ME343 Lecture Note 5
Temperature Measurements and Sensor
Characteristics
Objectives:
•
Temperature Measurement by TC
•
Sensor Characteristics
o Sensitivity
o Signal drifting
o Response time
•
Other methods for Temperature Measurement
o RTD
o Thermistor
o Infrared Thermometer
•
Lab Report Requirement of Lab 2
(See Lecture note 3 for geeral format requirement and Grading Criteria of Lab 2
for special requirement)
•
Resistance Thermometer (RTD)
R(T ) = R0 [1 + A(T − T0 ) + B(T − T0 ) 2 ]
(1)
Where, R0 is resistance at T0; A and B are coefficients.
or
R (T ) = α + β T + γ T 2
(2)
Thus, given some calibrated oints (R1, T1), (R2, T2), (R3, T3), α, β, γ are determined from
equation (2).
∴ sensitivity =
dR
= β + 2γ T
dT
(3)
For small temperature span or at low temperature
R (T ) = R0 [1 + A(T − T0 )] = α + β T
Table 16.2 Typical RTD’s
T (oc)
R0 (Ω)
A
Platinum
(Lab)
-190~540
25@0 oc
0.0039
Platinum
(Ind.)
-200~125
25@0 oc
0.0039
10-30
Copper
-70~120
10@0 oc
0.0038
20-60
nickel
0~120
100@0 oc
0.0067
20-60
Response time
-18~540
Most RTD’s are metal alloys
R(T) R(T) ↑as T ↑ T •
Thermistor
o Ceramic- type materials:
R(T) ⎛ dR ⎞
⎜
⎟ ~ sensitivity ⎝ dT ⎠1
⎛ dR ⎞
⎜
⎟ ⎝ dT ⎠2
T 1
R(T) ↑as T ↓ Highly non‐liner! T T 2
⎡ ⎛ 1 1 ⎞⎤
R (T ) = R0 EXP ⎢ β ⎜ − ⎟ ⎥
⎣⎢ ⎝ T T0 ⎠ ⎦⎥
Where β is a constant.
OR.
β
R (T ) = α exp( )
T
Thus, given two or more calibration points → α, β
o Various forms of thermistors (See Fig. 16.7 and Table 16.3)
o Self-heating (drifting in R)
q = i 2 R = TR ↑⇒ RT ↓
i Concept: (∴ from ∆RT ⇒ ∆T )
RT Testing:
Rfa Rfb eo ei Radj RT (1) Initially balanced by adjusting Radj (eo≈0)
(2) RT is changed by changing ei (or i)
(3) “self-heating” → eo≠0
R fb ⎤
eo ⎡ R fa
=⎢
−
⎥
ei ⎢⎣ Radj + R fa RT + R fb ⎥⎦
R fb (dRT )
R 2fa dRT
de
∴ o = ei
=
ei
( RT + R fb ) 2 ( R + R )2 R
adj
fa
fb
⎛ dR ⎞
⎛ dR ⎞
From ⎜
⇒ dT = dRT ⋅ ⎜
⎟
⎟
⎝ dT ⎠ balanced po int
⎝ dT ⎠ balanced po int
•
Thermocouple (TC)
A T1 T2 P q B * A, B are two dissimilar metals:
(1) Peltier effect: electromotive force at junction (emf)
(2) Thomson effect: electromotive fore by tempereature gradient
(Themoson effect << Peltier effect)
* A, B junction at p:
emf P A, B junction at q:
A B A emf
B q If T1 = T2 , (emf)p = (emf)q
If T1 ≠T2 , (emf)p ≠ (emf)q → iTC ≠ 0
If T1 is a cold ( or reference) junction (e.g. icy point.)
iTC = f (T2 )
* Typical Type of TC (See Table 16.4)
Type T
Type J
Type K
(Cu/Const)
(Iron/ Const)
(Chrom/Al)
T range (oc)
-180~260
-180~540
-180~1370
mV range
-5.3~19
-7.5~29.5
-5.6~54.8
All output are in mV
Need “ pre-amplifier” to do data-acquisition
Empirical relations (see Table 16.6)
Standard TC data base (e.g. TC manuals)
* Transient Temperature Measurement by TC
dT
= hA(T∞ − T )
dt
hA
⎧ d (T∞ − T )
=−
(T − T )
⎪
dt
ρc ∞
∴⎨
⎪T = T
0
⎩ t =0
T −T
hA
t)
∴ ∞
= exp(−
T∞ − T0
ρc
ρc
Let τ ≡
∴
ρc
hA
T∞ − T
t
= exp(− )
T∞ − T0
τ
(response time)
T∞ T ( Bi<<1 )
T∞ − T
T∞ − T0
1 e
t
τ Or (1) T∞ > T0
T
T∞
T0
t
τ
(2) T∞ < T0
T
T0
T∞
t
τ
(3) ln(
T∞ − T0
t
)=
τ
T∞ − T
ln(
T∞ − T0
)
T∞ − T
1
τ
t
0
•
Infrared Thermometer (IR Pyrometry)
o Thermal Radiation
(1) Monochrometic (single wavelength)
Planck’s law: Eλ =
C
λ (e
5
1
C2 / λ T
− 1)
Where, Eλ ( w / m 2 ⋅ µ m); T ( K ); λ ( µ m) C1 = 374.18MW µ m 4 / m 2 ; C2 = 14388µ mK Eλ
1100K
800K
500K
λ(µm)
Visible light
(2) Wien displacement law (
dEλ
= 0)
dλ
λmax ⋅ T = 2897.8µ mK
Eλ
λ
λmax
(3) Total radiation
∞
qr = ∫ Eλ d λ = σ T 4 (Stefan‐Boltzmann)
0
o IR Pyrometry
(1) IR region: λ=0.75~ 1000 µm (non-visible)
T oc
λmax
25 oc
9.7 µm
1100 oc
2 µm
-100oc
~15 µm
(2) Area-averaged (not point-measurement !)
(poor focusing!)
I. R.
(3) High-temperature (>1000 oc)
Distinct peak → good sensitivity
(4) Cryogenic-temperature (say < -50 oc)
a. Less distinctive peak
but can go to very low temperature
b. Important for outer-space applications