
view
ing
with
an
ocul
ar le
ns.
•T
he im
age
obse
rved
thro
ugh
the
eyep
iece
of t
he p
yrom
eter
is th
at o
f the
lam
p
filam
ent s
uper
impo
sed
on a
bac
kgro
und
inte
nsity
ow
ing
to th
e ho
tbod
y.14
7
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
•T
he c
urre
nt to
the
filam
ent o
f the
pyr
omet
er la
mp
is a
djus
ted
until
the
brig
htne
ss o
f the
fila
men
t mat
ches
that
of t
he b
ackg
roun
d
•T
he c
urre
nt to
pro
duce
brig
htne
ss m
atch
is m
easu
red
and
used
toes
tabl
ish
the
tem
pera
ture
of t
he h
ot b
ody
•P
yrom
eter
s ar
e ca
libra
ted
by v
isua
lly c
ompa
ring
the
brig
htne
ss o
f the
tung
sten
fila
men
t with
a b
lack
bod
y so
urce
of k
now
n te
mpe
ratu
re (
ε=1)
148
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
Sch
emat
ic il
lust
ratio
n of
the
optic
al p
yrom
eter
sys
tem
(a)
and
pyr
omet
er
lam
p w
ith fi
lam
ent b
right
ness
adj
ustm
ent i
n an
opt
ical
pyr
omet
er(b
)
(a)
(b)
149
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
The
brig
htne
ss o
f the
bac
kgro
und
and
the
filam
ent a
re m
atch
ed.
2r
f2
r
25
25
rr
c/
Tc
/T
2hc
2hc
e1
e1
−−
λλ
πλ
πλ
ε=
=−
−
λ r=
the
wav
elen
gth
of th
e re
d fil
ter
(=0.
63 m
m)
depe
ndin
g up
on th
eap
para
tus,
ε=
the
emis
sivi
ty o
f the
sur
face
of t
he h
ot b
ody,
Tf =
tem
pera
ture
of t
he fi
lam
ent,
T=
the
unkn
own
surf
ace
tem
pera
ture
.The
em
itted
ene
rgy
M fo
r th
e tw
o bo
dies
is th
e sa
me
150
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
Whe
n θ<
400
0 C
, the
term
and
redu
ces
to:
2r
fc
/T
e1
λ>>
()
f2
11
LnT
TCλ
=+
ε
151
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
Tab
le fo
r th
e em
issi
vity
of a
num
ber
of m
ater
ials
152
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.3.
The
Opt
ical
Pyr
omet
er
2
dTT
dT
Cλε
=−
ε
•F
or r
elat
ivel
y lo
w to
inte
rmed
iate
tem
pera
ture
a p
ortio
n of
the
surf
ace
can
be c
oate
d w
ith e
ither
a b
lack
pai
nt o
r a
blac
k ce
ram
ic la
yer
to
prov
ide
an e
mis
sivi
ty ε
appr
oach
ing
one
for
very
hig
h te
mpe
ratu
res,
•A
hol
e ca
n be
dril
led
in th
e bo
dy, w
ith a
dep
th-t
o-di
amet
er r
atio
to s
ix o
r m
ore.
Suc
h ho
le a
cts
as a
bla
ck b
ody
with
e ~
1, a
nd th
e te
mpe
ratu
re
mea
sure
d by
focu
sing
the
optic
al p
yrom
eter
on
the
hole
rep
rese
nts
the
corr
ect t
empe
ratu
res
of th
e ob
ject
.
•T
he d
isap
pear
ing
filam
ent o
ptic
al p
yrom
eter
is a
n ac
cura
te in
stru
men
t.
•If
the
emis
sivi
ty o
f the
hot
bod
y is
acc
urat
ely
know
n, th
e er
ror
in a
te
mpe
ratu
re m
easu
rem
ent i
s us
ually
less
than
1%
.
Cha
nge
of T
empe
ratu
re a
s a
func
tion
of c
hang
e of
em
issi
vity
:
153
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
In
man
y ap
plic
atio
ns, r
egar
dles
s of
the
tem
pera
ture
, the
mea
sure
men
t m
ust b
e m
ade
with
out c
onta
ctin
g th
e bo
dy.
T
he o
ptic
al p
yrom
eter
is e
ffect
ive
for
a te
mpe
ratu
re a
bove
700
C, w
here
a
sign
ifica
nt a
mou
nt o
f rad
iant
pow
er is
em
itted
in th
e vi
sibl
e-lig
ht r
egio
n of
the
spec
trum
.
A
t low
er te
mpe
ratu
res,
the
radi
atio
n em
issi
ons
are
conc
entr
ated
in th
e in
frar
ed r
egio
ns a
nd a
re n
ot v
isib
le to
the
hum
an e
ye.
In
frar
ed p
yrom
eter
s em
ploy
the
infr
ared
por
tion
of th
e sp
ectr
umby
usi
ng
a th
erm
al d
etec
tor
to m
easu
re th
e te
mpe
ratu
re o
f the
bod
y em
ittin
g th
e in
frar
ed w
aves
.
154
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
The
Fig
ure
of s
chem
atic
illu
stra
tion
of r
adio
met
er
155
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
•T
he le
ns c
olle
cts
the
infr
ared
rad
iatio
n em
itted
from
the
incl
uded
in th
e fo
cuse
d s
pot a
nd c
ollim
ates
the
radi
atio
n as
indi
cate
d.
•T
he r
adia
tion
is r
efle
cted
from
the
end
mirr
or a
nd fo
cuse
d on
ate
mpe
ratu
re
sens
or.
•T
herm
ocou
ples
or
ther
mis
tors
are
use
d as
tem
pera
ture
sen
sors
.
•T
he e
quili
briu
m te
mpe
ratu
re o
f the
sen
sor
is a
dire
ct m
easu
rem
ent o
f the
m
agni
tude
of t
he r
adia
tion
abso
rbed
by
the
sens
or
•T
he m
agni
tude
of t
he r
adia
tion
give
s th
e te
mpe
ratu
re o
f the
em
ittin
g su
rfac
e.
•T
arge
t siz
e an
d di
stan
ce fr
om th
e le
ns to
the
obje
ct a
re c
ritic
al in
the
oper
atio
n of
infr
ared
pyr
omet
ers.
•T
he fi
eld
of v
iew
of a
n in
frar
ed p
yrom
eter
s de
pend
s on
the
foca
l len
gth
and
diam
eter
of t
he c
olle
ctin
g le
ns
156
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
•T
he o
ptic
al s
yste
m o
f the
inst
rum
ent c
olle
cts
all t
he r
adia
tion
from
the
obje
cts
in
the
field
s of
vie
w
•T
he r
eadi
ng r
epre
sent
s an
ave
rage
of t
hese
tem
pera
ture
s.
Infr
ared
Pyr
omet
erO
bjec
t-
A-
Obj
ect
-B
-
Wal
l
157
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
•Mos
t inf
rare
d py
rom
eter
s ha
ve a
fixe
d-fo
cal-l
engt
h co
llect
ing
lens
that
de
fines
the
field
of v
iew
•F
ield
of v
iew
exp
ress
ed in
term
s of
d/D
-
d: d
ista
nce
from
the
lens
to th
e ob
ject
-D
: dia
met
er o
f the
fiel
d po
sitio
n d
-di
amet
er o
f the
fiel
d D
= d
iam
eter
of t
he c
olle
ctin
g le
ns w
hen
d =
2 ×
foca
l len
gth
of th
e le
ns
•G
ener
al p
urpo
se in
frar
ed p
yrom
eter
s us
e le
nses
with
foca
l len
gth
betw
een
500
and
1500
nm
,
•Clo
se fo
cus
inst
rum
ents
use
lens
es w
ith 1
0 m
foca
l len
gth.
•Pos
sibi
lity
of u
sing
fibe
r op
tics
to tr
ansm
it th
e ra
diat
ion
from
the
sour
ce to
th
e se
nsor
158
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.4.
Infr
ared
Pyr
omet
ers
•E
mis
sivi
ty a
ffect
s th
e re
adin
gs fr
om a
n in
frar
ed p
yrom
eter
just
as it
affe
cts
the
read
ing
from
an
optic
al p
yrom
eter
,
•W
hen
the
emis
sivi
ty is
less
than
one
, the
rad
iatio
n po
wer
act
ually
em
itted
from
th
e su
rfac
e of
the
body
is le
ss th
an e
xpec
ted
and
the
inst
rum
entg
ives
a r
eadi
ng
low
er th
an th
e tr
ue s
urfa
ce te
mpe
ratu
re,
•The
man
ufac
ture
rs o
f inf
rare
d py
rom
eter
s ac
com
mod
ate
the
emis
sivi
ty e
rror
by
inst
allin
g an
em
issi
vity
com
pens
ator
on
the
inst
rum
ent,
•T
he e
mis
sivi
ty c
ompe
nsat
or is
a c
alib
rate
d ga
in a
djus
tmen
t tha
tinc
reas
es th
e am
plifi
catio
n of
the
sens
or s
igna
l to
com
pens
ate
for
the
pow
er lo
st o
win
g to
an
emis
sivi
ty le
ss th
an o
ne,
•Thi
s ga
in a
djus
tmen
t can
als
o be
use
d to
cor
rect
for
tran
smis
sion
loss
es th
at
occu
r w
hen
view
ing
the
obje
ct th
ough
gla
ss o
r pl
astic
por
thol
es,s
mok
e, d
ust,
or
vapo
rs,
•Acc
urac
y of
infr
ared
pyr
omet
er c
an g
o up
to ±
0.3%
of t
he fu
ll sc
ale
read
ing
159
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
•A s
econ
d ap
proa
ch th
at u
ses
radi
atio
n to
mea
sure
tem
pera
ture
em
ploy
s a
phot
on d
etec
tor
•The
inst
rum
ents
equ
ippe
d w
ith p
hoto
n de
tect
ors
diffe
r fr
om th
ose
with
te
mpe
ratu
re d
etec
tors
in tw
o w
ays:
1.-
The
res
pons
e tim
e of
the
phot
on d
etec
tor
is s
ever
al o
rder
s of
m
agni
tude
fast
er th
an th
at o
f the
ther
mal
det
ecto
r.
-T
his
adva
ntag
e is
use
d to
dev
elop
inst
rum
ents
cap
able
of
scan
ning
a fi
eld
of p
rodu
cing
imag
es d
epic
ting
the
tem
pera
ture
di
strib
utio
n ov
er a
n ar
ea o
f a s
urfa
ce.
2.
The
pho
ton
dete
ctor
mus
t be
mai
ntai
ned
at a
ver
y lo
w te
mpe
ratu
redu
ring
oper
atio
n an
d it
is n
eces
sary
to h
ave
a so
urce
of l
iqui
d ni
trog
en.
160
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
A p
hoto
n de
tect
or is
a s
enso
r th
at r
espo
nds
by g
ener
atin
g a
volta
ge th
at
is p
ropo
rtio
nal t
o th
e ph
oton
flux
den
sity
Φim
ping
ing
on th
e se
nsor
161
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
•T
he p
hoto
n em
itted
from
a s
mal
l are
a A
, of a
sur
face
(no
t nec
essa
ry h
ot)
are
colle
cted
by
a le
ns a
nd a
re fo
cuse
d on
a p
hoto
n de
tect
or o
f are
aA
d.
•T
he p
hoto
n flu
x de
nsity
Φat
the
dete
ctor
, whe
n op
tical
sys
tem
is fo
cuse
d:
2 2
kDΦ
g(T
)4
fε
=
k : t
rans
mis
sion
coe
ffici
ent o
f the
lens
and
the
filte
r
D: d
iam
eter
of t
he le
ns
f : fo
cal l
engt
h of
the
lens
g(T
) : k
now
n fu
nctio
n of
the
tem
pera
ture
of t
he s
urfa
ce
ε: e
mis
sivi
ty o
f the
sur
face
162
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
The
out
put v
olta
ge V
0fr
om d
etec
tor,
as
a re
sult
of th
e flu
x de
nsity
Φ:
2
0t
2
DV
kg(
T)
4f
=ε
k t:
syst
em s
ensi
tivity
(tr
ansm
issi
on c
oeffi
cien
t of t
he le
ns, t
heam
plifi
er
volta
ge g
ain,
det
ecto
rs s
ensi
tivity
)it
is e
ssen
tially
a c
onst
ant h
owev
er a
zoo
m le
ns is
em
ploy
ed in
a
typi
cal i
nstr
umen
t to
prov
ide
for
diffe
rent
fiel
ds o
f vie
w w
here
the
solid
an
gle
may
ran
ge fr
om 3
.5 to
40
.
ε.g(
T)
depe
nds
only
on
the
tem
pera
ture
of t
he s
urfa
ce a
nd th
e em
issi
vity
163
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
Typ
ical
Res
pons
e cu
rve
164
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
The
equ
atio
n gi
ving
the
outp
ut v
olta
ge V
0ca
n be
sim
plifi
ed to
:
30
VK
..T
=ε
K: c
alib
ratio
n co
nsta
nt fo
r th
e in
stru
men
t
In
pra
ctic
e K
is d
eter
min
ed b
y ca
libra
ting
the
inst
rum
ent w
ith a
blac
kbod
y so
urce
(ε=
1) o
ver
an a
ppro
pria
te r
ange
of t
empe
ratu
res.
W
hen
the
tem
pera
ture
is u
sed
for
tem
pera
ture
mea
sure
men
ts, t
he
emis
sivi
ty ε
of th
e su
rfac
e m
ust b
e co
nsid
ered
.
165
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
•Any
cor
rect
ion
requ
ired
is e
asily
mad
e by
sub
stitu
ting
the
corr
ect v
alue
of th
e em
issi
vity
into
the
sim
plifi
ed e
quat
ion
givi
ng th
e ou
tput
volta
ge
V0.
03
VT
K.
=ε
•Err
ors
in T
empe
ratu
re o
win
g to
ina
ccur
acie
s in
em
issi
vity
are
miti
gate
d
by o
ne-t
hird
, sin
ce d
iffer
entia
tion
of te
mpe
ratu
re e
quat
ion
give
s:
dT1
dT
3ε
=−
ε
166
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
•Man
y D
iffer
ent c
omm
erci
al in
stru
men
ts e
mpl
oy th
e ph
oton
det
ecto
r, th
eref
ore,
it
is d
iffic
ult t
o lis
t spe
cific
atio
ns th
at c
over
the
full
rang
e of
prod
ucts
.
•Typ
ical
spe
cific
atio
ns fo
r sc
anne
rs in
dica
te th
at th
ey a
re u
sed
to m
easu
re
tem
pera
ture
in th
e ra
nge
from
-20
C to
160
0C
with
a s
ensi
tivity
of 0
.1 C
at 3
0C
•A r
ecen
t inn
ovat
ion
with
this
type
of i
nstr
umen
t per
mits
det
erm
inat
ion
of
tem
pera
ture
dis
trib
utio
n ov
er e
xten
ded
regi
on o
f a b
ody
•Thi
s im
prov
ed c
apab
ility
is a
ccom
plis
hed
by in
sert
ing
two
mec
hani
cally
driv
en
cylin
dric
al le
nses
into
the
optic
al p
ath.
•As
the
two
lens
es a
re o
scill
ated
, a r
egio
n of
the
surf
ace
of th
ebo
dy is
sca
nned
.
•At a
ny in
stan
t a r
elat
ivel
y sm
all t
arge
t are
a is
det
erm
ined
•To
redu
ce th
e sc
anni
ng ti
me,
sev
eral
pho
ton
dete
ctor
s (4
to 6
) ar
e in
corp
orat
ed
in th
e in
stru
men
t.
167
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
6. P
yrom
etry
6.5.
Pho
ton
Det
ecto
rs
•Sin
ce th
e en
tire
surf
ace
of th
e bo
dy is
sca
nned
in a
sho
rt p
erio
d of
tim
e, a
full-
field
s ph
otog
raph
of t
he te
mpe
ratu
re d
istr
ibut
ion
repr
esen
ting
an x
-y a
rray
of t
he
man
y sm
all t
arge
t are
as c
an b
e ob
tain
ed.
•A s
ingl
e fr
ame
typi
cally
con
tain
s 28
000
indi
vidu
al te
mpe
ratu
re (
280
lines
with
100
elem
ents
per
line
)
•The
vol
tage
out
put c
an b
e di
spla
yed
on a
TV
mon
itor
in e
ither
gre
y sc
ale
of c
olor
•Pho
ton-
dete
ctor
-typ
e in
stru
men
ts c
an c
ompl
ete
a sc
an o
f a fi
eld
in a
bout
40
ms.
•If a
vid
eo r
ecor
der
is u
sed
to s
tore
the
imag
es, t
he s
yste
m c
an b
e us
ed to
stu
dy
full-
field
dyn
amic
tem
pera
ture
dis
trib
utio
ns.
168
Dr.
Kar
im B
ouro
uni,
EN
IT 1
A G
M, C
ours
e of
Mea
sure
men
t and
Inst
rum
enta
tion
Tha
nk y
ou fo
r yo
ur
Atte
ntio
n
169
