Introduction to Temperature Introduction to Temperature sensors, Measurement and sensors, Measurement and

CalibrationCalibration

NIDHIN MANOHARNIDHIN MANOHAR

Temperature:Temperature:

Types of SensorsTypes of Sensors Calibration of sensorsCalibration of sensors Uncertainty CalculationUncertainty Calculation

Temperature :Temperature : A measure of a substance’s A measure of a substance’s

internal kinetic energyinternal kinetic energy The degree of hotness or The degree of hotness or

coldness of a substance (as coldness of a substance (as measured on a thermometer)measured on a thermometer)

Temperature Sensing TechniquesTemperature Sensing Techniques Changes in Physical DimensionsChanges in Physical Dimensions

• Bimetallic Thermometers Bimetallic Thermometers • Filled-Bulb and Glass-Stem Filled-Bulb and Glass-Stem

Thermometers Thermometers

Changes in Electrical PropertiesChanges in Electrical Properties• Integrated Circuitry (IC) Transistors Integrated Circuitry (IC) Transistors

and Diodes and Diodes • Resistance Temperature Detectors Resistance Temperature Detectors

(RTDS) (RTDS) • Thermistors Thermistors • ThermocouplesThermocouples

Temperature Sensing TechniquesTemperature Sensing Techniques

Changes in Chemical PhaseChanges in Chemical Phase• Quartz Crystal ThermometryQuartz Crystal Thermometry

Changes in Emitted thermal radiation Changes in Emitted thermal radiation • Radiation and Infrared PyrometersRadiation and Infrared Pyrometers

Temperature Sensing TechniquesTemperature Sensing Techniques

Temperature Range ComparisonTemperature Range Comparison

Bimetal ThermometerBimetal Thermometer Two metals with different coefficients of Two metals with different coefficients of

thermal expansion are bonded together. thermal expansion are bonded together. If one end is fixed, other end displaces in If one end is fixed, other end displaces in

response to temperature changes. response to temperature changes. Bimetal strips can be fabricated into coils, Bimetal strips can be fabricated into coils,

spirals, and disks. Frequently used in on-off spirals, and disks. Frequently used in on-off temperature control (thermostats)temperature control (thermostats)

Range of use Range of use -65 to 430 °C -65 to 430 °C Accuracy varies with range Accuracy varies with range ± 0.5 to 12°C ± 0.5 to 12°C Advantages:Advantages:

• Low cost, Negligible maintenance, StableLow cost, Negligible maintenance, Stable

Bimetal Thermometer Bimetal Thermometer r = Radius of curvaturer = Radius of curvaturet = total thicknesst = total thicknessm = ratio of thicknessesm = ratio of thicknessesn = ratio of Young moduli of n = ratio of Young moduli of

elasticityelasticity1 1 = lower coefficient of thermal = lower coefficient of thermal

expansionexpansion2 2 = higher coefficient of = higher coefficient of

thermal expansionthermal expansionT = Temperature ( °C)T = Temperature ( °C)TToo= Initial bonding temp. (°C)= Initial bonding temp. (°C)

Liquid Expansion ThermometerLiquid Expansion Thermometer

The volumetric expansion of liquids and The volumetric expansion of liquids and solids is used for temperature measurement. solids is used for temperature measurement. Expansion registered is actually the Expansion registered is actually the difference between the liquid and the glass. difference between the liquid and the glass.

Mercury filled thermometersMercury filled thermometers• Range= -37 to 320 °C , Range= -37 to 320 °C , • Best Accuracy ± 0.02 °CBest Accuracy ± 0.02 °C

Alcohol filled thermometers.Alcohol filled thermometers.• Range = -75 to 120 °C , Range = -75 to 120 °C , • Best Accuracy ± 0.6°CBest Accuracy ± 0.6°C

Advantage : Low cost, simple Advantage : Low cost, simple Disadvantage: No remote measurementDisadvantage: No remote measurement

Liquid in Glass ThermometersLiquid in Glass Thermometers Greatest sensitivity to temperature is at the bulb, Greatest sensitivity to temperature is at the bulb,

where the largest volume of liquid exists. However, where the largest volume of liquid exists. However, all portions of the thermometer are temperature all portions of the thermometer are temperature sensitive.sensitive.

• T = TT = T11+kT’(T+kT’(T11-T-T22) where) whereT = corrected temperature T = corrected temperature TT1 1 = indicated temperature (reading)= indicated temperature (reading)TT2 2 = ambient temperature (exposed tube portion)= ambient temperature (exposed tube portion)T’= correction related to exposed length.T’= correction related to exposed length.k = differential expansion coefficient between liquid k = differential expansion coefficient between liquid

and glassand glass (mercury in glass = 0.00016 °C scale)(mercury in glass = 0.00016 °C scale)

Fluid-Expansion ThermometerFluid-Expansion Thermometer

Fluid Expansion ThermometerFluid Expansion Thermometer A fluid filled bulb is connected to A fluid filled bulb is connected to

a pressure measuring device via a pressure measuring device via a capillary tube. As fluid is heated a capillary tube. As fluid is heated it expands increasing the it expands increasing the pressure. pressure. Pressure is linked to Pressure is linked to

temperature.Accuracy and temperature.Accuracy and range depends on fluid.range depends on fluid.

Advantages/DisadvantagesAdvantages/Disadvantages• Low cost,Stable in operation,Low cost,Stable in operation,• Remote readings are possible. Remote readings are possible. • Transient response is a Transient response is a

function of bulb size and function of bulb size and capillary tube length.capillary tube length.

Liquid CrystalsLiquid Crystals Liquid crystals possess the mechanical properties of a Liquid crystals possess the mechanical properties of a

liquid, but have the optical properties of a single crystal. liquid, but have the optical properties of a single crystal. Temperature changes can affect the color of a liquid Temperature changes can affect the color of a liquid crystal, which makes them useful for temperature crystal, which makes them useful for temperature measurement. measurement.

range and resolution of liquid crystal thermometers is range and resolution of liquid crystal thermometers is varied by adjustment of the formulation. varied by adjustment of the formulation. Range: 0°C to several hundred °C Range: 0°C to several hundred °C resolution : 1 °C to 0.5 °C ; Special types: 0.1 °C resolution : 1 °C to 0.5 °C ; Special types: 0.1 °C

Disposable thermometers for homes, clinical use.Disposable thermometers for homes, clinical use.

Infrared Thermometers (Non-contact Infrared Thermometers (Non-contact sensors)sensors)

IR: wavelength between 0.7 to IR: wavelength between 0.7 to 1000 microns. 1000 microns.

all objects warmer than absolute all objects warmer than absolute zero ( 0 °K) emit energy in IR zero ( 0 °K) emit energy in IR range.range.

IR thermometers sense IR IR thermometers sense IR emitted from the target object. emitted from the target object.

Most IR instruments can only Most IR instruments can only measure between 0.7 and 20 measure between 0.7 and 20 micron; are not sensitive enough micron; are not sensitive enough to measure the small energies to measure the small energies outside the range. outside the range.

Measurement PrinciplesMeasurement Principles Energy transmitted as electromagnetic waves or Energy transmitted as electromagnetic waves or

photons travelling at speed of light. photons travelling at speed of light. Radiation striking a surface is partially reflected, Radiation striking a surface is partially reflected,

absorbed, and transmitted.absorbed, and transmitted. Radiation Heat Transfer: Radiation Heat Transfer:

• q=Q/A=q=Q/A=FFBABA(T(TAA44-T-TBB

44))Where Where is the Stefan-Boltzmann constant, is the Stefan-Boltzmann constant, = (5.6705 x 10= (5.6705 x 10-8 -8 W/mW/m22KK44))

Law} s{Kirchoff'

1

)(

)()()(

tyabsorptivi

vitytransmissiemissivityyrefectivit

Basic IR ThermometerBasic IR Thermometer Lens to focus energy from object onto a Detector that converts Lens to focus energy from object onto a Detector that converts

the thermal energy to electrical signal. the thermal energy to electrical signal. signal conditioning (filters and amplifiers) and Emissivity signal conditioning (filters and amplifiers) and Emissivity

adjustment to correct for various surface finishes and materials. adjustment to correct for various surface finishes and materials. Temperature TTemperature TBB (internal temperature) must be known or (internal temperature) must be known or

determined through prior calibration. Ambient temperature determined through prior calibration. Ambient temperature compensation.compensation.

TTAA, the unknown temperature, is determined from the detector , the unknown temperature, is determined from the detector temperature. temperature.

Infrared CamerasInfrared Cameras

Operating Temperature 5 to 122 °F (-15 to 50 °C)

Measuring Temperature -40 to 3630 °F (-40 to 2000 °C)

Accuracy ±2% of range or ±4 °F ( ±2 °C)

Sensitivity 0.2 °F (0.1 °C)

Image Storage Capacity 700 (14 bit) on 100 MB Card

Digital Voice Recorder for Active Documentation

yes, 30 sec per image

Camera Weight 5 lbs.

Infrared Camera ExamplesInfrared Camera Examples PipingPiping

Heat transfer coilsHeat transfer coils Valve operationValve operation

ElectronicsElectronics

Engines/CompressorsEngines/Compressors

Building/StructuresBuilding/Structures92.2°F

100.6°F

95

100

73.5°F

106.4°F

80

100

SP01

LI01

Single-point IR Temperature SensorsSingle-point IR Temperature Sensors

Material EmmisivityMaterial Emmisivity

Material emissivity is subject to a great Material emissivity is subject to a great amount of uncertainty because it depends amount of uncertainty because it depends on surface finish, color, oxidation, aging, on surface finish, color, oxidation, aging, and several other factors.and several other factors.

IR Thermocouples (IR-t/c)IR Thermocouples (IR-t/c)

Functionally a combination of Functionally a combination of Thermocouple and an IR detectorThermocouple and an IR detector

Millivolt output signal is produced, Millivolt output signal is produced, is scaled to the desired is scaled to the desired thermocouple characteristics.thermocouple characteristics.

Adhere to the same laws as other Adhere to the same laws as other infrared thermometers.infrared thermometers.

IR Thermocouples (IR-t/c)IR Thermocouples (IR-t/c)

IR Thermometer AdvantagesIR Thermometer Advantages IR thermometers can measure IR thermometers can measure

objects that move, rotate, or vibrate.objects that move, rotate, or vibrate. They can measure temperatures > They can measure temperatures >

1500 °C1500 °C They do not damage or contaminate They do not damage or contaminate

the surface of the object of interest the surface of the object of interest (food, painted surfaces)(food, painted surfaces)

Response time is in the millisecond Response time is in the millisecond range.range.

Resistance ThermometersResistance Thermometers RTD (resistance temperature device or RTD (resistance temperature device or

detector) is a metal conductor, has a positive detector) is a metal conductor, has a positive coefficient of resistance. R increases with Tcoefficient of resistance. R increases with T

Thermistors are made from semiconductor Thermistors are made from semiconductor materials, have a large negative coefficient of materials, have a large negative coefficient of resistance. R decreases with Tresistance. R decreases with T

Resistance Temperature Resistance Temperature ThermometersThermometers

RTDRTD Metals have linear relationship with temperatureMetals have linear relationship with temperature

Platinum (high cost, highly linear, most Platinum (high cost, highly linear, most common)common)

Tungsten (highly linear)Tungsten (highly linear) Copper (lower temperature ranges)Copper (lower temperature ranges) Nickel (lower temperature, low cost, nonlinear)Nickel (lower temperature, low cost, nonlinear) Nickel alloys (lower temperature, low cost)Nickel alloys (lower temperature, low cost)

Each metal has a specific resistivity, Each metal has a specific resistivity, , which , which varies with temperature and is determined varies with temperature and is determined experimentally. experimentally.

ALR

T o 1 a(T To )

RTD Response:RTD Response:R Ro 1 a T To b T To 2 (derived from Callendar - Van Dusen equation)

whereR o = reference resistance measured at T o (To is typically 0 C)T = measured temperaturea and b = calibration constants

simple linear verson is often used over smaller temperature interval

R Ro 1 a T To Coefficients a and b depend on the wire material and its Coefficients a and b depend on the wire material and its

purity. Example: Platinumpurity. Example: Platinum a=3.9083 E -03 a=3.9083 E -03 b=-5.775 E -07 b=-5.775 E -07

Low resistanceLow resistance 100 100 (most common) to 1000 (most common) to 1000

Wide operating range (-200 °C to 850 °C)Wide operating range (-200 °C to 850 °C) High sensitivity High sensitivity High accuracy (to 0.1°C or better 0.01 °C )High accuracy (to 0.1°C or better 0.01 °C ) High Repeatability and StabilityHigh Repeatability and Stability

Low drift (0.0025 °C/year)Low drift (0.0025 °C/year) Industrial models drift < 0.1 °C/yearIndustrial models drift < 0.1 °C/year

RTDRTD

Lead wire resistance can be Lead wire resistance can be significant. significant.

3-wire provides sufficient 3-wire provides sufficient accuracy in accounting for the accuracy in accounting for the lead wire resistance. lead wire resistance.

accuracy using 4-wire RTD.accuracy using 4-wire RTD. Internal/self-heating :To measure Internal/self-heating :To measure

resistance must pass current resistance must pass current through sensor. Joule through sensor. Joule Heating=IHeating=I22RR

RTDRTD

RTDRTD

+Vs -

R1

G

R2

R3

A

B

RTD

Balanced Bridge : Galvanometer I = 0R1+ R3 = R2+A+B++RTDR3 = A+ B+ RTD

Two Wire Measurement

RTDRTD

+Vs -

R1

Vo

R2

R3

A

B

RTD

Un Balanced Bridge : Voltmeter Reading = VoVo = Vs (R3/(R3+ A+B+RTD))-Vs/2A+ B+ RTD = R3(Vs-2Vo)/(Vs+2Vo)

Two Wire Measurement

RTDRTD

+Vs -

R1

Vo=0

R2

R3

A

B

RTD

At balanced Condition, R1+ R3+A+C = R2+B+C+RTDIf R1=R2, R3 = RTD+B-AIf A+B, R3= RTD

Three Wire Measurement

c

RTDRTD

+Vs -

R1

Vo=0

R2

R3a

A

B

RTD

R1+ R3a+A+C = R2+B+C+RTDWhen R1=R2, R3a+A = RTD+B

Four Wire Measurement

c

Switch in position “A”

1

RTDRTD

+Vs -

R1

Vo=0

R2

R3b

A

B

RTD

R1+ R3b+B+D = R2+A+RTD+DWhen R1=R2, R3b+B = RTD+A

Four Wire Measurement

C

Switch in position “B”

D

21 + 2, R3a+A+R3b+B = B+RTD+A+RTDR3a +R3b = 2RTDR3 = (R3a+R3b)/2 = RTD

ThermistorsThermistors High resistance 1 kHigh resistance 1 k to 100 k to 100 k

Eliminates most lead resistance Eliminates most lead resistance issuesissues

Highly non-linear resistance-to-Highly non-linear resistance-to-temperature relationships.temperature relationships. Mostly NTC (metal oxides) but Mostly NTC (metal oxides) but

PTC (barium and strontium PTC (barium and strontium titanate mixtures) models titanate mixtures) models availableavailable

Small physical size, Fast response Small physical size, Fast response timetime

Lower cost than RTD’sLower cost than RTD’s Very high sensitivity and Very high sensitivity and

resolution : Up to 1000 times more resolution : Up to 1000 times more sensitive than RTD’ssensitive than RTD’s

Thermistor :Thermistor :

R Roe 1

T 1

To

whereRo = reference resistance measured at T o

T = measured temperature = material constant

Integrate Circuit Thermometer (IC)Integrate Circuit Thermometer (IC) IC temperature sensors built onto Silicon chip IC temperature sensors built onto Silicon chip Voltage or current output that is nearly linear Voltage or current output that is nearly linear

with temperature.with temperature. An input voltage must be applied to the sensor.An input voltage must be applied to the sensor. Accuracy is about 1 °C TO 0.5 °CAccuracy is about 1 °C TO 0.5 °C Low cost sensorLow cost sensor Not susceptible to voltage noise and lead-wire Not susceptible to voltage noise and lead-wire

errors are minimal.errors are minimal.

ThermocoupleThermocouple Thermocouples operate under the principle Thermocouples operate under the principle

that the junction of two dissimilar metals that the junction of two dissimilar metals produces a measurable voltage (emf-produces a measurable voltage (emf-electromotive force) when the two ends of electromotive force) when the two ends of the thermocouple are at different the thermocouple are at different temperatures.temperatures.

They are inexpensive, small in size, rugged, They are inexpensive, small in size, rugged, and remarkably accurate when used with an and remarkably accurate when used with an understanding of their peculiarities.understanding of their peculiarities.

Thermocouples PrincipleThermocouples Principle In, 1821 T.J. Seebeck observed the existence of In, 1821 T.J. Seebeck observed the existence of

and electromotive force (EMF) at the junction of and electromotive force (EMF) at the junction of two dissimilar metals two dissimilar metals

Seebeck effect is actually the combined result of Seebeck effect is actually the combined result of two other phenomenon, two other phenomenon,

Thomson Thomson observed EMF due to contact of two observed EMF due to contact of two dissimilar metals and the junction temperature.dissimilar metals and the junction temperature.

PeltierPeltier discovered that temperature gradients discovered that temperature gradients along conductors in a circuit generate an EMF.along conductors in a circuit generate an EMF.

Thomson EMF is much smaller in than Peltier Thomson EMF is much smaller in than Peltier EMF and can be minimized and disregarded with EMF and can be minimized and disregarded with proper thermocouple design.proper thermocouple design.

Thermocouple EffectThermocouple Effect Any time a pair of dissimilar wires is joined Any time a pair of dissimilar wires is joined

and a junction is formed an emf voltage will and a junction is formed an emf voltage will be generated.be generated.

Voltage or EMF produced depends on:Voltage or EMF produced depends on: Types of materials used, A and B Types of materials used, A and B Temperature of the junctions, measuring Temperature of the junctions, measuring

and referenceand reference

Ungrounded: Electrical isolation is obtained at the cost of response time.

Grounded : Good heat transfer to junction.

Exposed : Best response time, but is limited to noncorrosive and non-pressurized applications.

Cu + - Cu Cu V3 + + J3 V1 J1 V1 - - + - + - Cu C Cu C V2 V2 J2 J2 Fig.14.

V= (T1-T ref)

Example 2 Consider J type thermocouple J3 Cu Fe + + V1

Fe C - J1 - Cu J4 Voltmeter - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Ice bath

J3 J3 Cu Cu Fe + + V1

Fe C - J1 - Cu Cu J4 J4 Voltmeter - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tref- - Ice bath Removing junctions of DVM Terminals

Let’s replace the ice bath with another isothermal block. Hi Cu Fe + + J3 V1

Fe C - J1 . - Cu Cu J4 Voltmeter Jref Tref Isothermal block Fig 17. Eliminating the ice bath

Cu - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Fe + J3 J1 - Cu J4 Fe Jref C Tref Fig. 18. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Joining the Isothermal blocks

(Metal A) (Metal B) (Metal C) Cu Fe C - - - - - - - - - - - - - - - - - - - - - - - - - - - - Tref Fig.20 - - - - - - - - - - - - - - - - - - - - - - - - - - - . becomes Cu C - - - - - - - - - - - - - - - - - - - Tref - - - - - - - - - - - - - - - - - - -

So finally it becomes + Cu - - - - - - - - - - - - - Fe V J3 J1 - Cu C J4 Tref - - - - - - - - - - - - -

Hardware compensation Software compensation

Fast because it eliminated Requires more computer

computation manipulation time Each gain resistor is suited to Accepts any thermocouple compensate only a particular type of thermocouple

Hard to reconfigure Easy to reconfigure (requires hardware change for new thermocouple type)

Thermocouple Color CodingThermocouple Color Coding

Thermocouple Materials TypesThermocouple Materials Types Copper-Constantan (T Curve)

The Copper-Constantan thermocouple, with a positive copper wire and a negative Constantan wire is recommended for use in mildly oxidizing and reducing atmospheres up to 400ºC. They are suitable for applications where moisture is present. This alloy is recommended for low temperature work since the homogeneity of the component wires can be maintained better than other base metal wires. Therefore, errors due to the non-homogeneity of wires in zones of temperature gradients is greatly reduced.

Iron-Constantan (J Curve) The Iron-Constantan thermocouple with a positive iron wire and a negative Constantan wire is

recommended for reducing atmospheres. The operating range for this alloy combination is 870ºC for the largest wire sizes. Smaller wire sizes should operate in correspondingly lower temperatures.

Chromel-Alumel (K Curve) The Chromel-Alumel thermocouple, with a positive Chromel wire and a negative Alumel wire, is

recommended for use in clean oxidizing atmospheres. The operating range for this alloy is 1260ºC for the largest wire sizes. Smaller wires should operate in correspondingly lower temperatures.

Thermocouple MaterialsThermocouple Materials Chromel-Constantan (E Curve)

The Chromel-Constantan thermocouple may be used for temperatures up to 870ºC in a vacuum or inert, mildly oxidizing or reducing atmosphere. At sub-zero temperatures, the thermocouple is not subject to corrosion. This thermocouple has the highest emf output of any standard metallic thermocouple.

Platinum-Rhodium (S and R Curve) Three types of noble-metal thermocouples are in common use. They are:

1.The S curve shows a positive wire of 90% platinum and 10% rhodium used with a negative wire of pure platinum,

2.The R curve indicates a positive wire of 87% platinum and 13% rhodium used with a negative wire of pure platinum, and

3.(not shown) a positive wire of 70% platinum and 30% rhodium used with a negative wire of 94% platinum and 6% rhodium.

They have a high resistance to oxidation and corrosion. However, hydrogen, carbon and many metal vapors can contaminate a platinum-rhodium thermocouple.

The recommended operating range for the platinum-rhodium alloys is 1540ºC although temperatures as high as 1780ºC can be measured with the Pt-30% Rh vs Pt-6% Rh alloy combination.

Tungsten-Rhenium (C Curve) Three types of tungsten-rhenium thermocouples are in common use for measuring

temperatures up to 2760ºC. These alloys have inherently poor oxidation resistance and should be used in vacuum, hydrogen or inert atmospheres.

Grades of TC wireGrades of TC wire Grade is based on calibration accuracy of the Grade is based on calibration accuracy of the

wire. wire. Precision grade -Precision grade - (± 0.5 % reading or 1°C) , (± 0.5 % reading or 1°C) ,

greater of the twogreater of the two Standard grade -Standard grade -(± 0.75 % reading or 2°C), (± 0.75 % reading or 2°C),

greater of the twogreater of the two Extension or Lead-wire grade -Extension or Lead-wire grade - (± 1 % reading (± 1 % reading

or 4 °C)or 4 °C) Wire diameterWire diameter

0.001 inches and up is possible0.001 inches and up is possible Standard diameters are: 0.01”, 0.02”, 0.032”, Standard diameters are: 0.01”, 0.02”, 0.032”,

0.040”, 1/16”, 1/8”, 3/16”, and 1/4”0.040”, 1/16”, 1/8”, 3/16”, and 1/4” Smaller the better but fragility is an issueSmaller the better but fragility is an issue

Type of probesType of probes Ungrounded: Electrical isolation

is obtained at the cost of response time.

Grounded : Good heat transfer to junction.

Exposed : Best response time, but is limited to noncorrosive and non-pressurized applications.

Thermocouple Laws or RulesThermocouple Laws or Rules A thermocouple must contain two

dissimilar materials and at least two junctions at different temperatures to have an emf voltage output.

Law of Intermediate MetalsLaw of Intermediate Metals Insertion of an intermediate Insertion of an intermediate

metal into a thermocouple circuit metal into a thermocouple circuit will not affect the emf voltage will not affect the emf voltage output as long as the two output as long as the two junctions are at the same junctions are at the same temperature. temperature. (Permits solder and weld joints.)(Permits solder and weld joints.)

Law of Intermediate TemperaturesLaw of Intermediate Temperatures If a thermocouple circuit If a thermocouple circuit

develops a net emfdevelops a net emf1-21-2 for for measuring junction measuring junction temperatures Ttemperatures T11 and T and T22, and a , and a net emfnet emf2-32-3 for temperatures T for temperatures T22 and Tand T33, then it will develop a , then it will develop a net voltage of emfnet voltage of emf1-31-3 = emf = emf1-21-2 + + emfemf2-32-3 when the junctions are at when the junctions are at temperatures Ttemperatures T11 and T and T33. .

emfemf1-21-2++ emfemf2-32-3= emf= emf1-31-3

T2

T3 T1

T3 T2

T1

If a thermocouple circuit of materials A and C If a thermocouple circuit of materials A and C generates a net emfgenerates a net emfA-CA-C when exposed to when exposed to temperatures Ttemperatures T11 and T and T22, and a thermocouple of , and a thermocouple of materials C and B generates a net emfmaterials C and B generates a net emfC-BC-B for the for the same two temperatures Tsame two temperatures T11 and T and T22, then a , then a thermocouple made from materials A and B will thermocouple made from materials A and B will develop a net voltage of develop a net voltage of

emfemfA-BA-B = emf = emfA-CA-C + emf + emfC-BC-B

between temperatures Tbetween temperatures T11 and T and T22..Sometimes useful in the calibration of different Sometimes useful in the calibration of different

thermocouple wires.thermocouple wires.

Temperature changes in the wiring Temperature changes in the wiring between the input and output ends do between the input and output ends do not affect the output voltage, provided not affect the output voltage, provided the wiring is of a thermocouple alloy.the wiring is of a thermocouple alloy.

Hot or Cold Zone

Specialty Thermocouple CircuitsSpecialty Thermocouple Circuits Thermopile-Thermocouples connected in

series between two temperature zones. Good for determining small temperature

differences Amplification affect

Averaging Circuit- Thermocouple are connected in parallel between two temperature zones. Ambient Temp. = 24 °C

+-Voltmeter 100 °C

Cu

Cu

Ice Bath

130 °C

110 °Ciron

constantan

?