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Sheet 3
Thermocouples and Pyrometers
Thermocouples
A thermocouple is a device for measuring temperature. It comprises
two dissimilar metallic wires joined together to form a junction. When
the junction is heated or cooled, a small voltage is generated in the
electrical circuit of the thermocouple which can be measured, and this
corresponds to temperature.
12/19/2023 PRESENTATION TITLE 2
Thermocouples
12/19/2023 PRESENTATION TITLE 3
Thermocouples
Types
12/19/2023 PRESENTATION TITLE 5
Thermocouples
Laws
1st Law
The e.m.f. of a thermocouple depends only on the temperatures of the
junctions and is independent of the temperatures of the wires
connecting the junctions. This means that the leads connecting the
instrument can be exposed to temperature fluctuations without
affecting the measurement.
12/19/2023 PRESENTATION TITLE 7
2nd Law
The e.m.f. is not changed when a new conductor is introduced into one
of the metals provided that both of the new junctions are at the same
temperature. The practical bonus from this law is that a voltmeter can
be added to the circuit without affecting the e.m.f.
12/19/2023 PRESENTATION TITLE 8
3rd Law
If a third metal, C, is inserted at one of the junctions, the e.m.f. is
unchanged provided that both of the new junctions are at the same
temperature. This means that a third material may be used to braze
the thermocouple materials together without affecting the
measurement. It also means that a voltmeter could be connected
between a junction
12/19/2023 PRESENTATION TITLE 9
4th Law
The law of intermediate metals states that the e.m.f. of materials AC
can be predicted if the e.m.f.s of materials AB and BC are known.
12/19/2023 PRESENTATION TITLE 10
5th Law
The law of intermediate temperatures states that if two junctions at
temperatures T1 and T2 produce a Seebeck voltage V2, and
temperatures T2 and T3 produce voltage V1, then temperatures T1
and T3 will produce a voltage V3 = V1 + V2.
12/19/2023 PRESENTATION TITLE 11
Thermocouples
Problems
12/19/2023 PRESENTATION TITLE 13
Using Interpolation, we get:
12/19/2023 PRESENTATION TITLE 14
Applying the 5th Law, we
get:
Using Interpolation, we get:
12/19/2023 PRESENTATION TITLE 15
12/19/2023 PRESENTATION TITLE 16
Using Interpolation, we get:
12/19/2023 PRESENTATION TITLE 17
Applying KVL:
𝑉 = 𝐸1 − 𝐸2 − 𝐸3
𝑉 = 21 𝑚𝑉
𝐸1 = 𝑒𝑚𝑓(0−𝑇)
𝐸2 = 𝐸3 = 𝑒𝑚𝑓(0−50) = 1.34 𝑚𝑉
21 = 𝐸1 − 1.34 − 1.34
𝐸1 = 23.68 𝑚𝑉
Using Interpolation, we get:
𝑇 = 678.34 ℃
Wheatstone
Bridge
Wheatstone Bridge
The Wheatstone bridge is used
for the precise measurement of
low resistance.
𝑉𝑜𝑢𝑡 = 𝑉𝑖𝑛
𝑅𝑥
𝑅𝑥 + 𝑅3
−
𝑅2
𝑅1 + 𝑅2
12/19/2023 PRESENTATION TITLE 19
Wheatstone
Bridge
Problems
12/19/2023 PRESENTATION TITLE 21
The temperature measured
at thermocouple junction
can be estimated from J-
type table as shown,
12/19/2023 PRESENTATION TITLE 22
12/19/2023 PRESENTATION TITLE 23
The Resistance of the RTD
can be calculated as:
𝑉𝑜𝑢𝑡
= 𝑉𝑖𝑛
𝑅𝑥
𝑅𝑥 + 𝑅3
−
𝑅2
𝑅1 + 𝑅2
12/19/2023 PRESENTATION TITLE 24
Now we have,
12/19/2023 PRESENTATION TITLE 25
For the sensitivity,
Pyrometers
Pyrometers
The disappearing-filament pyrometer is an
optical pyrometer, in which the temperature
of a glowing incandescent object is
measured by comparing it to the light of a
heated filament.
1
𝑇
−
1
𝑇𝐵
=
λ
𝐶2
ln(𝜏λ𝜀λ)
12/19/2023 PRESENTATION TITLE 27
Pyrometers
Problems
12/19/2023 PRESENTATION TITLE 29
• spectral transmissivity (𝜏λ)
• spectral emissivity (𝜀λ)
• Wavelength (λ)
• Planck's second radiation
constant (𝐶2 = 14390 𝜇𝑚. 𝐾)
• The actual temperature can
be calculated as:
12/19/2023 PRESENTATION TITLE 30
The uncertainty can be
calculated as:
Thank you
Mahmoud Galal

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