aphy 101 lecture 2

8/6/2019 APHY 101 Lecture 2

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Temperature SensorsProf. Nelio C. Altoveros

IMSP Physics Division



Definition of Temperature

For most people, temperature is described by the feelingsof hot and cold given by the subjective responses of the

human body.




In science and technology, the quantitative definition of

temperature comes from the concept of thermodynamics.One approach uses the notion of efficiency of an ideal

reversible heat engine which is defined as

efficiency = (1 ± T 1 /T 2 )

where T1/T2 is the ratio of two absolute temperatures, oneof the heat source and the other of the exhaust of theengine.




A nother definition of temperature came from thedefinition of the Kelvin which gives a figure of 273.16 K for

the triple point of water as the reference temperature.




A nother definition is based on a study of the motion of molecules that gives a value of

E k

= 3/2 RT

for the kinetic energy per mole of an ideal gas.




Neither ideal heat engines nor ideal gases exist in nature.

The experiments needed to measure true temperaturesfrom these definitions are long and expensive, and areonly carried out by national standards laboratories aspart of their continuing improvement of standards.

For everyday use, the range of fixed pointtemperatures can be adopted.



T

(Kelvin)

t

(rC)

Uncertainty

(Kelvin)

Standard

Triple point of water 273.16 0.01

exact by

definition

Primary

Triple point of hydrogen 13.81 -259.34 0.01

Boiling point of hydrogen at 25/76

atm pressure 17.042 -256.108 0.01

Boiling point of hydrogen at 1 atm 20.28 -252.87 0.01

Boiling point of neon at 1 atm 27.102 246.048 0.01

Triple point of oxygen 54.361 218.789 0.01

Boiling point of oxygen at 1 atm 90.188 182.962 0.01

Melting point of ice at 1 atm 273.15 0.00 0.01

Boiling point of water at 1 atm 373.15 100.00 0.005

Melting point of zinc at 1 atm 692.73 419.58 0.03

Melting point of silver at 1 atm 1,235.58 1,064.43 0.2




These values are used for calibration of secondary standardthermometers, as they are easily reproduced in thelaboratory.



Active and Passive Sensors

Sensors can be classified as

y passive

y active




A passive sensor is one in which a material change isproduced in the sensor by the variation of an external

parameter. This parameter must then be monitoredexternally (usually by an electrical circuit).




For example, the platinum resistance thermometer (PRT) isa passive sensor.

The external parameter is temperature and the materialchange is the resistance of the platinum metal.

The external monitoring circuit is an ohm-meter or abridge circuit.




A problem common to passive sensors is change producedby the monitoring circuit. The bridge circuit for the PRT forexample can cause self-heating producing a temperaturechange.




Examples of passive sensors are photoconductors,capacitive displacement gauges, etc.




A ctive sensors generate energy when the externalparameter varies.

The thermocouple is an active sensor employing theSeebeck Effect.

The Seebeck Effect leads to an emf being generated ina circuit with two intermetallic junctions at differenttemperatures.




In principle, the Seebeck effect voltage can be used to drive

a voltmeter and no external power is needed.

However, as common with all active sensors, thethermocouple emf is small a few Q V per degree of temperature difference and its value is limited by thephysics of the system.

Extra amplifying circuit is still essential to give aneasily readable display, or a signal compatible withanalog to digital converter circuits.




Using the transducer directly to run a voltmeter wouldcreate problems of potential drop in connecting leads andof self-heating.

Potentiometric or high impedance operational amplifiertechniques are needed to reduce the junction current asmuch as possible.




Examples of active sensors are photodiodes, piezoelectricdevices, etc.




A nother kind of sensor is the integrated circuit (IC) type.These sensors can be active or passive.

Modern device technology permits the inclusion of many circuit elements on a single slice of silicon or othersemiconductor.

The sensing device and associated amplifying and othercircuitry can be made in a single package.




A n example of a solid-state temperature detector is the AD590 IC. The sensing element of this IC is a forward-biased junction diode which has a voltage dropproportional to absolute temperature:

¹¹

º

¸©©

ª

¨!

o

f

I

I

e

kT V ln




Integrated circuit sensors are available for a number of physical variables (magnetic field Hall effect sensors,pressure integrated strain gauges, etc.)



The Measurement of Thermodynamic Temperature

Temperature is measured indirectly (as most of thephysical parameters).

It is necessary to find a physical quantity which isknown to vary consistently with temperature, then toderive a relationship between the change in this

quantity and a corresponding change inthermodynamic temperature.



Gas Thermometry

The most widely used method of measuring temperature isgas thermometry. The method is based on Boyles law for a

perfect gas:

pV = nRT



Gas Thermometry

For a given number of moles of gas (n), it is necessary tomeasure p1 V 1 and p0 V 0 to relate the temperatures at T1 andT0

, that is

00

11

0

1

V p

V p

T

T !



Gas Thermometry

Unfortunately, there is no ideal gases and so correctionsmust be made for this.

With painstaking care, temperatures may be measuredfairly accurately from liquid helium temperature (4.2K) to the freezing point of gold (1336 K).



Noise Thermometry

A n attractive alternative to the rather elaborate gasthermometers is to make use of the temperature of JohnsonNoise in resistors.



Noise Thermometry

N yquist, using thermodynamic arguments, showed thatthe mean square noise voltage developed across a

conductor is related to its temperatures by

V 2 = 4k TR(v

One technique used is to amplify the noise voltage of aprobe resistor and pass the signal through a bandpassfilter to define bandwidth ( v.



Noise Thermometry

A resistor R 0 at a known temperature T0 is then adjusted in value until the noise voltage from it is the same as that of

the probe resistor R p. The temperature is then given by

¹¹

º

¸

©©

ª

¨

p p

R

RT T 00



Optical Pyrometry

A bove the freezing point of gold, optical pyrometry isused to establish the temperature scale.



Optical Pyrometry

There are number of ways in which the radiation from abody may be used to measure temperature.

We may use the radiated power at single frequency,the ratio of the radiated powers at two frequencies,the frequency of maximum radiated power (Wiens

displacement law,0

mTm=const), or the total radiatedpower (Plancks radiation law, P w T4).



Resistive Temperature Transducers

The previous temperature transducers, while employingsimple principles, require elaborate and expensive

measurement apparatus.

For industrial and most scientific applications whereabsolute accuracy is not a prime concern, less expensive

transducers may be used.



Resistance Thermometry

In general, the resistance of metals increases withincreasing temperature, while that of semiconductors andinsulators decreases.




In the case of the metals, this increase of resistance with temperature can be explained in terms of theconductivity W of conduction band electrons in themetal.

A t higher temperatures, the electrons collide moreoften with vibrating metal ions and their mobility

decreases.




This effect is overwhelmed in semiconductors by thermalgeneration of electrons and holes.

This leads to anexponential increase incharge carrierconcentration and the

typical exponentialdecrease in resistance of athermistor.



The Platinum Resistance Thermometer

Of the metallic resistance thermometers, platinum isuniversally employed in the temperature range 90 K to

900 K.




Over this range, the relationship of resistance totemperature is defined by the Callender- V an Dusenequation

¼½

»¬«

¹¹ º

¸©©ª

¨¹ º

¸©ª

¨¹

º

¸©ª

¨¹ º

¸©ª

¨!

31

111

11

1T T T T

T R

RT FH E

where R T

is the resistance at temperature T

R 0 is the resistance at 0 rC

E, F and H are characteristic constants for each sensor

(typically E = 0.003925, H = 1.49 and F = 0 for T < 0 rC;

F = 0.11 for T >0 rC.)




Below 90 K, this equation is inaccurate, however,resistance thermometers as purchased are usually calibrated to 20 K or may be calibrated by measuring

the resistance at three known temperatures.

¼½

»¬«

¹¹ º

¸©©ª

¨¹ º

¸©ª

¨¹

º

¸©ª

¨¹ º

¸©ª

¨!

30 100

1100100

1100

1T T T T

T R

RT FH E




The resistance of a platinum thermometer is normally measured in a bridge circuit where compensation for theresistance change in bridge leads is accounted for.



The Carbon Resistance Thermometer

Traditionally, carbon resistors have been used as lowtemperature thermometers (below 30 K). Theresistance increases rapidly as the temperature isreduced so that an A llen-Bradley resistor which isnominally 10 ; at 10 rC will be approximately 14 ; at 77K (liquid N2 temperature).



The Carbon Resistance Thermometer

The resistance R is related to the temperature T by therelationship

T

B A

R

K R !

1010

loglog



The Thermistor

Thermistors are beads of semiconducting material usually made of sintered metal oxides. They are small (therefore of

low heat capacity), have a high temperature coefficient(typically 4% per rC at room temperature) and arephysically rugged.

A wide range of resistance values are available at

temperatures in the range 0 to 200 rC whichfacilitates matching with the associated electronicequipment.



The Thermistor

The relationship between resistance R and Kelvintemperature T is approximately exponential.

RT = aeb/T



The Thermistor

The temperature coefficient of resistance is

2T

b

dT

dR

R

I !

and most thermistors are of negative temperaturecoefficient (NTC) type.



The Thermistor

Some materials show a restricted range of positivetemperature coefficient (PTC) behavior.



The Thermistor

y The temperature range for a particular thermistor islimited.

While thermistors may have a significant sensitivity advantage, there are several disadvantages

Thermistors exhibit aging effects and so are not asstable with time as metal resistance thermometers.

Manufacturers calibrations are not as precise as

metal resistance thermometers.



The Thermistor

The resistance of a thermistor may be measured with asimple bridge circuit as lead compensation isunnecessary, however, for most applications,thermistors are used in a continuous mode by monitoring the current with a constant voltage applied.



Thermocouples

If two dissimilar metals ( A and B) are joined together, acontact potential will exist between them. This contactpotential is a result of the difference in electrondensities between the two metals and as a function of the junction temperature (T1 and T2).



Thermocouples

In a circuit, which would be necessary to measure thiscontact potential, two junctions exist simultaneously,hence there is a difference in contact potential between the

two junctions. This potential difference has a quadraticform

I = aT + bT 2

where T = T2 T1, the difference between the two junction temperatures.



Thermocouples

Used as a thermometer,the usual measuringcircuits forthermocouples areshown in the figure.



Thermocouples

In (a), the terminals of the measurementinstrument provide theother junction.

If these terminals areat different

temperatures, then anerror will beintroduced.



Thermocouples

In (b), this problemhas been overcome by introducing a further junction at 0 rC insuch a way that similarmetal leads may betaken to the

measurementinstrument.



Thermocouples

In (c), copper leads canbe taken to themeasuring instrument,for maximum accuracy (junction dissimilarity minimized at the voltmeter).



Thermocouples

The materials to be used depend on a number of factors:temperature range, desired sensitivity, desired linearity or

response. One of the most useful combinations isChromel- A lumel which is fairly linear to ~400 K and has asensitivity of ~40 Q V/K.

A t higher temperatures platinum/platinum-rhodium

(10

%, 13% or 20

%) can be used, but these have very much reduced sensitivities ~6 Q V/K.



Thermocouples

y Kinks and strain introduced into the thermocouple wires will generate anomalies which behave as partial junctions.

Corrosion may introduce impurities into the

thermocouple junction.

Parasitic emfs are caused by junctions at varyingtemperatures.

V oltaic effects can be serious if insulation is porous

and can form a chemical cell with moisture.

Sources of Error



Thermocouples

y Radiation effects.

Sources of Error (continuation)

Conductive errors occur.

Time response of a thermocouple can vary widely.



Thank You!!

aphy 101 lecture 2

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