Temperature Measurement
Introduction
Heat. Temperature. Two words around which the major industrial processes revolve, heat being the raw energy used to generate electrical power and temperature being the measure of level or quality of the heat. Heat and temperature are often confused as being essentially the same thing whereas the differences between them are critical to their understanding.
Consider two vessels one having a capacity of a pint (0.568 litre) the other's capacity being 4.5 litres (approximately 1 gallon). The larger container is filled with water and the small one is then filled from it, both containers will be at the same temperature but the larger of the two will possess the greater amount of heat. This can easily be tried and proved simply by adding ice to each, it will be found that the larger vessel will melt more ice than the smaller. (The experiment is carried out by slowly adding the ice and stirring until no more ice melts). From this it should be obvious that an expression of an object's temperature is not an expression of the heat it contains. Also, that in order to measure the heat content of a body, it is almost always necessary to partly or totally use up that heat.
Heat is expressed in several ways:-
British Imperial Units S. I. Units
1 British Thermal Units (Btu) = 1055.06 Joules
1 Calorie = 4.1868 Joules
1
1 therm = 0.105506 Giga Joules
The British Thermal Unit is that amount of heat required to raise 1 pound weight of water through 10 Fahrenheit.
The calorie is that amount of heat required to raise the temperature of 1 gram of water through 10 Centigrade.
The
The therm is equivalent to 100, 000 Btu.
The Joule (pron. jule) is 1 watt dissipated for 1 second.
The term Giga - pronounced Gigger - represents a factor of 109 so that a Giga Joule is 10 Joules or 1,000,000,000 (one thousand million) Joules.
SECTION 1:
EFFECTS OF HEAT
When objects and materials are subjected to a change in temperature the heat involved will manifest itself in the following ways:-
1. Expansion or Contraction
2. Change of State
3. Change of Shape
4. Change of Colour
5. Change in electrical resistance
6. Thermo-electric effects.
Change of State
When heat is added to a body it has several effects, some of which are visible, all resulting from the effects of heat on molecular structures.
Water exists as a liquid between 0°C and 100°C; below 0°C it is a solid, above 100°C it behaves as a gas. Heating gives the molecules the energy necessary to cause these changes of state. The heat required to change the state of a substance is called "latent heat". The latent heat (L), is the amount of heat required (Q), to change the state of one gram of substance without changing its temperature.
Q = M x L (kJ/kg)
In the ice or solid state of water the molecules posses very little energy and are tightly bound together by a force known as cohesion.
Note that the individual atoms of the group are shown to be vibrating, so causing the whole structure to vibrate. If heat is now added the atoms, and hence the molecules, start to vibrate faster. In fact they are absorbing the heat energy and converting it into energy of movement (Kinetic energy). They cannot, at this stage, move out of their places. As the level of heat is increased so the vibration increases until a point is reached when the molecules are vibrating so fast that the bonds between them suddenly break.
Molecules at the surface of the solid 'peel off and slide about nearby. Temporarily they may stick to other molecules but soon separate again. Gradually all the molecules become mobile and at this point the ice has changed to water. During the time taken for the change of state of ice to water, the temperature will have remained fixed at 0°C. Even if the heat input had been increased the temperature would have remained fixed at zero, only the time taken would have been affected. The heat involved in this operation cannot be 'sensed' and is often referred to as 'insensible heat', or, in this case, the latent (hidden) heat of fusion of ice.
Fig. 2
If the water produced by the molten ice is further heated the molecules of it gather speed, going faster as the temperature rises. At 100°C the water starts to boil, the molecules are now moving so fast that the water moves quite violently, and it evaporates into invisible water vapour. (The white clouds of visible steam are not the gas, they are water vapour in the process of condensing into tiny droplets of water). Again there has been a change of state, molecular structure and arrangement. At the temperature stated the molecular speed energy is so great that it completely overcomes the cohesive force that held the molecules together in the ice and liquid states. High energy molecules travel up through the water, travelling away from the source of heat and escape at the surface. In this state they are quite independent and free to travel about in the atmosphere. On cooling the molecules lose speed, moving more slowly. Slow speed molecules of water vapour will meet and conglomerate into a droplet of water, in doing so they lose the latent heat imparted to them on boiling. This second quantity of latent heat is called the "latent heat of vaporisation," and as in the previous case it is “insensible heat".
Many substances can exist as solids, liquids or gases and, like water, change their state when they are either heated or cooled. Some substances will change straight from the solid to the gas state, missing out the liquid stage, this is called 'sublimation'.
Fig. 3
Expansion of Solids
Perhaps a better known effect of heat, although it is not always a visible effect, is that it causes objects and materials to expand and change shape. Different materials expand by different amounts for a given increase in temperature. Some materials, such as invar steel, expand by amounts that are so small that their increase in volume over a considerable rise in temperature is hardly measurable.
Substances expand when they are heated because as the heat energy is absorbed it causes the molecules to vibrate faster enabling them to move away from each other. This can easily be proved when one considers the expansion of, say, a block of metal.
Fig. 4
A block of metal, say 10 cubic centimetres, is heated uniformly through a rise of 100°C. The block will expand uniformly in each direction. Supposing the coefficient of expansion for the material to be .001, (i.e. it expands by one thousandth of a centimetre for each degree rise in temperature Centigrade), then the change in volume would be:-
100°C x 0.001 x 3 (length and breadth height) = 0.3
The material would increase its volume by 3 tenths of its original volume. Or the block would have a new volume of 13 cubic centimetres. It would, however, still have the same mass. Therefore as the volume increased some other factor, affecting mass, must have proportionally decreased.
Mass = Volume x Density
Originally M = l0 x r (
= lO r
after heating M = 13 x r
M =13r
So as the mass (M) remains constant the density of the material must have decreased. This is in fact the case, because density is the weight per unit area that is determined, in part, by the number of molecules of material per unit area. As heating causes the molecules to spread apart and occupy more space, the number per unit area must decrease.
Coefficients of linear Expansion
per °Celsius
Aluminium 0.000023
Brass 0.000018
Copper 0.000017
Iron 0.000011
Platinum 0.000009
Steel 0.000012
Linear expansion of materials can be used to determine their temperature. If the block of material, used to demonstrate volumetric expansion, had been 10 cms long by 1 sq. cm. then the linear expansion would have been ten times greater than the expansion in the other two planes (breadth and height). So that, for the same rise in temperature (100°C) the bar would have expanded linearly by:-
10 x 0.001 x 100 = 1 cm
While its height and breadth would only have increased by:-
1 x 0.001 x 100 = 0.1 cms each
To measure the change in temperature of a piece of material using this, somewhat crude method, the information required would be:
The original length of the material Lo
The coefficient of linear expansion of the material C.
The final length of the material after heating Lf.
(Lf-Lo)
LoC = t (temperature)
However, from the table of coefficients of linear expansion given, it is obvious that this method of temperature measurement is very impractical and does not lend itself to use, in the form shown, in this industry.
Expansion of Liquids:
Because the cohesive forces between molecules are already weakened, liquids expand considerably more per degree rise in temperature than solids. However, taking measurements of the amount by which a liquid expands is not a straightforward operation. The difficulty is that a liquid must be contained and the container will expand as the liquid is heated. The increase in capacity of the container therefore masks the true expansion of the liquid. In practice the true expansion of a liquid is calculated by adding the increase in volume of the container to the apparent, or measured, expansion of the liquid.
Like metals, liquids expand by varying amounts per unit change in temperature, dependent upon the densities of them. Furthermore, not all liquids expand uniformly per unit rise in temperature. Water, for example, is one that behaves in a very unusual manner. From 4°C down to 0°C it expands as it is cooled. (Hence the bursting of pipes during freezing as well as thawing).
The fact that certain liquids expand uniformly and visibly with a change in temperature is made use of in the most popular form of thermometer.
Expansion of Gases
As you may expect, gases expand considerably more per unit rise in temperature than solids or liquids. The reason being that the cohesive forces encountered in the other two states of matter has been completely overcome in the gas state.
Gases have no shape of their own and must therefore be contained in a closed vessel. If the container is rigid the gas cannot, of course, expand on heating. Only if the container rails are elastic will expansion take place. A partially inflated balloon will, when heated, expand considerably, however the rubber envelope of a balloon is not perfectly elastic and some pressurisation of the gas takes place, so that a measurement of the expansion would not be an accurate measure of the gas expansion against temperature change.
The gas holder, or gasometer, provides a better example of gas expansion. If gas is either entering or leaving the holder, and there is a rise in atmospheric temperature, the enclosed gas will expand and the holder will rise. Say the temperature rose from 20°C to 22°C, and the gas holder was at 6Oft at the former, then it would rise by approximately 5 inches for this change. A change of 5°C would cause the holder to rise by just over a foot.
When a gas is heated and allowed to expand freely, without increases in pressure, the molecules of the gas move further apart. A certain volume of gas will then contain fewer molecules and will become lighter in weight.
Fig. 5
The physicist Professor Jacques Charles (1746 - 1823) performed experiments to find the exact relationship between the temperature and volume of a gas. He deduced that if a certain mass of gas at 0°C was heated, to 273°C, keeping it at constant pressure, its volume would have doubled and at 546°C it would have trebled. The apparatus he used to prove this consisted of a bulb of dry air connected to a flexible U-tube containing mercury.
Fig. 6
When the pressure in the bulb is the same as the pressure of the atmosphere acting on the surface of the mercury in the open limb of the U-tube the two levels of mercury will be coincident. If the pressure of the gas in the bulb is greater than atmospheric pressure, the level of mercury in the limb connected to it will be depressed.
To maintain a constant pressure, throughout the experiment, the free limb of the U-tube must be positioned and repositioned such that the levels of mercury are always coincident.
The water bath, containing the gas bulb, was heated and at certain temperatures the volume of the gas was noted. An interesting fact, uncovered by this experiment, is that all the different gases used gave exactly the same results, (i.e. they all expand by the same amount for a given rise in temperature), unlike liquids and solids which expand by varying amounts according to their densities.
The graph obtained, from the results of this experiment, was in the form of a straight line. From this it can be deduced that if the line was extended, it would cross a point where the gas would have no volume at all. This point occurs at a temperature of -273°C or 0°K. In fact this would not happen as all known gases liquefy and then solidify well before this temperature is reached.
For convenience the Kelvin scale of temperature is used in calculations involving gases.
O°K = -273°C Therefore 0°C = 273°K
Thus, add 273 to any centigrade value and it becomes the equivalent value on the absolute scale. The convenience of using this scale lies in the fact that if the absolute temperature is doubled then the volume of the gas is likewise doubled, or, the volume of a gas is directly proportional to its absolute temperature. This is Charles' Law, which states that; if the pressure of a fixed mass of gas is kept constant, then the volume varies directly with the absolute temperature.
V1 = V2 Where V1 and T1 are the initial volume and
T1 T2 temperature respectively.
There are several other effects of heat used in thermometry, which will be described in other sections. The effects described so far form the basis of a considerable range of thermometers.
SECTION 2:
Temperature Scales
In common with the majority of our units of measurement, those used to express temperature have recently been reviewed and in some instances discarded in favour of others. In 1968 the "International Practical Temperature Scale" was adopted. Some important features of this were:
(i) The Kelvin, symbol K, is now the basic unit of temperature measurement. It is defined as being:-
1/273.15 of the thermodynamic temperature of the triple point of water.
(The triple point occurs when there is equilibrium between the solid, liquid and vapour phases of water).
(ii) The centigrade scale of temperature would remain in use in its present form but would be known as the Celsius Scale, after its innovator.
(iii) The degree Kelvin will become the basic unit of temperature measurement in the new S.I. system of units.
E
SCALE CONVERSIONS
Kelvin and Celsius
Degrees Celsius (°C) = Degrees Kelvin (K) -273.15
Degrees Kelvin (K) = Degrees Celsius (°C) +273.15
Fahrenheit and Celsius
Very soon this piece of information will become of no other use than simply a mathematical exercise in schools and colleges as the Fahrenheit Scale will disappear from use. However, with the ice point at 32°F, there is an interval of 180 °F between the two. This corresponds to 100 degrees on the Celsius Scale.
Therefore, a span of 180 degrees Fahrenheit = a span of 100 degrees Celsius.
(i) to convert from °C to °F
D 100°C = D 180°F
Therefore, at any temperature, t°C = 180 x t°F
100
but 0°C = 32°F
therefore, t °C = (180/100 + 32)°F
t°C = (9/5 + 32)°F (t°C x 9/5) + 32 = °F
(ii) to convert from °F to °C (t°F - 32) 5/9 = °C
The Rankine
Symbol R the Rankine is defined as being equal to 5/9 of a degree Kelvin. On this basis then: 273.15K = 491.67R
E
Degree Absolute
This scale of temperature is referred to as degrees Celsius absolute, it commences at absolute zero. To convert to degrees absolute, simply add 273.15 to the value in degrees Cesius. So, obviously degrees absolute are the same as degrees Kelvin, this being the case, the use of the absolute scale may, like the Fahrenheit scale, disappear from use.
SECTION 3:
Liquid Expansion, Vapour Pressure and Gas Expansion Thermometers
Liquid in Glass
The ‘liquid in glass thermometer’, especially the ‘mercury in glass’, is undoubtedly the most widely used instrument for the measurement of temperature. It is not surprising that many different forms of this thermometer have been produced to suit a vast range of practical applications and conditions. Basically the form of the thermometer is a glass bulb, joined to a length of glass tube having a uniform capillary bore.
Fig. 7. The Orthodox Liquid in Glass Thermometer
The range of the thermometer is governed by the size relationship, (bulb vs. capillary bore capacities), and the liquid used. Short range thermometers usually have extremely fine capillaries and small bulbs. In order to make the mercury thread readily visible the stem or 'cane' of the thermometer is drawn into a shape such that it acts as a lens. Sometimes a fine strip of red glass is incorporated into the cane such that the rising mercury obscures it, making readings easier to take.
A thermometers range can be suppressed in order to spread out the interesting portion of it over the whole of the stem. Forming a second bulb immediately above the reservoir does this. The expanding liquid has to first fill this second bulb before it can move into the capillary, the size of the second bulb will determine how much of the range is suppressed. It is usual to have a similar cavity at the top of the capillary tube, the purpose of which is to protect the thermometer in the event of it being immersed in a fluid whose temperature is higher than the range of the thermometer.
As stated, mercury is probably the liquid most commonly used as a thermometer filling. Its boiling point is 356.7°C, but can be used above this temperature provided that it is not allowed to boil. This is achieved by pressurising the mercury under Nitrogen (an inactive gas which will not contaminate the mercury). The pressure is governed by the amount by which the boiling point is to be increased and, in some cases, is surprisingly high. In this way the useful range of a mercury thermometer can be raised to about 500°C.
| Liquid | Minimum Temp. ( C) | Maximum Temp. ( C) |
| Mercury | -40 | 510 |
| Alcohol | -80 | 70 |
| Toluene | -80 | 100 |
| Pentane | -200 | 30 |
| Creosote | -5 | 200 |
There is much more that could be said about liquid in glass thermometers but as their direct application is not common in power stations enough has been said of them here.
Liquid in Metal Thermometers
In a typical liquid in metal thermometer a bourdon tube is connected to a metal bulb via a metal capillary tube.
Fig. 8
The system is fully charged with a liquid chosen for its suitability to the temperature range to be measured. Other considerations governing the choice of liquid are:
(i) it must have a large coefficient of cubical expansion
(ii) its vapour pressure should be very low, (to overcome the effects of formation of vapour the system is charged and sealed at a high pressure)
(iii) it is desirable that the liquid chosen expands uniformly/unit rise in temperature
(iv) it must be chemically stable and not react with, nor attack, nor become contaminated by any of the metal parts of the system.
(NOTE: In the case of the mercury in steel thermometers the charging pressure may be as high as 1, 000 lbs. f/ins2 in order to overcome the effects caused when vapours are formed).
Principle of Operation
The bulb, which is by far the largest part of the total volume of the system, is inserted into a protective pocket or sheath at a place where the temperature is to be measured. For the purpose of this explanation, suppose that the temperature, at the point of measurement now rises. The liquid in the bulb will start to expand. The capillary tube will transmit the change in volume to the bourdon tube that will deflect. Note that it is a change in volume that is being measured and not, as is a popular misconception, a change in pressure. Any pressure changes that may occur are purely incidental. The law governing this action is
V2= V1 (1 +a(T2-T1))
where V2 = the volume of the liquid at T2
V1 = the volume of the liquid at T1
a = the coefficient of cubical expansion/°C.
This is a simplified version of the full equation, removing such terms as are considered unnecessary for this treatment of thermometers. It does show that the scale of the indicator can be substantially linear.
As with the ‘liquid in glass’ variety of thermometer, mercury is perhaps the most popular and universally used filling medium. However, alcohol and xylene are also used, especially where contents of a burst bulb in a mercury filled system may contaminate a whole process. Also, if mercury is chosen as the filling liquid, the choice of metals used in the construction of the system is very limited due to the fact that mercury will readily form amalgams with many of them.
Liquid | Minimum Temperature (°C) | Maximum Temperature (°C) | Coefficient of Expansion (°C) |
| Mercury | -40 | 650 | 0.182 x 10-3 |
| Alcohol | -45 | 150 | 1.143 x 10-3 |
| Xylene | -40 | 400 | 1.121 x 10-3 |
Depending on a change in volume as a means of temperature measurement incurs certain disadvantages. The system described can be split into three basic parts.
It should be obvious that both the capillary and the bourdon tubes are also sensitive to any temperature changes in their environment and will cause the same effect, a change in liquid volume detected by the indicator, should the ambient temperature rise or fall. As the system is calibrated to respond accurately to changes in bulb temperature only, any variation of temperature elsewhere will result in errors. In some cases the variation of temperature along the capillary run may be quite considerable both in magnitude and number. Take, for instance, such a system with its bulb immersed in a P. F. mill and the indicator mounted in the control room panel. In such a case the length of capillary may be as much as 150 metres or more, and can run through rooms and areas where the temperature variations can be as high as 4 or 5°C.
Ambient temperature errors and compensating devices
If a typical thermometer bulb, having an internal volume of say V1 cubic centimetres, is connected to a capillary tube with a volume of say V2 cubic centimetres, is subjected to a temperature change of t°C, then the error (e) in °C is given by
e = V2/V1 x t
As an example of what this can mean consider:
V2 = 1 cubic centimetre (approximately equivalent to 5 metres of
0.05 cm capillary)
V1 = 12.5 cubic centimetres
t = 15°C (e.g. a change from say 10°C to 25°C) then
= V2/V1 x t
= 1/12.5 x 15
= 1.2°C
Thus for an indicated change in temperature of only 15°C there can be error of 1.2°C.
You can readily see that the larger the bulb volume is in relation to that of the capillary, the smaller the error becomes. In fact the British Standard specification covering this aspect of thermometry states that, “the error should not be greater than 0.5 per cent of the maximum scale reading for a 15.5°C (30°F in fact) change in capillary and bourdon temperature.”
To avoid error due to changes in ambient temperatures the manufactures try to keep capillary volumes very small in relation to bulb dimensions. If this does not reduce the error to within tolerances a specified compensating device must be used.
Negretti and Zambra Compensating Link
This device comprises a small chamber, constructed of the same material as the capillary, housing a core of metal with a negligible coefficient of expansion such as Invar Steel.
Fig. 10
The annular space between the Invar and the chamber walls is filled with the liquid of the system e.g. mercury. The chamber should have the same internal volume as the length of capillary over which it exercises its compensating influence, and at a certain predetermined temperature the invar occupies 5/6 of the internal volume. The mercury therefore only occupies 1/6 of the total space within the chamber.
A change of one degree in ambient temperature would cause the capillary (say stainless steel in this case) to expand linearly and cubically by say 1 unit. As mercury expands approximately 6 times as much as stainless steel then the indicator would detect the extra volume as a change in temperature at the bulb. However, with the compensating link inserted into the capillary line, the outer walls of the chamber, being made of stainless steel would expand, whereas the invar block would hardly change its dimensions at all. The result would be that some space would be created between the chamber walls and the invar block, and if the designer has done his arithmetic correctly then that space should just accommodate the excess volume of mercury created by the change in ambient temperature.
In some cases an invar wire is threaded along the whole length of the capillary line. Although this adds considerably to the cost of the system it does provide complete ambient temperature compensation.
An alternative compensating system is the one that uses a second capillary line and bourdon tube exactly the same in composition and length as the one connected to the bulb.
Fig 11
Fig 12
The compensating capillary is run close to the main one and terminates in the neighbourhood of the bulb. The bourdon tube to which it is connected acts in opposition, either directly, or, as is more often the case via linkages, to the main bourdon tube. In this way ambient temperature changes affect both systems equally and by virtue of this arrangement one cancels out the other.
Fig. 13
Finally there is the bourdon tube itself to consider; as stated this is also a thermometer in that it will react to a change in ambient temperature. In doing so it will introduce errors in indication. To overcome or compensate for this a bi-metallic strip or spiral can be used between the moving end of the tube and the pointer.
The arrangement is such that the movement of the bi-metallic strip or spiral, due to effects of temperature changes in its environment, opposes the action of the bourdon tube.
(The action and operation of bi-metallic devices will be fully explained in another section of these notes.)
Head Errors
When installing liquid in a metal thermometer it is obvious that if the bulb lies above the level of the gauge, the gauge will indicate a positive head error. Alternatively, if the bulb lies below the level of the gauge there will be a negative head error. The size of the error will depend on the height above or below the gauge and the density of the filling liquid (e.g. very approximately one foot of mercury exerts a pressure of 6 lbs f/ins2). From this you can see that even though the manufacturer calibrates the gauge under conditions similar to those specified by the customer, a slight change in installation made by the fitter can introduce an error in indication. However, should this occur it can easily be remedied, simply by removing and resetting the pointer, only the zero of the system having been affected.
Vapour Pressure Thermometers
The appearance of vapour pressure thermometers is almost always identical to that of the liquid expansion types. They comprise basically, a bulb, connected via a capillary line, to a bourdon tube actuated indicator. The major difference between the two systems lies in the way in which they are filled, and their principles of operation. In section one of these notes, an explanation was given about how liquids vaporise as their temperature is raised. Even at temperatures we normally refer to as ambient, in order of 20°C, most liquids produce vapour at a rate proportional to their temperature. As you may already have surmised, some liquids vaporise more readily than others (e.g. liquids like methylated spirits, petrol, carbon tetrachloride, ether etc., which we call volatile, produce vapours readily even at low temperatures.) The vapour produced by such liquids exerts its own pressure, increasing with temperature, this being particularly evident in a confined space. Therefore, by introducing some suitable vapour producing liquid into a sealed system we have a means of measuring temperature by relating it to the pressure of the vapour produced.
Principle of operation
Figure 15 shows two glass tubes immersed in a liquid, which does not produce vapours at low temperatures e.g. mercury. The tubes are connected to a vacuum pump and are exhausted. During the process the liquid in the reservoir will rise up the tubes by an amount proportional to barometric pressure. The stop-cocks are closed and both levels should be equal. If now some vapour producing liquid, such as carbon-tetrachloride, is added at the base of one leg of the system, it will rise, due to its lower density to the surface of the mercury. Vapours will be produced and, depending of course on how much liquid was added and the pressure and temperature, the added liquid will probably disappear. At the same time the vapour produced will exert a pressure on the mercury and depress its level. By adding more of the carbon tetrachloride, or whatever liquid is chosen, until some of it floats on the mercury, a saturated vapour condition can be reached and the mercury level will be depressed by the maximum amount proportional to the temperature.
Fig. 15
Fig. 16
The bulb is partially filled with a suitable vaporising liquid like Methyl Chloride; Freon; Alcohol; Toluene etc. (a full list will be given later). The amount of liquid used is determined by the range of temperature to be measured. One of the requirements of this type of thermometer is that at any given temperature within the range of the thermometer, there must always be a liquid/vapour surface interface within the bulb. The rest of the system is evacuated of air. Immediately the liquid will produce vapour, a drop in pressure having the same effect on it as would a rise in temperature, until an equilibrium of pressure is achieved throughout the system.
If the temperature of the bulb is now raised the liquid will at first start to expand, in much the same way as does the mercury in a ‘mercury in glass thermometer.’ Simultaneously the increased temperature will promote the production of more vapour molecules. These will leave the liquid and enter the space above it, due to molecules colliding with the vessel wall and cooling, some will lose energy and fall back into the liquid state. Initially however, more vapour molecules will be produced than there are returning. In this state the vapour is said to be unsaturated. After a short time lapse, the rate of production of vapour becomes equal to the rate at which molecules are returning to the liquid state. At this stage of equilibrium the vapour is said to be saturated. A saturated vapour means that the maximum amount of vapour at that given temperature has been achieved.
Under conditions of saturation, the vapour pressure is quite independent of the volume of liquid present in the bulb, it is solely dependent on temperature. The pressure generated by this action is transmitted by the capillary tube to the bourdon-tube that deflects proportionally.
Described above is a somewhat simplified view of the operation of a vapour pressure thermometer, especially the final statement concerning the transmission of the pressure signal to the bourdon-tube. In general the capillary line and the bourdon-tube will both be considerably cooler than the bulb. This being so, vapour formed in the bulb will condense in the capillary and bourdon-tube. Alternatively, if the bulb is being used to monitor temperatures below ambient the capillary and the bourdon-tube will be vapour filled, whilst the bulb contents would be mainly liquid except for a small volume of vapour locked between the liquid in the bulb and that in the line.
Fig. 17.
In both instances described above the fluid in the capillary, whether vapour or liquid, acts as a transmitter of information from bulb to bourdon-tube, without affecting it in such a way as to affect accuracy. However, if the temperature being measured by the bulb is close to and sometimes crossing the ambient temperature of the capillary line etc. serious lags and fluctuations of indication will be the result. These effects result from energy transformations involved in changes of state, liquid to vapour or vapour to liquid, in the capillary and bourdon tubes each time the temperatures ‘cross’.
Vapour pressure thermometers cover a considerable range of temperatures (-51°C to 260°C) as shown in the following table.
| Liquid | Boiling Point (°C) | Critical Temperature (°C) | Typical Range (°C) |
| Argon | -185.7 | -122.0 | Very Low Temperatures Down To -253 |
| Methyl Chloride | -23.7 | 143.1 | 0-50 |
| Freon | -29.2 | | |
| | -10.0 | 157.2 | 30-120 |
| Alcohol | 78.5 | 243.1 | 82-205 |
| Toluene | 110.5 | 320.6 | 150-250 |
| Ether | 34.5 | 193.8 | 60-160 |
| Butane | -0.6 | 154.0 | 20-80 |
The relevance of the boiling point and the critical temperatures, given in the table, is that the maximum temperature at which a given liquid can be used in vapour thermometry, must be below its critical temperature. Similarly, the minimum temperature at which the liquid may be used must be above its boiling point, (below this the liquid would not produce vapour).
The Critical Temperature of a gas is that temperature above which the gas will not change state - to a liquid - regardless of its pressure.
You will also note from the graph lines produced when vapour pressure is plotted against temperature, that the relationship is non-linear. The graduations on the gauge face of a vapour pressure thermometer will therefore also be non-linear, in each case they will be cramped at the start of the scale gradually widening over the scale span.
Head errors can affect the accuracy of indication of this class of thermometer in exactly the same manner as was the case with liquid expansion thermometers. Vapour pressure thermometers are also affected by changes in barometric pressure, unlike liquid expansion thermometers, however the effect will only be to cause a slight zero error that can be easily remedied.
Dual filled vapour pressure system
Yet again the construction of the system is the same as the liquid in metal thermometers except that, as shown in the diagram, the capillary tube is extended into the bulb.
Fig 18.
The practical application of this principle works in exactly the same manner. The vapour producing liquid floats above the transmitting fluid, above it there is a space in which the vapours are formed. A change in temperature will cause production of vapour until the saturated state is reached. The pressure of the vapour will react on the liquid producing it, which in turn will act upon the surface of the transmitting fluid a certain amount of which will be displaced from the bulb into the capillary and bourdon tube.
As the vapour produced against temperature is not a direct relationship, the scale of the associated indicator will be non-linear, graduations being cramped at the lower end of the scale.
Lags with Thermometer Bulbs
A second order lag occurs in all of the liquid in metal and vapour thermometers so far described. The cause of this is due mainly to the method of construction of the bulb and its protective pocket.
Fig. 19
The slow response to temperature change starts at the area called the boundary layer. This is a region of heat formed around the pocket that tends to resist a change of temperature. The pocket itself has a certain capacity for heat and will, therefore, take time to respond to a temperature change in its surroundings. The air space between the pocket and the bulb will resist a change in temperature and the bulb and its filling will also have a considerable capacity for heat. Taking all of these features in to account, the system's response to a change in temperature can be compared to an R.C. circuit.
Fig 20
If the system is subjected to a sudden or step change in temperature there will be a time constant involved, which is the time taken for the temperature (T2 in Fig. 21) to reach 63.2% of its final value. (T1 in Fig. 21). Figure 22 shows the exponential curve obtained by plotting T2 against time.
From the graph the nature of the lag can clearly be seen.
Fig 21.
GAS THERMOMETERS
Gas Expansion
The molecules of a gas are already in free random motion, there being no cohesive force between them. As a gas always completely fills its containing vessel, the coefficients of expansion are very difficult to measure directly. However, the effects of gas expansion are almost always readily visible. As an example, consider inflating a car tyre with a foot pump.
a) A large volume of air is forced under pressure into a small space, there is a large reduction in volume.
b) The force required to operate the pump increases as the tyre inflates i.e. the pressure is increased.
c) Due to the factors expressed in (a) and (b) there is a marked rise in the temperature of the pump.
Therefore, it can be safely assumed that there is a definite relationship between the volume, pressure and temperature of a gas. This relationship is expressed by the combined gas equation (a combination of Boyle's and Charles' Laws) i.e.
P.V. = R.T.
Volume
Where P = Absolute pressure, V = Mass
T = Absolute temperature, R is the constant for any particular gas.
Since the volume and the mass of gas in a gas thermometer are of a constant value and R is also a constant, the pressure of the gas is proportional to its temperature. Therefore, when a gas in metal thermometer bulb is immersed into a fluid whose temperature is to be measured, the pressure change caused in the gas is proportional to the temperature and the Bourdon tube shown in figure 23, will act directly as a pressure responsive device.
Fig. 22
Ambient Temperature Compensation
The expansion of a gas per unit rise in temperature relative to the bulb, capillary etc; is extremely high. Therefore, it might be expected that the bulb size would be smaller than a liquid in metal thermometer of equivalent range. However, it must be considered that the gas enclosed in the capillary and Bourdon tube, or bellows, will also respond to ambient temperature changes. (As the gas in metal system is based on changes in pressure and not volume, the compensation devices used with liquid in metal thermometers cannot be used here.)
Effective ambient temperature compensation for gas in metal thermometers is complicated, since the error caused by a one degree change in ambient temperature varies directly with the bulb temperature i.e. as the bulb temperature rises the error increases and vice versa. To overcome this, the volume of the bulb is so large in comparison with the capillary and pressure sensitive element that errors due to ambient temperature changes are reduced to within specified limits. Simply, the volume of the bulb is so great that the change in pressure caused by unit rise in temperature deflects the Bourdon tube and attached pointer by a considerable amount. As the volume of the capillary and pressure sensitive element are considerably smaller than the bulb, one unit change of temperature will only cause the pointer to move fractionally.
Suitable Gases
Nitrogen is the most common gas used as the filling medium. It is inert has a high coefficient of cubical expansion and is easily obtainable.
Head Errors
These are so small as to have negligible effect on readings.
Barometric Pressure Errors
Again these have very minor effects of the accuracy of readings especially where the
system is originally charged at a high pressure.
SECTION 4.
1. Bi-Metallic Thermometers
2. Resistance Thermometers (including Thermistor Thermometers)
3. Thermocouples
Bi -Metallic Thermometers
The basis of this form of temperature sensitive device is a sandwich of two strips of dissimilar metals. One of the pair will have a coefficient of expansion much greater than the other, example Brass (coefficient of expansion = 19 x 10-6) and Invar (coefficient of expansion = 1.5 x 10-6). The two metals are joined together along their length and are fixed immovable at one end and free at the other. When heat is applied, the free end of the sandwich will deflect either upwards or downwards; the direction of movement will depend upon which of the two is on the top. The degree of deflection is proportional to the temperature.
Fig. 23.
If the strip was wound into a helical spiral form, again with one end fixed and the other free to move, on heating the free end will move in a rotary manner. The amount of rotation is proportional to the temperature.
Fig. 24
The spindle is attached to the free end of the helix, formed from the bi-metallic sandwich, and carries a pointer at its free end, the scale is calibrated in terms of temperature. Any tendency for the strip to lengthen as it turns is compensated for by the design of the helix. The lateral movement of one turn being counteracted by the same amount of lateral movement in the opposite direction, in another. One major advantage of this thermometer is that it needs no bearings, only a simple spindle centralising disc (as shown). It is therefore very robust and can be used for local indication of temperature in areas where vibration would preclude the use of other thermometers.
The disadvantages of it are very much that of most thermometers that have to come into physical contact with the media whose temperature is being measured. It measures the temperature of its surroundings by absorbing heat from them and eventually reaches the same temperature, at this point the thermometer actually measures its own temperature. Due to this, and the fact that the device is usually immersed in a pocket, with an air space between it and the pocket, there will be a lag in time between temperature change and indication.
Finally, the accuracy of bi-metallic thermometers is generally +/-1 % range and this is not affected by changes in ambient conditions of either temperature or pressure.
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