1
Temperature
1.1 Basic Behaviour of Materials to Temperature
Our physical world consists of solids, liquids and gases. With solids, the holding force between
molecules gives the material a fixed, definite shape. Liquids, on the other hand, are less tightly
bound, and they shape themselves to their containers. But gases, which have only weak attractive forces between molecules, move about so as to fill completely the enclosed spaces
which confine them. When a body is heated, the vibrational speed of its molecules increases
rapidly. This has a number of physical effects : in the case of solid its dimensions change ; in
the case of confined liquid, its pressure increases. But in both cases the temperature rises as a
result of increased heat. Sometimes the addition of heat can cause a solid to become a liquid,
and then the addition of more heat converts it into a gas (e.g., Ice → Water → Steam). The heat
energy gives the gas molecules the ability to move with speeds that are related to temperature. In measuring the temperature, the relative change of the molecular activity is defined by
a quantitative expression. An instrument measures temperature because it is sensitive to atleast one of the physical effects produced by the increased molecular activity.
1.2 Physical Effects Utilised to Measure Temperature
1.2.1 Expansion of Liquid or a Solid
This is one of the most important principles used in thermometry, the measurement of
temperature.
e.g.
(i) Mercury-in-glass Thermometers-Volumetric change.
(ii) Bimetallic Thermometers-Linear Expansion.
1.2.2 Change in Pressure
When a fluid is confined its pressure increases when the temperature rises.
e.g.
(i) Filled-System Thermometer. Fluids are confined by hermetically sealed systems
and their pressure response is used as a measurement of temperature.
(ii) Gas Filled Thermometer. As per Charles’s law, the pressure of a gas changes
linearly with the temperature when the volume of the gas is kept constant. Here
again the pressure measurement is indirect way of measuring Temperature.
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1.2.3 Change in Electrical Resistance
Electrical resistance of a wire (Copper, Platinum and Nickel) changes with respect to
temperature as given by the equation
RT = R0 (1 + αT)
where R0 = Resistance at zero temperature (0°C)
RT = Resistance at temperature T°C
α = Temperature-resistance co-efficient
e.g. Resistance Temperature Detectors (RTDs) made of either Copper, Nickel or Platinum.
1.2.4 Thermoelectricity
As discovered by Scientist Seeback, when two dissimilar metal wires are twisted together and heated, an emf is generated which is directly proportional to the difference in
temperature between the heated or hot junction and the other end which is called the cold
junction. This arrangement is called ‘Thermocouple’ which is widely used for temperature
measurement.
e.g.
(i) Copper—Constantan Thermocouple
(ii) Iron—Constantan Thermocouple
(iii) Nickel Chrome—Nickel Thermocouple
(iv) Platinum Rhodium—Platinum Thermocouple
1.2.5 Radiation
Radiation of a hot body can be measured and the temperature of the body deduced from
it. This principle is used for non-contact measurement of high temperatures.
e.g.
(i) Radiation Pyrometers
(ii) Optical Pyrometers
(iii) Colour Ratio Pyrometers
1.2.6 Temperature-Indicating Paints and Crayons
Temperature-indicating paints, applied by brush or spray (thermo-colours) may show a
single or several successive colour transformations as certain temperature levels are reached.
The colour changes are irreversible and somewhat affected by the duration of the heating.
Temperature-Indicating crayons (Thermochromes) with which the work piece is stoked,
usually show a single colour change.
1.2.7 Temperature-Indicating Pellets
Shapes formed of selected metals or metal alloys will melt at pre-established temperatures.
1.2.8 Seger Cones
In the ceramic industry, cones prepared of mixtures of suitable minerals have some
pyrometric value since they behave like the products in the Kiln. The point at which the tip of
the cone softens and bends over to touch the base gives the desired temperature for which the
cone was prepared.
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TEMPERATURE
1.3 Temperature Scales
1.3.1 Centigrade Scale
In temperature scale in °C (Centigrade or Celsius), 0°C is assigned to the ice point, and
100°C to the boiling point of water.
1.3.2 Kelvin Scale
The Kelvin scale has no negative range and is counted up form its origin at – 273°C, the
absolute zero in the thermodynamic scale.
1.3.3 Fahrenheit Scale
This scale like centigrade scale is based on the freezing point (ice point) and boiling
point of water : 32°F and 212°F.
1.3.4 Rankine Scale
This scale like Kelvin scale has no negative range and counted up from its origin at
– 460°F, the absolute zero in the thermodynamic scale.
The scales used are purely artificial and arbitrary. The absolute zero temperature in
the thermodynamic scale is the point at which the pressure caused by the movement of molecules
is zero. The relationship between absolute pressure and temperature in different scales are
shown in Fig. 1.1 and Fig. 1.2. The exact values of absolute zero in Kelvin scale corresponds to
273.16 and in Rankine scale to 459.6 instead of 273 and 460, taken for all practical purposes.
Absolute
pressure
Absolute
pressure
–273°
0°C +100°C +273°C
(a) Centigrade scale
0°K 273°K 373°K 546°K
(b) Absolute scale (or Kelvin scale)
Fig. 1.1 Absolute pressure vs temperature
–460°F
0°F
+460°F
(a) Fahrenheit scale
0°R
460°R
(b) Rankine scale
Fig. 1.2 Absolute pressure vs temperature
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920°R
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INDUSTRIAL INSTRUMENTATION
1.3.5 Comparison of Temperature Scales
If C, K, F and R are the temperatures in Centigrade, Kelvin, Fahrenheit and Rankine
scales, the following conversion formulae can be used to convert them into other scales.
5
5
(F – 32) = (R – 492)
9
9
5
5
K = C + 273 = (F – 32) + 273 = (R – 492) + 273
9
9
Or
C = K – 273 =
...(1)
5
5
F + 255 = R
...(2)
9
9
9
9
F = C + 32 = K – 460 = R – 460
...(3)
5
5
9
9
R = F + 460 = C + 492 = K
...(4)
5
5
The reference points, namely, freezing point of water and boiling point of water in different temperature scales are shown in Fig. 1.3 for clear understanding.
K = C + 273 =
100°C
373°K
0°C
273°K
–273°C
0°K
Boiling point of water
Freezing point of water
Absolute temperature
212°F
672°R
32°F
492°R
–460°F
0°R
Fig. 1.3 Temperature reference points
1.4 Temperature Measurement
Temperature measurements can be in many ways. They have been divided into two
general classifications : those which are primarily mechanical in nature (Non-Electrical methods) and those which are primarily electrical or electronic in nature. Most of the mechanical
and electrical types are contact thermometers. Non-contact type thermometers for high temperature measurements are normally called as Radiation Pyrometers. Some special devices
such as paints, crayons, pellets and seger cones are also available for the temperature indications.
Another classification of temperature sensing devices might be made by using the temperature ranges of the units as the basis of comparison. Several methods may be available for
a given temperature span. However, all will not be equally well suited to any given temperature measurement. Therefore, the selection must be based not only on the range and span but
also on such factors as life, speed of response, accuracy and means of mounting the sensing
element.
Table 1.1 indicates the different types of Thermometers and Temperature ranges.
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TEMPERATURE
Table 1.1 Temperature measuring devices and their applications
thermometers
thermometers
pyometers
devices
Special
Radiation
Electrical contact
Mechanical contact
Total range, ...... Typical range ...... Range of exceptional application
R|
||
||
||
||
|S
||
||
||
||
||
T
R|
||
||
||
|S
||
||
||
||
T
R|
|S
||
T
R|
|S
||
T
Liquid-in-glass thermometer (– 200 to 750°C)
Pentane (– 200 to 20°C)
Alcohol (– 70 to 100°C)
Tolune (– 70 to 100°C)
Mercury in vacuum (– 30 to 280°C)
Mercury in gas under pressure,
quartz glass (– 30 to 750°C)
Pressure-filled expansion thermometers (– 35 to 600°C)
Hg at 100 to 150 at (– 35 to 600°C)
Vapor-pressure thermometers (– 200 to 360°C)
Metallic expansion thermometers (– 30 to 100°C)
Bimetal types (– 30 to 400°C)
Expansion rod types (up to 100°C)
Resistance thermometers (– 220 to 550, 750°C)
Copper (– 50 to 150°C)
Nickel (– 60 to 180°C)
Platinum (– 220 to 550 ; 750°C)
THERNEWID semiconductors (– 20 to 180°C)
Thermocouples (– 200 to 1300 ; 1600°C)
Copper constant, manganin-constantan
(– 200 to 400 ; 600°C)
iron-const (– 200 to 700 ; 900°C)
Nickel-chrome a nickel (– 200 to 1000 ; 1200°C)
Platinum rhodium-platinum
(– 100 ; 0 to 1300 ; 1600°C)
Radiation pyrometers (– 40°C)
Total radiation pyrometers (– 40°C) ................
Part rad. pyam (200, 800°C).............................
Temperature indicating paints (40 to 650°C)]
Temperature-Indicating crayons (85 to 600°C)
Temperature-indicating pellets 100 to 1600°C)
Seger cones (600 to 2000°C)
– 200 0
200 400
600
800
1000
1200
1400
1600 1800
Temperature t →
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2000
°C
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INDUSTRIAL INSTRUMENTATION
1.4.1 Mechanical Thermometers
The following classifications can be made as far as mechanical thermometers are concerned.
(i) Filled-System Thermometers
(ii) Metallic-expansion Thermometers
(iii) Special Devices.
1.4.1.1 Filled-System Thermometers
The temperature is converted into a mechanical motion caused by pressure or expansion, and this motion is measured. The instruments working with this principle are much
simpler ones. The thermal system of a filled-system thermometer comprises the thermometer
bulb, an expansion element, such as a Bourdon tube, diaphram, capsule or bellows, and a
capillary tube connecting the bulb and the expansion element.
The Scientific Apparatus Manufacturers Association has issued standard classifications
which are used by practically all manufacturers. They divide filled system thermometer into
four basic classes.
Class-I : Liquid Filled Thermometers
The thermal system is completely filled with a non metallic liquid and operate on the
principle of liquid expansion. (This group does not include mercury-filled thermometers.)
Class-II : Vapour-Pressure Thermometers
The thermal system is partially filled with a volatile liquid and operates on the principle
of vapour pressure.
Class-III : Gas Thermometers
The thermal system is filled with gas and operates on the principle of pressure change
with temperature.
Class-IV : Mercury-Filled Thermometers
The manufacturers of American instruments use this class, but the Scientific Apparatus Manufacturers Association classifies as Class-V as given below.
Class-V : Mercury-Filled Thermometers
The thermal system is completely filled with mercury or mercury-thallium eutectic
amalgam and operates on the principle of liquid expansion.
1.4.1.1.1 Liquid Filled (Non-Mercury) System (Class-I)
The use of volume changes to indicate temperature changes is probably one of the oldest
methods employed for temperature determination, yet it is as important today for temperature measurements in the general range of – 200 to + 300°C as any other method available. In
many instances, it offers definite advantages. It is probably the one used in thermometers of
our common acquiantance. The height of the column of liquid indicates the temperature by
measuring the volume of that liquid at that temperature. This is an accurate way to express
temperature.
The Cubical expansion of liquid is governed by the formula :
Vt = Vo (1 + αt + βt2 + ...... + ktn)
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TEMPERATURE
For all practical purposes it can be simplified as
Vt = V0 (1 + αt)
where,
Vt = Volume at temperature ‘t’
V0 = Volume at temperature ‘0’
α = Coefficient of Cubical expansion
Though theoretically any liquid could be used, the commonly used liquid in practice are
alcohol, pentane, toluene and of course mercury under class IV/V.
When the liquid is allowed to expand into a glass tube so that its height may be read,
some limitations are experienced : a person must determine the temperature by observation
avoiding Parallalex error, the object whose temperature to be measured must be freely accessible and the upper limit should be below the boiling point of the liquid employed. For these
reasons, this type of thermometer is limited to on the spot reading and to the lower temperature ranges. One such thermometer used in Industries is shown in Fig. 1.4.
Taylor
F
240
220
200
180
160
140
120
100
80
60
Taylor
230
210
190
170
150
130
110
90
70
50
40
30
Fig. 1.4 Volumetric types of thermometers come in many styles to facilitate reading
Stem Correction
If the temperature distribution in the thermometer liquid differs from the conditions
prevailed when the thermometer was calibrated, a stem correction becomes necessary. If the
entire stem was immersed during calibration, as is customary for precision thermometers, the
correction (in °C) becomes.
∆t = γn(ta – tm) where
γ = Effective expansion coefficient per °C
[For Mercury filled one
γ = 1/6300 = 0.00016,
For Organic liquids like pentane, alcohol and toluene γ =1/800 = 0.00125.]
n = length of emergent liquid column in °C
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INDUSTRIAL INSTRUMENTATION
ta = Temperature reading in °C
tm = Mean Temperature of emergent column in °C
(Measured by another thermometer)
Example : [Refer Fig. 1.5]
1
= 9.5°C
6300
Measurement Using Bellows : (Capsule, Diaphram or Bourdan tube)
∆t = 185 (395 – 70)
With the bellows method of temperature measurement, the pressure established in a
close system when a liquid attempts to expand or contract as it is heated or cooled is measured.
The instrument dial is calibrated in terms of the temperature which created the pressure.
When the liquid expands in a closed system, it has to do so by changing the volume of the
system which holds it. The materials used for the bellows are selected especially for their
ability to change their dimensions at a rate which is almost exactly proportional to the pressure applied to them. One of the advantages of the closed pressure system is that the indicating portion can be located at a distance from the sensing bulb. Depending on the ranges and
applications capsules, diaphrams or Bourdan tubes are used as pressure sensing elements in
place of bellows.
tm =
70°C
ta =
395°C
n = 185°
210°C
Seal
carefully
Small amount
of liquid
Fig. 1.5 Example of stem correction
Errors and Compensation
The filling fluid in the entire thermal system is normally temperature sensitive This
can produce errors because of ambient temperature changes along the capillary tubing and
the expansion element. To compensate for changes in ambient temperature, two methods are
used :
(1) Case Compensation, which counter acts ambient temperature effects at the instrument case only, and (2) full compensation, which includes the capillary also called the measuring tubing.
Case Compensation : (Refer Fig. 1.6A)
Here the measuring spiral is fastened to a bimetallic strip, which in turn is fastened to
the case support. When the temperature inside the case rises, the measuring spiral dilates in
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TEMPERATURE
proportion to the change and tends to move the pointer (or pen) upward ; simultaneously,
however, the bimetallic strip moves the spiral in the opposite direction and the resulting net
movement transferred from the spring to the pointer (or pen) is zero.
Full Compensation : (Refer Fig. 1.6B and Fig. 1.7)
Two tubings and two spirals are used—two thermal systems in fact, filled with the same
temperature-sensitive fluid and having the same dimensions. Only one tubing, however, is
interconnected with the bulb. The other one (c) is a compensating tubing and is dead—ended
at the bulb entrance. The consequent effect is that both tubings react to the ambient temperature, but only one responds to the additional bulb effect. The two spirals are so mounted that
they are coupled together, but they move in opposite directions. The resulting net effect, then,
is due only to the bulb temperature, and complete compensation of ambient temperature influences on measuring spiral and capillary tube is obtained.
Measuring spiral
Measuring spiral
Bimetallic
metal strip
A
Compensating
spiral
B
Measuring
tubing
Dead
end
Compensating
tubing (C)
Fig. 1.6 (A) Case compensation (B) Full compensation.
Measuring element
Capillary tubing
Temperature
sensitive bulb
Compensating capillary tubing
Mechanical connection
Compensating element
Pen arm
Fig. 1.7 When capillary lengths exceed 3 metres, complete compensation may be required for
liquid-filled systems. Two systems are required. With the exception of the bulb, the
two systems are identical and work in opposition to each other
If the volume of the bulb is made large with respect to the volume of the tubing and
spring, ambient temperature errors are further minimised.
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1.4.1.1.2 Vapour-Pressure Thermometer (Class-II)
Because the Vapour-Pressure of a liquid is a function of temperature, it is vary often
used in commercial temperature-measuring devices. Its high speed of response, lower cost,
ease of repair and non-linear scale (the scale can be large where the thermometer is normally
used) are reasons for its extensive use.
This system has all of the major components of the liquid-filled and the gas filled systems for temperature measurements. The thermal system is filled with a volatile liquid and its
vapour. It is a hybrid in that its sensing bulb contains a liquid but is not full of it and the
pressure transmitted to the spring is created by vapour. That means the bulb is partly filled
with the liquid, the rest of the thermal system being filled with same material in its vapour
state. The whole assembly can be compared with that of a steam boiler where, by well-known
relations, the vapour pressure is a function of the temperature of the liquid. Under operating
temperature conditions, with the bulb at higher temperature than the capillary tube, the
capillary and the spiral are filled with some of the liquid. Conversely, when the bulb is at a
lower temperature than the instrument, all the liquid in the bulb, and the capillary and measuring spiral are filled with vapour.
All liquids with free surfaces have molecules leaving and returning to the surface at all
times ; the number leaving depends upon the temperature. These molecules develop a pressure which is indicative of the temperature. If enough leave so that the pressure that they
10
1
–100
Bu
tan
Me
e
thy
len Ethe
ec
r
Eth hlor
yl a ide
lco
ho
l
M
-X
yle
ne
lor id
e
100
Meth
yl ch
Pressure, pounds/square inch, absolute
1,000
0
100 200 300 400
Temperature, °F
500
600
Fig. 1.8 Vapour pressure-temperature relationships of common charging liquids
develop is equal to the atmospheric pressure, we say that the liquid is boiling. If we reduce the
pressure above the liquid, the boiling will take place at a lower temperature because it is
easier for the molecules to escape ; if the surrounding pressure is increased above atmospheric, boiling will take place at a higher temperature. In a confined space these escaping
molecules will increase the surface pressure and automatically raise the boiling point. So long
as liquid is present in the bulb there will always be a perfect definite relationship between the
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