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The Measurement of Temperature

Temperature is an intuitive concept that tells whether a body is “hot” or

“cold.” The two temperature scales are the Fahrenheit and Celsius scales

The relation between scales can be shown in figure (1).

Fig.(1) Relationship between Fahrenheit and Celsius temperature scales

Temperature Measurement by Mechanical Effects

The liquid-in-glass thermometer is one of the most common types of

temperature measurement devices. The construction details of such an

instrument are shown in Figure (2). A relatively large bulb at the lower

portion of the thermometer holds the major portion of the liquid, which

expands when heated and rises in the capillary tube, upon which are

etched appropriate scale markings.

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Fig.(2) Schematic of a mercury-in-glass thermometer

Mercury-in-glass thermometers are generally applicable up to about

600◦F (315◦C), but their range may be extended to 1000◦F (538◦C) by

filling the space above the mercury with a gas like nitrogen. This

increases the pressure on the mercury, raises its boiling point, and thereby

permits the use of the thermometer at higher temperatures.

A very widely used method of temperature measurement is the bimetallic

strip. Two pieces of metal with different coefficients of thermal

expansion are bonded together to form the device shown in Fig.(3). When

the strip is subjected to a temperature higher than the bonding

temperature, it will bend in one direction; when it is subjected to a

temperature lower than the bonding temperature, it will bend in the other

direction. Eskin and Fritze have given calculation methods for bimetallic

strips. The radius of curvature r may be calculated as:

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(1)

where

t = combined thickness of the bonded strip, m or ft

m = ratio of thicknesses of low- to high-expansion materials

n = ratio of moduli of elasticity of low- to high-expansion materials

α1 = lower coefficient of expansion, per ◦C

α2 = higher coefficient of expansion, per ◦C

T = temperature, ◦C

T0 = initial bonding temperature, ◦C

Fig.(3) The bimetallic strip.

The thermal-expansion coefficients for some commonly used materials

are given in Table (1). Bimetallic strips are frequently used in simple on-

off temperature-control devices (thermostats). Movement of the strip has

sufficient force to trip control switches for various devices. The bimeta-

llic strip has the advantages of low-cost, negligible maintenance expense,

and stable operation over extended periods of time. Alternate methods of

construction can use a coiled strip to drive a dial indicator for tempera-

tures.

Table (1) Mechanical properties of some commonly used thermal materials

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Ex: Curvature and deflection of bimetallic strip

A bimetallic strip is constructed of strips of yellow brass and Invar

bonded together at 30◦C. Each has a thickness of 0.3 mm. Calculate the

radius of curvature when a 6 cm strip is subjected to a temperature of

100◦C.

Solution

We use Eq. (1) with properties from Table (1).

T − T0 = 100 − 30 = 70◦C

m = 1.0

n = 147/96.5 = 1.52

α1 = 1.7 × 10−6

◦C−1

α2 = 2.02 × 10−5

◦C−1

t = (2)(0.3 × 10−3

) = 0.6 × 10−3

m

Thus,

r = (0.6 × 10−3

)[(3)(2)2 + (1 + 1.52)(1 + 1/1.52)]/6(2.02 − 0.17)

(10−5)(70)(2)2 =0.132 m

Fluid-expansion thermometers represent one of the most economical,

versatile, and widely used devices for industrial temperature measure-

ment applications. The principle of operation is indicated in Fig.(4). A

bulb containing a liquid, gas, or vapor is immersed in the environment.

The bulb is connected by means of a capillary tube to some type of

pressure-measuring device, such as the bourdon gage shown.

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Fig.(4) Fluid-expansion thermometer

An increase in temperature causes the liquid or gas to expand, thereby

increasing the pressure on the gage; the pressure is thus taken as an

indication of the temperature. Fluid-expansion thermometers are usually

low in cost, stable in operation, and accurate within ±1◦C.

Thermoelectric Effects (Thermocouples)

The most common electrical method of temperature measurement uses

the thermocouple.

There are three emfs present in a thermoelectric circuit: the Seebeck

emf, caused by the junction of dissimilar metals; the Peltier emf, caused

by a current flow in the circuit; and the Thomson emf, which results

from a temperature gradient in the materials.

Fig.(5) Junction of two dissimilar metals indicating thermoelectric effect.

When the two dissimilar materials are connected to a measuring device,

there will be another thermal emf generated at the junction of the

materials and the connecting wires to the voltage-measuring instrument.

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This emf will be dependent on the temperature of the connection, and

provision must be made to take account of this additional potential.

Two rules are available for analysis of thermoelectric circuits:

1. If a third metal is connected in the circuit as shown in Fig. (6), the

net emf of the circuit is not affected as long as the new connections

are at the same temperature. This statement may be proved with the

aid of the second law of thermodynamics and is known as the law

of intermediate metals.

Fig.(6) Influence of a third metal in a thermoelectric circuit; law of intermediate

metals.

2. Consider the arrangements shown in Fig. (7). Simple thermocouple

circuits are constructed of the same materials but operate between

different temperature limits.

Fig.(7) Circuits illustrating the law of intermediate temperatures.

The circuit in Figure (7-a) develops an emf of E1 between temperatures

T1 and T2; the circuit in Fig. (7-b) develops an emf of E2 between

temperatures T2 and T3. The law of intermediate temperatures states

that this same circuit will develop an emf of E3 = E1 + E2 when operating

between temperatures T1 and T3, as shown in Figure (7-c).

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The arrangement in Figure (8-a) maintains both thermocouple wires at a

reference temperature of 32◦F, whereas the arrangement in Figure(8-b)

maintains only one at the reference temperature.

Fig.(8) Conventional methods for establishing reference temperature in

thermocouple circuit. Iron-constantan thermocouple illustrated.

It is common to express the thermoelectric emf in terms of the potential

generated with a reference junction at 32◦F (0◦C). Standard thermocouple

tables have been prepared on this basis, and a summary of the output

characteristics of the most common thermocouple combinations is given

in Table (1). These data are shown graphically in Fig. (9). The output

voltage E of a simple thermocouple circuit is usually written in the form

(2)

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where T is the temperature in degrees Celsius and E is based on a

reference junction temperature of 0◦C. The constants A, B, and C are

dependent on the thermocouple material

The sensitivity, or thermoelectric power, of a thermocouple is given by

(3)

Table(1-a) Thermal emf in absolute millivolts for commonly used thermocouple

combinations, (Reference junction of 0◦C).

Table(1-b)

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Table(1-c)

Fig.(9) Emf temperature relations for thermocouple materials, positive electrode

listed first.

Legend:

1 Chromel-constantan (type E) A Rhenium-molybdenum

2 Iron-constantan (type J) B Rhenium-tungsten

3 Copper-constantan (type T) C Iridium-iridium rhodium

4 Chromel-alumel (type K) D Tungsten-tungsten rhenium

5 Platinum-platinum rhodium (type R) E Plat. rhodium-plat. 10% rhodium

6 Platinum-platinum rhodium (type S)

7 Nicosil-Nisil (type N)

Thermopiles:

Thermopile is a multi-thermocouples connected in series to provide

more sensitive circuit as shown in figure (10). For a three-junction

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situation the output would be three times that of a single thermocouple

arrangement provided the temperatures of the hot and cold junctions are

uniform.

Fig.(10) Thermopile

The thermopile arrangement is useful for obtaining a substantial

emf for measurement of a small temperature difference between the

two junctions. When a thermopile is installed, it is important to ensure

that the junctions are electrically insulated from one another.

Consider the series thermocouple arrangement shown in Fig. (11). The

four junctions are all maintained at different temperatures and connected

in series. Since there are an even number of junctions, it is not

necessary to install a reference junction because the same type of

metal is connected to both terminals of the potentiometer.

Fig.(11) Series connection of thermocouples

The total emf measured at the potentiometer terminals is

E=eA-eB+eC-eD

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Effect of Cold Junction Level of Thermopile

Ex: A thermopile consisting of five junction pairs of Chromel-constantan

is used to measure a temperature difference of 50◦C with the cold

junctions at 25◦C. Determine

1. The voltage output of the thermopile.

2. Suppose the cold-junction temperature is incorrectly stated as 75◦C

(in reality, the hot-junction temperature). What error in

temperature-difference measurement would result from this

incorrect statement?

Solution

From Table 1-a the data needed are:

E25 = 1.495 mV

E75 = 4.657 mV

E125 = 8.054 mV

all referenced to 0◦C. For the correct statement of the cold junction at

25◦C, with a hot-junction temperature of 75◦C, the voltage output reading

of the thermopile would be:

EΔT = Number of thermocouples× (E75-E25)= (5)×(4.657 − 1.495) =

15.810 mV

By incorrectly stating the cold-junction temperature as 75◦C, we have not

changed the actual reading value of 15.810 mV; however, the reading

now indicates a different value of ΔT. To obtain the new high

temperature we would calculate a new high-temperature emf as

ET = 4.657 + 15.810/5= 7.819 mV

From table 1-a

6.319mV 100oC

7.819mV X

9.789 150oC

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Or

From which X=121.61oC

And

Ex. An iron-constantan thermocouple is connected to a potentiometer

whose terminals are at 25◦C. The potentiometer reading is 3.59 mV.

What is the temperature of the thermocouple junction?

Solution

The thermoelectric potential corresponding to 25◦C is obtained from

Table 1-a as: E25 = 1.277 mV

The emf of the thermocouple based on a 0◦C reference temperature is

thus

ET=E25+EPT

ET = 1.277 + 3.59 = 4.867 mV

From Table (1-a), the corresponding temperature is

75oC 3.918mV

X 4.867

100

5.26

Or

X-75=17.73

Or X=92.7 oC

(Q)A certain mercury-in-glass thermometer has been calibrated for a

prescribed immersion depth. The thermometer is immersed too much,

such that the extra depth is equal to a distance of 10◦ on the scale. The

true temperature reading may be calculated with

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( )

where:

Tind = indicated temperature

Tamb = ambient temperature of the exposed stem

D = extra immersion depth of the thermometer past the correct mark

Calculate the thermometer error for an indicated temperature of 210◦F

and an ambient temperature of 70◦F.

Solution

( )

( )

Error=|Ttrue-Tind|= | | 4 oF

(Q) A chromel-alumel thermocouple is exposed to a temperature of

1560◦F. The potentiometer is used as the cold junction, and its

temperature is estimated to be 83◦F. Calculate the emf indicated by the

potentiometer.

Solution

Since 83oF can be converted to

oC as

Or (83-32)×5/9=28.33oC

And 1560 oF=848.8888

oC

From table(1) E83 can be determined by interpolation as

1.133mV and ET=E1560=35.28mV

ET=E83+EPT

35.28=1.133+EPT

EPT=35.28-1.133=34.147mV

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(Q) Result of Installation Mistake

A heat-exchanger facility is designed to use type J thermocouples to

sense an outlet gas temperature. A safety device is installed to shut down

the flow heating system when the gas temperature reaches 800◦C. During

a periodic maintenance inspection, the thermocouple is judged to need

replacement because of oxidation. By mistake, a type K thermocouple is

installed as the replacement. What may be the results of such an

installation?

Solution

The voltage output of a type J thermocouple at 800◦C (from table 1-a)is

E800(J)=45.494mV. For this same voltage output from a type K

thermocouple the corresponding temperature can be evaluated as:

41.276mv 1000oC

45.494mV X

48.838 1200oC

Or X=1111.55oC

It can be concluded that the safety device would not be activated until a

temperature 311.5◦C higher than the design value is reached. This could

easily result in material failure of parts of the equipment.

(Q) 1. State the law of intermediate metals for thermocouples.

2. What is the Seebeck effect?

3. State the law of intermediate temperatures for thermocouples.

4.Why is a reference temperature necessary when using thermo-

couples?

5. Where might one use a bimetallic strip thermometer?