Temperature Measuremnts

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Budapest University of Technology and EconomicsDepartment of Energy Engineering

Temporary laboratory note for practicaltemperature measurements

This temporary laboratory note has been made for international students participatingin the English course of Measurement at Energy and Environment Protectionat theBudapest University of Technology and Economics to give them backgroundknowledge in the field of temperature measurement and control. This material is

based on the OMEGA Temperature Measurement Handbook & Encyclopedia.

Compiled byAxel Groniewsky

Budapest, 2008


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3

THERMOCOUPLE

In 1821 Thomas Johann Seebeck found that a circuit made from two dissimilar metals, with

junctions at different temperatures would deflect a compass magnet. Seebeck initiallybelieved this was due to magnetism induced by the temperature difference. However, it was

quickly realized that it is an electrical current that is induced, which by Ampere's law deflects

the magnet

DEFINITION

When two wires composed of dissimilar metals are joined at both ends and one of the ends is

heated, there is a continuous current which flows in the thermoelectric circuit. This effect is

known as the PeltierSeebeck effect or thermoelectric effect (See in Figure 1)

Figure 1: The Seebeck effect

If this circuit is broken at the centre, the net open circuit voltage (the Seebeck voltage) is afunction of the junction temperature and the composition of the two metals. (See in Figure 2)

Figure 2: The Seebeck voltage (eAB)

All dissimilar metals exhibit this effect. The most common combinations of two metals are

listed in the table below, along with their important characteristics. (Listed in Table 2)

HEATED

JUNCTIONeAB

METAL A

METAL B

+

-

HEATED

JUNCTION

METAL A

METAL B


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METAL/DOUBLE

FOOT

SEEBECK

COEFFICIENT

C

STANDARD

WIRE

ERROR

NBS SPECIF

MATERIA

RANGETYPE

+ - 20AWG S( CV / )T

(C)

B*Platinum-

6% Rhodium

Platinum-

30% Rhodium0.2 6 600 4.4-8.6 4.4-8.6

ENickel- 10%Chromium

Constantan 0.71 58.5 0 1.7-4.4 1.7-4.4

J Iron Constantan 0.36 50.2 0 1.1-2.9 1.1-2.9

KNickel- 10%Chromium

Nickel 0.59 39.4 0 1.1-2.9 1.1-2.9

N

(AWG14)Nicrosil Nisil 39 600 - -

N

(AWG28)Nicrosil Nisil 26.2 0 - -

R*Platinum-13%

RhodiumPlatinum 0.19 11.5 600 1.4-3.8 1.4-3.8

S*Platinum-10%

RhodiumPlatinum 0.19 10.3 600 1.4-3.8 1.4-3.8

T Copper Constantan 0.30 38 0 0.8-2.9 0.8-2.9

CTungsten-

5% Rhenium

Tungsten-

26% Rhenium19.5 600 - -

*- Noble Metal Thermocouples (with high stability)

Table 2: The most common combinations of two metals, along with their important characteristic


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5

For small changes in temperature the Seebeck voltage is linearly proportional to temperature:

TeAB =

Where (the Seebeck coefficient) is the constant of proportionality.

MEASURING THERMOCOUPLE VOLTAGE

The Seebeck voltage cannot be measured directly because the thermocouple must be

connected to a voltmeter, and the voltmeter leads themselves create a new thermoelectric

circuit as it shown in Figure 3.

Figure 3: Measuring junction voltage with a DVM

v1voltage cannot be measured directly because by connecting the voltmeter in an attempt to

measure the output of Junction J1, the voltmeter creates two more metallic junctions: J2and

J3.as shown in Figure 4.

Figure 4: To Figure 3 equivalent circuit

Since J3 is a copper-to-copper junction, it creates no thermal Electromotive Force (EMF)

(v3= 0) but J2is a copper-to-constantan junction which will add an EMF (v2) in opposition to

v1. The resultant voltmeter reading v will be proportional to the temperature difference

between J1 and J2. This means that the temperature at J1 cannot be found before the

temperature of J2

THE REFERENCE JUNCTION

One way to determine the temperature of J2is to physically put the junction into an ice bath,forcing its temperature to be 0C and establishing J2 as the reference junction. Since both

+

-

Cu

Cu

C

J2

V2

-

+

V1 J1

Cu

Cu

CVOLTMETER

Cu

+

-

Cu


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6

voltmeter terminal junctions are now copper-copper, they create no thermal EMF and the

reading v on the voltmeter is proportional to the temperature difference between J1 and J2.

(See Figure 5):

Figure 5: External reference junction

Now the voltmeter reading is:

)()( 2121 JJ ttvvv =

If we specify TJ1in degrees Celsius:

11 15.273)( JJ tCT =+

Then v becomes:

)0()()]15.273()15.273[( 1212121 ==++== JJJJJ TTTTTvvv

1JTv =

This protracted derivation has been used to emphasize that the ice bath junction output (v2) is

not zero volts. It is a function of absolute temperature.

By adding the voltage of the ice point reference junction the reading of v has been referenced

to 0C. This method is very accurate because the ice point temperature can be precisely

controlled. The ice point is used by the National Bureau of Standards (NBS) as the

fundamental, reference point for their thermocouple tables, so with help of the NBS tables it

can be converted directly from voltage v to Temperature TJ1.

The copper-constantan thermocouple (Figure 5) is a unique example because the copper wire

is the same metal as the voltmeter terminals. Using a different wire, such as iron-constantan

(Type J) thermocouple, the iron wire increases the number of dissimilar metal junctions in the

circuit, as both voltmeter terminals become Cu-Fe thermocouple junctions. If both front panel

terminals are not at the same temperature, there will be an error. For a more precise

measurement the copper voltmeter leads should be extended so that the copper-to-iron

junctions are made on an isothermal block (Figure 6).

J2

C

Cu

ICE BATH

Cu

V2

-+

-V1

J1+

Cu

T=0C


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7

Figure 6: Removing junctions from DVM terminals

The isothermal block is an electrical insulator but a good heat conductor and it serves to hold

J3and J4at the same temperature. The absolute block temperature is unimportant because the

two Cu-Fe junctions act in opposition. The equation is still

)( 1 REFJ TTv =

REFERENCE CIRCUIT

If the ice bath is replaced with another isothermal block and the extra Fe wire in the negative

lead is eliminated by combining the Cu-Fe junction (J4) and the Fe-C junction (JREF) the two

isothermal blocks can be joined to each other as shown in Figure 7.

Figure 7:Joining the isothermal blocks

If the new block is at reference temperature (TREF) and the output voltage (v) has not been

changed it can be shown again that

)( 1 REFTTV = .

Fe

JREF

Cu

Fe

CJ3

J4

Cu

J1

+

-

ISOTHERMAL

BLOCK

Fe

Cu

Cu

CuFe C

V

J3

J4

Cu

J1

JREF

VOLTMETER

+-

ISOTHERMAL

BLOCK


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The extra junction can be eliminated by using the principle of intermediate metals. This

empirical rule states that a third metal (in this case, iron) inserted between the two dissimilar

metals of a thermocouple junction will have no effect on the output voltage as long as the two

junctions formed by the additional metal are at the same temperature. (See Figure 8)

Figure 8Principle of intermediate metals

With the use of this principle the iron (Fe) wire in the negative lead can be eliminated as

shown in Figure 9.

Figure 9: Eliminating the reference junction

In this circuit (shown in Figure 9) the )( 1 REFTTv = equation is still valid. Junctions J3and

J4now become the reference junctions and therefore the temperature of the isothermal block

(TREF) can be measured directly with a Thermistor or an RTD and that information can be

used to compute the unknown temperature (TJ1).

To synthesize an ice-point reference either hardware compensation has to be used which is

fast but restricted to one thermocouple type per card or software compensation which requiresmore computer manipulation time but is versatile and accepts any thermocouple.

VOLTAGE-TO-TEMPERATURE CONVERSION

The temperature-voltage relationship of a thermocouple is not linear therefore the conversion

between voltage and temperature is not simple either. There are two ways to perform the

temperature-to-voltage conversion.

Method A

This technique uses a power series polynomial. The thermoelectric voltage is calculated fromthe equation below:

C

TREF

CuJ3

J4

Cu

J1

+

-

v

Metal CMetal BMetal A

ISOTHERMAL

BLOCK

Metal CMetal B

Fe


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n

nTaTaTaTaaE +++++= ...

3

3

2

210

Where:

E is the thermoelectric voltage in microvolts;

na is the type-dependent polynomial coefficients;

T is the temperature in C;n is the order of polynomial (the number of terms in the polynomial).

The National Institute of Standards and Technology (NIST) has tables of polynomial

coefficients for each type of thermocouple. In these tables the coefficients, order, valid

temperature ranges for each list of coefficients, and error range are shortlisted. Some types of

thermocouples require more than one table of coefficients to cover the entire temperature

operating range.

Two techniques can be used to convert thermocouple reference junction temperatures into

millivolts. Generally it can be said that the power series method is more accurate and has

fewer errors than linear approximation, on the other hand linear approximation is faster. Insome cases even the power series method might cause major errors. In this case the gravity of

the errors can be reduced by increasing the number of terms (or their order). Figure 11

includes coefficient tables that convert temperature values to the appropriate thermoelectric

voltages using lower order polynomials

Figure 10: Voltage to temperature conversion with the method of power series and linear approximation [20]

Method B

This method of conversion uses an equation that represents a linear approximation of the

temperature versus thermoelectric voltage function over a limited temperature range (0C-50C):

bxmy +=

Where:

m is a constant which represents the slope of the temperature versus thermoelectric voltage

line;

b is the offset voltage.

All thermocouple types listed by NIST have an offset voltage equal to zero therefore term bcan be dropped. The temperature range selected for the linear approximation must represent


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the operating extremes of the reference junction. The accuracy of the voltage approximation is

increased by physically limiting the reference junction temperature range by housing it in a

temperature-controlled chamber (zone box).

Voltage-to-Temperature Conversion

The first operation in converting the measured thermoelectric voltage (V) to an equivalent

temperature value is the algebraic addition of the voltage measured at the reference junction

terminals and the calculated reference junction voltage. The sum represents an approximation

of the thermoelectric voltage generated at the temperature-sensing junction (J1in Figure 9).

The calculated thermoelectric voltage generated at J1 is converted into an equivalent

temperature value using a power series polynomial along with type-dependent coefficient

tables. The power series polynomial takes the form:

nn EaEaEaEaaT ++++= ...3322110

Where:

E = thermoelectric voltage (microvolts)

an= type-dependent polynomial coefficients

T = temperature (C)

n = order of polynomial

NIST publishes three tables for each thermocouple type containing coefficients representing

quadratic- (second order), cubic- (third order), or quartic (fourth order) forms. Voltage-to-

temperature conversion accuracy can be increased by using higher order coefficient tables, butat the cost of longer processing time to perform the calculations. Accuracy can be further

enhanced by selecting tables representing the narrowest temperature range for the specific

measurement application.

BASIC STRUCTURE OF THERMOCOUPLES

Figure 11shows the parts of a thermocouple integrated in a measuring circuit.

Figure 11: Measuring circuit [22]

Where:

1. Sensing2. Positive and negative wires

1 2 3 4 5 6 7 8


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11

3. Connecting points4. Extension wires5. Cold junction6. Measuring line7. Additional resistance

8. Signal input processor

When using thermocouples in practice there are three important properties to be considered to

avoid large errors: wire size, location of the thermocouple and the length of the thermocouple

probe.

Selecting the wire size used in the thermocouple sensor depends upon application. Generally,

when longer life is required for higher temperatures, larger size wires should be chosen. When

sensitivity is the prime concern, smaller sizes should be used.

Since the heat conduction from the hot junction of the thermocouple must be minimized, the

thermocouple probe must last long enough. Unless there is sufficient immersion, readings will

be low. It is suggested that the thermocouple be immersed for a minimum distance equivalent

to four times the size of the outside diameter of a protection tube or well.Thermocouples should always have a definite temperature relationship to the work load.

Usually, the thermocouple should be located between the work load and the heat source and

off approximately 1/3 of the distance between the work load and the heat source.

THERMOCOUPLE MOUNTING

There are four common ways in which thermocouples are mounted within a stainless steel or

Inconel sheath and electrically insulated with mineral oxides (See in Figure 12). Each method

has its advantages and disadvantages.

Figure 12: Thermocouple Sheath Options [21]

Sealed and Isolated from Sheath: Good, relatively trouble-free arrangement. The principal

reason for not using this arrangement for all applications is its sluggish response time - the

typical time constant is 75 seconds.

Sealed and Grounded to Sheath: Can cause ground loops and other noise injection, but

provides a reasonable time constant (40 seconds) and a sealed enclosure.


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Exposed Bead: Faster response time constant (typically 15 seconds), but lacks mechanical and

chemical protection, and electrical isolation from material being measured. The porous

insulating mineral oxides must be sealed.

Exposed Fast Response: Fastest response time constant, typically 2 seconds but with fine

gauge of junction wire the time constant can be 10-100ms. In addition to problems of theexposed bead type, the protruding and light construction makes the thermocouple more prone

to physical damage.


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THERMOCOUPLE CALIBRATION

The aim of the measurement: to accomplish a temperature versus voltage calibration curve of

a thermocouple.

Steps of measurement: The Cold Junction has to be put into the ice bath while the hot junction

(measuring junction) has to be put into the electronic thermostat. At each setting point one has

to wait until the temperature sets in (delay time). If the temperature is stable the voltage can

be read from the display of the voltage divider.

The temperature range of the measurement is from 0 to 100C and it is has to be done within

5 or 10C divisions.

The result of the measurement has to be notified in a table

t [C] 0 5 10 15 20 25

U[mV]

Analysis of the results of the measurement and accomplishment of the calibration curve

1. The calibration curve has to be defined/figured2. The measuring errors have to be rated3. The function of the calibration curve has to be calculated with Ordinary Least

Squares (OLS)

4. The result has to be compared to the data of a thermocouple catalog

The determination of the time constant at cooling and heating

1. The junction has to be replaced from the ice bath to the 100C thermostat.2. The heating curve and the heating curve related time constant have to be

defined.

3. The process has to be done the way round to define the cooling curve and thecooling curve related time constant.


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THE RTD

DEFFINITION

Resistance Temperature Detectors (RTDs) rely on the predictable and repeatable phenomena

of the electrical resistance of metals changing with temperature. This discovery has beenmade by Sir Humphrey Davy the same year that Seebeck discovered the thermoelectric effect.

The temperature coefficient for all pure metals is of the same order - 0.003 to 0.007C

o

.

The most common metals used for temperature sensing are platinum, nickel, copper and

molybdenum (Listed in * -average temperature coefficient over the 0 to 100C temperature range

Table 3). While the resistance - temperature characteristics of certain semiconductor and

ceramic materials are used for temperature sensing, such sensors are generally not classified

as RTDs.

MetalTemperature

Range* Comments

Copper Cu-200C to

260C0.00427 Low cost

Molybdenum Mo-200C to

200C

0.00300

0.00385

Lower cost alternative to platinum in the lower temperature

ranges

Nickel Ni-80C to

260C0.00672 Low cost, limited temperature range

Nickel - IronNi-

Fe

-200C to

200C0.00518 Low cost

Platinum Pt-240C to

660C

0.00385

0.003920.00377

Primary element in all high-accuracy resistance thermometers,

long-term stability in air, PRTD used as an interpolation

standard from the oxygen point (-182.96C) to the antimonypoint (630.74C), precise. Extends temperature range to

1000C

* - average temperature coefficient over the 0 to 100C temperature range

Table 3: Types of RTDs [21]

RESISTANCE MEASUREMENTS

The common values of resistance for a platinum RTD range from 10 ohms for the bird-cage

model to several thousand ohms for the film RTD. The single most common value is 100

ohms at 0C. The DIN 43760 standard temperature coefficient of platinum wire is = 0.00385. For a 100 ohm wire this corresponds to + 0.385 ohms/C at 0C. This value for is actually the average slope from 0C to 100C. Most chemically pure platinum wiresused in platinum resistance standards have an of + 0.00392 ohms/(ohmC).Both the slope and the absolute value are small numbers. The measurement wires leading to

the sensor may be several ohms or even tens of ohms. Small lead impedance can contribute a

significant error to the temperature measurement (See in Figure 13).


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Figure 13: Effect of lead resistance

Ten ohm lead impedance implies an 10/0.385 26C error in the measurement. Even the

temperature coefficient of the lead wire can cause a measurable error. The classical method of

avoiding this problem has been the use of a Wheatstone bridge (See in Figure 14).

Figure 14: Wheatstone bridge

The bridge output voltage is an indirect indication of the RTD resistance. The bridge requires

four connection wires, an external source, and three resistors that have a zero temperaturecoefficient. To avoid subjecting the three bridge-completion resistors to the same temperature

as the RTD, the RTD is separated from the bridge by a pair of extension wires (See in Figure

15):

Figure 15: Wheatstone bridge with a pair of extended wires

These extension wires recreate the same problem: The impedance of the extension wires

affects the temperature reading. This effect can be minimized by using a three-wire bridge

configuration as shown in Figure 16.

DVM

RTD

+

-

DVM

RTD

+

-

LEAD RESISTANCE

RTD

LEAD RESISTANCE


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Figure 16: Three-wire bridge

If wires A and B are perfectly matched in length, their impedance effects will even out

because each is in an opposite leg of the bridge. The third wire, C, acts as a sense lead and

carries no current. The Wheatstone bridge shown in Figure 16 creates a non-linear

relationship between resistance change and bridge output voltage change. This compounds the

already non-linear temperature-resistance characteristic of the RTD by requiring an additional

equation to convert bridge output voltage to equivalent RTD impedance.

4-Wire Ohms - The technique of using a current source along with a remotely sensed digital

voltmeter alleviates many problems associated with the bridge (See in Figure 17).

Figure 17: Four-wire ohms measurement

The output voltage read by the DVM is directly proportional to RTD resistance, therefore

only one conversion equation is necessary. The three bridge-completion resistors are replaced

by one reference resistor. The digital voltmeter measures only the voltage dropped across the

RTD and is insensitive to the length of the lead wires.

The one disadvantage of using 4-wire ohms is that compared to the 3-wire bridge one extra

extension wire is needed but the accuracy of the temperature measurement is increased.

3-WIRE BRIDGE MEASUREMENT ERRORS

If Vs and V0 are known, Rg can be found and then it can be solved for temperature. The

unbalanced voltage V0of a bridge built with R1= R2is:

DVM

RTD=Rg

+

-

R3R1

R2

RTDDVM

+

-

0

0

I

DVM

RTD

A

B

C


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+=

2

1)(

3

3

0 S

g

S VRR

RVV

If Rg= R3, V0= 0 and the bridge is balanced. This can be done manually, or it can be solved

for Rgin terms of V0:

+

=

0

03

2

2

VV

VVRR

s

s

g

This expression assumes that the lead resistance is zero. If Rgis located to some distance from

the bridge in a 3-wire configuration, the lead resistance RLwill appear in series with both Rg

and R3as shown in Figure 18.

Figure 18: Three-wire bridge measurement errors

Again it can be solved for Rg:

+

+

=

0

0

0

03

2

4

2

2

VV

VR

VV

VVRR

s

L

s

s

g

The error term will be small if V0 is small, i.e., the bridge is close to balance. This circuit

works well with devices like strain gauges, which change resistance value by only a few

percent, but an RTD changes resistance dramatically with temperature.

If the measuring of RL is not possible or the bridge cannot be balanced, the basic 3-wire

technique is not an accurate method for measuring absolute temperature with an RTD. A

better approach is to use a 4-wire technique.

RESISTANCE TO TEMPERATURE CONVERSION

The RTD is a more linear device than the thermocouple, but it still requires curve-fitting. The

Callendar-Van Dusen equation has been used for years to approximate the RTD curve:11. 13

+=

1001

1001001

100[

3

00

TTTTTRRRT

Where:

RTis the resistance at Temperature T

R0is the resistance at T = 0C

is the temperature coefficient at T = 0C (typically + 0.00392//C) is 1.49 (typical value for .00392 platinum)

DVM

RL

RL

Rg

R3

V3/2

R1

R2


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= 0 T>0; = 0.11 (typical) T


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RTDs have: fast response time, low thermal shunting and high self-healing error; large RTDs

on the other hand have slow response time, poor thermal shunting and low self-healing error.

The platinum-to-copper connection that is made when the RTD is measured can cause a

thermal offset voltage. The offset-compensated ohms technique can be used to eliminate this

effect. (Thermal EMF)


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RTD CALIBRATION

The aim of the measurement: To accomplish a temperature versus resistance calibration curve

of an RTD.

Steps of the measurement: The measuring junction has to be put into the electronic

thermostat. At each setting point one has to wait until the temperature sets in (delay time). If

the temperature is stable the voltage can be read from the display of the voltage divider.

The temperature range of the measurement is from 0 to 100C and it is has to be done within

5 or 10C divisions.

The result of the measurement has to be notified in a table

t [C] 0 5 10 15 20 25

U[mV]

Analysis of the results of the measurement and accomplishment of the calibration curve

5. The calibration curve has to be defined6. The measuring errors have to be rated7. The function of the calibration curve has to be calculated with Ordinary Least

Squares (OLS)

8. The result has to be compared to the data of an RTD catalog

The determination of the time constant by cooling and heating

4. The junction has to be replaced from the ice bath to the 100C thermostat.5. The heating curve and the heating curve related time constant have to be

defined.

6. The process has to be done the way round to define the cooling curve and thecooling curve related time constant.


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BIBLIOGRAPHY

1 The Omega Temperature Measurement Handbook and Encyclopedia, 1992.2 Charles Herzfeld, F.G. Brickwedde: Temperature Its Measurement and Control

in Science and Industry, Vol. 3, Part 1, Reinhold, New York, 1962.3 3Robert P. Benedict: Fundamentals of Temperature, Pressure and Flow

Measurements, John Wiley & Sons, Inc., New York, 1969.

4 4Manual on the Use of Thermocouples in Temperature Measurement, ASTMSpecial Publication 470A, Omega Press, Stamford, Connecticut, 06907, 1974.

5 5Thermocouple Reference Tables, NBS Monograph 125, National Bureau ofStandards, Washington, D.C., 1979. Also Temperature-Millivolt Reference Tables-

Section T, Omega Temperature Measurement Handbook, Omega Press, Stamford,

Connecticut, 06907, 1983.

6 6H. Dean Baker, E.A. Ryder, N. H. Baker: Temperature Measurement inEngineering, Omega Press, Stamford, Connecticut, 06907, 1953.

7 7Temperature Measurement Handbook, Omega Engineering, Ins., Stamford,Connecticut

8 8R.L. Anderson: Accuracy of Small Diameter Sheathed Thermocouples for theCore Flow Test Loop, Oak Ridge National Laboratories, ORNL-5401, April, 1979.

9 9R.P. Reed: Branched Thermocouple Circuits in Underground Coal GasificationExperiments, Proceedings of the 22nd ISA International Instrumentation

Symposium, Instrument Society of America, 1976.

10 10R.J. Moffat: The Gradient Approach to Thermocouple Circuitry, fromTemperature Its Measurement and Control in Science and Industry, Reinhold,

New York, 1962.

11 11R.P. Reed: A Diagnostics-oriented System for Thermocouple Thermometry,Proceedings of 24th ISA International Instrumentation Symposium, Instrument

Society of America, 1978.

12 12Harry R. Norton: Handbook of Transducers of Electronic Measuring Systems,Prentice-Hall, Englewood Cliffs, New Jersey.

13 13C.H. Meyers: Coiled Filament Resistance Thermometers, NBS Journal ofResearch, Vol. 9. 1932.

14 14Bulletin 9612, Rev. B: Platinum Resistance Temperature Sensors, RosemountEngineering Co., 1962.

15 15Burley, Powell, Burns & Scroger: The Nicrosil vs. Nisil Thermocouple:Properties and Thermoelectric Reference Data, NBS Monograph 161, U.S. Dept.

of Commerce, Washington, D.C., 1978.16 16J.P. Tavener: Platinum Resistance Temperature Detectors State of the Art,Measurements & Control, Measurements & Data Corporation, Pittsburgh, PA.,

April 1974

17 17J.P. Evans, and G.W. Burns: A Study of Stability of High Temperature PlatinumResistance Thermometers, in Temperature - Its Measurement and Control in

Science and Industry, Reinhold, New York, 1962.

18 18D.D. Pollock: The Theory and Properties of Thermocouple Elements, ASTMSTP 492, Omega Press, Stamford, Connecticut, 06907, 1979

19 19YSI Precision Thermistors, Yellow Springs Instruments, Yellow Springs, Ohio,1977.

20 Rex Klopfenstein, Jr.: Software Linearization of a Thermocouple, Sensors,December 1997


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21 Official website of Capgo Pty Ltd22 Fazekas M.: Termoelem hmrk, elmleti sszefoglal, 200523 Fazekas M.: Ellenlls hmrk, elmleti sszefoglal, 200524 Official website of ISE inc.

Temperature Measuremnts

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