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The thermometer consists of a liquid filled bulb connected to a thin capillary with a temperature scale as shown in Figure 2.1.. Assuming that the bulk volume, Vb, is much greater than t

Non-Electric Thermometers

Liquid-in-glass thermometers are based upon the temperature dependent variation of the volume of the liquid which is used The thermometer consists of a liquid filled bulb connected to a thin capillary with a temperature scale as shown in Figure 2.1

Assuming that the bulk volume, Vb, is much greater than that of the liquid contained in the capillary, the volume variation, AV, of the liquid corresponding to the measured temperature variation, d6, is:

where /3a is the average apparent coefficient of cubic thermal expansion of the thermometric liquid in the given glass This coefficient, which also covers small changes of the bulb volume as a function of the measured temperature, has an average value for a given application range of the thermometer It equals the difference between the respective coefficients of cubic expansion, A,of the liquid and, Pg of the glass so that:

Assume that the inner capillary has a diameter, d,and that the temperature difference,

AO, corresponds to a change of length, A/, of the liquid column Using equation (2.1) the

thermometer sensitivity is:

At9 7rd2Az9 / 4 trd2

Equation (2.3) indicates that the sensitivity increases in direct proportion with increase

in bulb volume, Vb , and coefficient, Pa , but as the inverse square of capillary diameter,d.

There are some practical limits to increasing this sensitivity Firstly, an increase in bulb volume increases the thermal inertia of the thermometer Secondly, if the bore of the capillary is too small, the liquid column may break easily under the influence of surface tension In mercury-in-glass thermometers, for the Celsius scale, the bulb volume is about

ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic)

CAPILLARY LIQUID COLUMN BULB

Figure 2.1 Liquid-in-glass thermometer

6000 times the capillary volume, corresponding to the length of one Celsius of the thermometer scale

Laboratory thermometers are standardised for use with a liquid column which is totally immersed in the heating medium When such a standardised thermometer is used without total immersion of the liquid column, the non-immersed portion of the column will be at a different temperature from that of the bulb, To compensate for any systematic error due to the partial immersion, a correction should be applied to the indicated value The correction can be calculated from the formula:

The average apparent coefficient of cubic thermal expansion of the thermometric liquid

in the given glass is equal to Pa ,n is the length of the emergent liquid column, given in degrees of the thermometer scale, 0j, is the indicated temperature and 79m is the average value oftemperature of the emergent liquid column In the case when Om is higher than the indicated temperature, the correction, of course, is negative

Under ordinary industrial conditions, it is not generally possible to arrange that the whole liquid column ofthe thermometer is immersed in the medium to be measured Special thermometers, standardised with a partially immersed liquid column, are then employed Normally, the nominal immersion depth and the average value of the temperature of the emergent liquid column are stated on the thermometer scale If such a thermometer is used

at the correct immersion depth, with the emergent column temperature, 0m , different from the nominal value, t9n, , a corresponding correction must be applied Such acorrection is

given by:

In equation (2.5), 6n, is the nominal value of the average temperature of the emergent liquid column whilst the other symbols are the same as in equation (2.4) In both cases, the

mean temperature of the emergent liquid column is calculated by measuring its temperature

at some points along its length Alternatively, this average emergent temperature may by directly estimated by using a special thermometer with an elongated bulb placed close to the emergent column

Numerical example

A mercury-in-glass laboratory thermometer has been standardised by total immersion When immersed up to the scale division +50 °C in hot water it indicated a water temperature of +95 °C

If the average value of the emergent column temperature is +35 °C calculate the correction which

is required Assume that the effective coefficient of cubic thermal expansion, 9a , is

0.000 16 1/'C

Solution :

Using equation (2.4) the calculated correction is:

AO=Pan(Oi-On,)=0.00016x(95-35)=0.43 °C

Commonly used thermometric liquids and thermometric glasses are summarised in Table 2.1 from BS 1041 Suitable liquids for use in liquid-in-glass thermometers should have the following properties :

" Physical and chemical properties which do not change with time,

" Coefficient of cubic thermal expansion is constant in the measuring temperature range,

" Low freezing temperature,

" High boiling temperature,

" Easily obtained in pure form.

Table 2.1 Liquids and glasses for liquid-in-glass thermometers.

(Reproduced with permission from BS 1041, Section 2 1, 1985.)

Glass type Borasilicate glass Other normal glasses

Temperatu re (°C) Apparent coefficient ofcubic thermal expansion,R(1/°C)

-180 - 0.9)<10 -3 -

120 - 1 0;<10 -3 -

80 - 1 0x10 -4 0.9x10 -3 1 04x10 -3

-40 - 1 2x10 -3 I OX I O -3 1.04x10 -3

0 l 1 64x 10 -4 Ax10 -3 1 0X10-3 1 04x lO"3 1 58x10-4

20 - 1 5x10 -3 l.1xlO -3 1 04x10 -3

200 1 1 67x 10" 4 59x 10 -4

300 1 74x 10-4 1 64x 10 -4

400 1,82x 10"4

500 1 95x 10-4

Mercury-in-glass thermometers, used up to about 200 °C, have a vacuumised capillary For measuring temperatures in excess of 200 °C a suitable compressed inert gas is used This gas prevents both boiling of the mercury and condensation of its vapours in the upper part of the capillary When glass is heated and then allowed to cool to its original temperature, it does not return to its original dimensions immediately This phenomenon of hysteresis causes what is called a depression of the zero of a glass thermometer It may take several hours or even days to recover The amount of the zero depression and the recovery time depend upon the type of glass

Laboratory and industrial thermometers are available in two main forms described by Busse (1941) Etched stem thermometers, which are more popular in the UK, are made from a glass rod of about 4 mm to 6 mm diameter with an axial capillary, as shown in; Figure 2.2 Their stems may be straight or angled The scale is etched on the rod surface, whose curvature acts as a magnifying lens for the liquid column

In the enclosed scale type, which is shown in Figure 2.3, a thin-walled capillary and a milk glass scale are contained inside an outer thin-walled glass tube As in the former type the capillary curvature acts as a magnifying lens

As shown in Figure 2.4, industrial glass thermometers are generally protected by a steel sheath Whereas industrial glass thermometers have accuracies of ±0.02 °C to ±10 °C, laboratory thermometers may even have accuracies around ±0.0 I 'C

A great diversity of types of glass thermometers exists They include such categories as maximum thermometers, max-min thermometers, domestic thermometers and others Most types have been standardised to ISO 386 adopted as BS 1041 Detailed information on liquid-in-glass thermometers may be found in the works by Thomson (1962), Busse (1941) and also in BS 1041

EXPANSION VOLUME WHITE ENAMEL

CAPILLARY

BULB

Figure 2.2 Etched-stem thermometer

"¬ v

I

GLASS TUBE

0C

00

" ,

¬

4o -0

70

i 60

'

II,

u~ms i

BULB

Figure 2.3 Enclosed scale thermometer (a) straight, Figure 2.4 An industrial glass

1 Using Expansion 1 Solids

1ilatation thermometers

b-may

where 1 is the sensor length, al and a2 are the coefficients of linear thermal expansion of the two materials used and AO is the temperature difference

In most cases the sensors are constructed as a tube of material having a bigger expansion coefficient, a), with a coaxial rod made ofthe material of smaller coefficient, a2 They are respectively called the active and passive materials as indicated in Figure 2.5 The pairs of materials used should have as big a difference as possible between the coefficientsaland

a2, high permissible working temperature and good resistance against corrosion and oxidation Relative expansion coefficients of different materials are plotted as a function of temperature in Figure 2.6 The temperature range of suitable active and passive materials and their a coefficients are given in Table 2.2

As the expansion difference of two materials of reasonable length is usually too small to give a direct indication of temperature, it needs to be amplified by a mechanical transmission Dilatation thermometers, which can measure temperatures below about

1000 °C with errors of±1 % to ±2 % of the temperature range, indicate the average value of temperature along their length The cross-section of a dilatation thermometer is given in Figure 2.7 That part of the sensor inner rod which is outside the nominal immersion length

a, > a2

PASSIVE MATERIAL (oc2 ) ACTIVE MATERIAL (a',)

l

li t cc 2 6%

STATE AT ~~ STATE AT ~i A-'5

Figure 2.5 Principles ofdilatation thermometers

a

5 ~~~ , PQEtGE~~N

PASSIVE MATERIAL

w 0

dI >CC2

0 200 400 600 800 1000

TEMPERATURE, O'C

Figure 2.6 Relative thermal expansion of Figure 2.7 Cross-section of a dilatation materials used for dilatation thermometers thermometer

Table 2.2 Materials used in dilatation thermometers

Materials Temperature Coefficient of linear thermal

range (°C) expansion, a (1/°C)

Chromium-Nickel alloy 0-1000 16x10-6*

Invar(64%Fe,36%Ni) 0-200 3x10-6

*Approximate values depending upon the exact material composition

is made from a material having the same expansion coefficient as the outer tube In this way the variations of the ambient temperature and the possible heating of the emergent part of the sensor have no influence on the reading When measuring the temperature of metallic parts, the thermal elongation of these parts may be used as a direct replacement for the active material They are rarely used and only produced by very few firms

2.2.2 Bimetallic thermometers

Two metal strips with different coefficients of linear thermal expansion, a, welded or hot-rolled together, form a bimetallic strip similar to that shown in Figure 2.8 As in dilatation thermometers, the metal with the high value coefficient is called the active metal and the other with the low value, the passive metal A bimetallic strip, which is designed to be flat

at a neutral temperature, 20 °C most often, bends towards the passive metal at higher temperatures Commonly applied forms ofbimetallic strips are as shown in Figure 2.9 The shift,f,in mm or the rotation angle, ,6, in radians of the end of the bimetallic strip may be expressed with the aid of the specific bending coefficient, k This is the bending of a flat strip of length 100 mm and thickness 1 mm at a temperature 1 °C over neutral

Huston (1962) gives formulae for the movement,f of the end of the strip and rotation angle, 6, as follows:

PA SIVE METAL(oCZ) ACTIVE METAL (Xi )

Figure 2.8 Structure of a bimetallic strip

r t shaped strip as in Figure 2.9(a)

2 U-shaped strip as in Figure 2.9(b)

dxlO

2 9(')l

CYLINDRICAL HELIX-SHAPED STRIP

FLAT HELIX-SHAPED STRIP

3 Helix-shaped strip as in Figure 2.9(c), (d)

2At9 l dx104 where AO is the temperature difference above neutral temperature, l mm is the strip length,

k 1/°C is the specific bending, and d mm is the strip thickness In equation (2.9) the expression for the rotation angle in radians has been derived with 1 given, neglecting the bent endings

Numerical example

A bimetallic helical thermometer of the type illustrated in Figure 2.9(c) has k = 0.156 1PC and thickness d = 0.2 mm How long should the strip be to give a rotation angle, p = 7r rad over the temperature change 0 °C to 200 °C?

Solution :

From equation (2.9) it follows that:

1-0dx104 - 7rx0.2 x104 -101 mm

The mean values of the coefficients, k, for the working range of a bimetallic strip for different metals are given in Table 2.3 Overheating of a bimetallic strip may cause the elastic limit of the materials used to be exceeded In that case permanent deformation ofthe bimetallic element renders it useless.

Table 2.3 Materials used for bimetallic thermometers

(64 % Fe, 36 % Ni) 68 % Fe, 5 % Me)

(58 % Fe, 42 % Ni) 68 % Fe, 5 % Mo)

53%Fe,5%Na

*Approximate values depending upon the exact material composition

Cylindrical helical bimetallic strips are predominantly used in the manufacture of bimetallic thermometers As shown in Figure 2.10, they are inserted in a stainless steel protective tube of length around 250 nun or occasionally as long as 1 m The tube diameter may vary between 6 mm and 10 mm Useful temperature ranges covered by these thermometers may be from -40 °C to as high as 500 °C with errors between ±1 % to ±2

of full scale Bimetallic thermometers are simple and robust in structure They possess accuracies and physical sizes which are suitable for most industrial applications They have

a settling time, of less than 1 min and low sensitivity to both vibration and electrical disturbances They are also especially suitable for the measurement of the temperatures in live electrical equipment and also when only local, non-remote, readings are required Other typical applications may be encountered in measuring the temperature of liquids and gases

in containers, boilers and baths and also the temperature of the oil in power transformers It

is also possible to apply thermometers, made from a flat helical strip, for surface temperature measurement More detailed information is available in the work reported in Huston (1962) and in the Temperature Measurement Handbook (Omega Engineering Inc., USA).

POINTER SCALE HOUSING

ROD BIMETAL PROTECTION TUBE

Figure 2.10 A bimetallic thermometer using a cylindrical helical strip

2.3 Manometric Thermometers

Although the physical principles for these thermometers depend upon the particular type, they have similar physical structure They may be considered under the heading of variable volume or variable pressure types Variable volume thermometers are liquid-filled units while the variable pressure class depends upon the thermometric behaviour of vapours and gases.

2.3 1 Liquid-filled thermometers

This type of manometric thermometer is illustrated in Figure 2.11 Its whole system, which comprises a steel tube, connecting capillary and elastic element, is filled with thermometric liquid An increase in bulb temperature causes the liquid to expand and to dilate the elastic element Subsequently this dilatation moves the pointer through the transmission element.

As the liquid may be regarded as incompressible, the deformation of the elastic element is proportional to the increase in temperature so that the scale is practically linear Diverse

forms of elastic element, which may be used depending upon the internal pressure in the system, are shown in Figure 2.12 For example, membranes are suitable for pressures around 0.5 MPa (or 5 arm), Bourdon tubes and bellows between 0.2 MPa and 2.5 MPa Flat helical tubes or cylindrically wound flat tube are! suitable for the range 2.5 MPa to 60 MPa The temperature induced increase in the liquid volume, AV, resulting in a deformation

of the elastic element, is given by:

where Vb is the bulb volume, /31 is the coefficient of cubic thermal expansion of the liquid,

a is the coefficient of linear thermal expansion of the bulb material, and AO is the temperature difference.

°C

O

ELEMENT

ELASTIC ELEMENT

A_A CAPILLARY

MEMBRANE WOUND FLAT TUBE

L N

STEEL SENSOR

Figure 2.11 A liquid-filled manometric Figure 2.12 Basic elements ofliquid-filled