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Gary S. Coyne - A Practical Guide to Materials, Equipment, and Technique.pdf
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150

Measurement

space between the two glass layers prevents heat transfer by both conduction and convection. Finally, the walls of the Dewar are silvered to prevent loss of heat by radiation and absorption.

2.5.3 Expansion-Based Thermometers

Because most materials expand as heat increases, the measurement of such expansion is used as a basis of heat measurement. Because the expansion of most materials is reasonably constant across a given range of temperatures, the amount of expansion can be quantified by a coefficient of expansion formula.

A linear coefficient of expansion is based on the following formula:

a =L-f£

(2.3)

LAt

 

where a = linear expansion

Lt = final length

LQ = original length

At = change in temperature

A volumetric coefficient of expansion is based on the following formula:

where p = volume expansion

Vt = final volume

VQ = original volume

At = change in temperature

A pressure coefficient of expansion is based on the following formula:

where (3V = volume expansion

Pt = final volume

Pg = original volume

At = change in temperature

As can be seen, all coefficients of expansion are based on the amount of size change divided by the product of the original size and the change of temperature that occurred. The result of this type of equation can be calculated for any material. Because a coefficient of expansion is not necessarily consistent across a range of temperatures, coefficient of expansion tables (or listings) will be an average

Temperature 2.5

151

Metal with

greater

 

 

 

coefficient

of

— * - ^ | &

Metal with

expansion

^ffi*

|esser

coefficient of expansion

Fig. 2.29 Bimetal thermometers use two metals of different expansion to create spiral thermometers.

across a given temperature range. For example, to state that the coefficient of expansion of glass is O.OOOOO33 means nothing unless you specify that you are talking about laboratory borosilicate glass in the temperature range of 0 to 300°C.

It is critical to be precise about the composition and/or nature of the material being analyzed. By changing the composition of any material, even a small amount, the coefficient of expansion can be altered significantly.

2.5.4 Linear Expansion Thermometers

Linear expansion is most commonly used in bimetal spiral thermometers, which use two metals with different coefficients of expansion (see Fig. 2.29). The two metals can be welded, soldered, or even riveted together. As the metals are heated, the metal with the greater expansion will cause the spiral to flex open or close depending on which side the metal with the greater coefficient of expansion is on. A reverse in temperature will cause a commensurate reversal in the flexing.

Spiral thermometers are easily recognized as part of most room thermostats. They also are used in meat and oven thermometers.

2.5.5 Volumetric Expansion Thermometers

When you mention thermometers, volumetric expansion thermometers are what typically come to mind (see Fig. 2.30). The material that expands within a volumetric expansion thermometer is typically mercury or (ethyl) alcohol. Another name for a volumetric expansion thermometer is a liquid-in-glass thermometer.

The parts of a standard liquid-in-glass laboratory thermometer are as follows:*

1. The bulb. The storage area for the liquid. The size of the bulb is based on the size of the thermometer.

*Not all liquid-in-glass thermometers have all these parts.

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Measurement

2.The stem. The main shaft of the thermometer.

3.The capillary. The channel that carries the liquid up the stem. The narrower the capillary, the greater the accuracy that can be achieved. However, at a certain point, temperature readings are affected by surface tension of the liquid and the glass of the thermometer, so manufacturers are limited as to how accurate a liquid-in-glass thermometer can be.

4.The main scale. This scale is where the temperature is read. Some thermometers are designed to read a specific temperature range for a specific test. A doctor's thermometer is one example of this type of scale.

5.The immersion line. Sets the placement depth for partial-immersion thermometers.

6.The expansion chamber. An expanded region at the top of the capillary designed to prevent a buildup of excessive pressure from the expanding liquid.

7.The contraction chamber. Used to reduce the necessary length of a thermometer when the desired temperature range would otherwise require a very long thermometer.

8.The auxiliary scale. Required on thermometers whose calibrated region does not include an IPTS (International Practical Temperature Scale) calibration point. For example, say you have a thermometer with the range of 20° to 80°C. The auxiliary scale would include the range of

 

Contraction

Immersion

 

Expansion

Bulb

chamber

line

stem

chamber

Capillary Auxiliary

scale

M a i n

S c a l e

Fig. 2.30 * The principle features of the solid-stem liquid-in-glass thermometer. From Figure 3 from the NBS Monograph 90, "Calibration of Liquid-in-Glass Thermometers," by James F. Swindells, reprinted courtesy of the National Institute of Standards and Technology, Technology Adminstration, U.S. Department of Commerce. Not copyrightable in the United States.

Temperature 2.5

153

-5° to 5°C so that the thermometer could be verified against the triple point of water.

Along the shaft of the thermometer, above the liquid in the thermometer capillary, is an air space typically filled with nitrogen. The nitrogen is under pressure to prevent condensation of the liquid in the upper portions of the thermometer. The pressure of the gas in the confined space will vary according to changes in temperature. Therefore, exposing the air space of a thermometer to unusually hot or cold temperatures can affect readings.

Within the bulb is a large repository of the expansion liquid. However, be aware that you cannot obtain an accurate temperature reading by placing just the thermometer bulb in the test material. When only the thermometer's bulb is under the heat's influence, the amount of expansion (or contraction) of the liquid beyond the bulb region is unknown. Any liquid not immersed in the sample being measured is not under the same influence as the liquid that is immersed. For example, if the bulb were placed in a boiling solution while the stem was in an arctic frost, the liquid in the stem would be contracted more than it would be if the stem was in a warm room.

It is possible to compensate on the calibration lines for these limitations to a certain degree. To make this compensation, three different types of liquid-in-glass thermometers have been designed with three different immersion requirements. They are:

1.Total-immersion thermometers. Thermometers that require the liquid in the stem to be completely immersed in the measured liquid. The placement of the thermometer must be adjusted during use so that the liquid in the bulb and stem are always immersed in the sample. These thermometers are the most accurate.

2.Complete-immersion thermometers. Thermometers that require the entire thermometer to be immersed in the measured liquid.

3.Partial-immersion thermometers. Thermometers that require only the bulb and a specified portion of the stem to be immersed in the measured liquid. There will be a mark or a line on the thermometer stem designating how far into the material the thermometer must be placed. The standard partial-immersion thermometer has a line 76 mm (3 inches) from the end of the bulb.

There are many specialized thermometers available. Some are used to obtain maximum and minimum temperatures, while others are used for specific tests. The ASTM has defined a series of special partial-immersion thermometers for specific tests. These thermometers are identified as ASTM thermometers and are marked with a number followed by a "C" (for centigrade) or an "F" (for Fahrenheit). The number is strictly an identifying number with no relation to the temper-

154 Measurement

ature range the thermometer can read. Because these thermometers are specialized, they have immersion lines at unique locations on their stems.

Some thermometers have standard taper joints or ridges on the body of the glass to fit specific equipment such as distillation or melting point apparatus. These thermometers provide two types of position control. They set the bulb at just the right height within specialized equipment and ensure that the liquid column is sufficiently immersed in the heated sample. However, most thermometers do not have built-in controls and the user must not only select the right thermometer, but also adjust the thermometer to its proper level within the equipment.

The use of complete-immersion thermometers is fairly obvious. However, it is not always possible or practical to completely immerse a thermometer. For example, if the solution is not transparent, it is not possible to see the temperature.

There are tables that provide correction values for readings made when totalimmersion thermometers are not sufficiently immersed. In the absence of such tables, use the formula for calculating stem correction given in the following equation.

Stem correction = Kn{tb - ta)

(2.6)

where K = the differential expansion of the liquid

n = number of units (in degrees) beyond the immersed stem section

tb = is the temperature of the bath

ts = is the temperature of the liquid column (a second thermometer is required for this reading)

Some general values for K* are

K = 0.00016 for centigrade mercurial thermometers and

K = 0.001 for centigrade organic liquid thermometers

To better understand stem corrections, consider the following example:

Thermometer reading:

105°C

Temperature of thermometer stem:

37°C

Number of units (in degrees) of stem

 

beyond immersed liquid:

43

Stem correction = 0.00016 x 43(105°C -

37°C)

Stem correction = 0.47°C

 

Final thermometer reading:

105.47°C

Although this stem correction is relatively small, stem corrections of 10 to 20 degrees are not out of the question. Stem correction may be unnecessary depending on the difference between the sample and room temperature, the temperature

'Although the specific value of K varies as the mean temperature of the thermometer liquid varies, these values are sufficient for most work.

Temperature 2.5

155

ranges you are working with, or your tolerance requirements. It is a good practice to see what the stem correction would be to see if it is significant or not before assuming that it is not necessary.

If you make stem corrections, be sure to indicate this fact in any work you publish. Likewise, when temperature measurements are cited in literature and no stem correction is mentioned, it is safe to assume that no stem correction was made.

Partial-immersion thermometers have a greater tolerance (and therefore less precision) than total immersion thermometers.* Interestingly enough, when a total immersion thermometer is only partially immersed and no stem correction is made, the accuracy is likely to be less than a partial-immersion thermometer.

The tolerance ranges for all thermometer designs are quite different from tolerance ranges for other calibrated laboratory equipment such as volumetric ware (see Sec. 2.3). Tolerance varies mostly with graduation ranges and secondly with whether the thermometer is of totalor partial-immersion design. Table 2.32 shows NIST tolerance and accuracy limitations. Remember that tolerance is a measure of error (±), or how different a measurement is from the real value. A large tolerance indicates less accuracy, whereas a small tolerance indicates greater accuracy. Accuracy is the agreement of the thermometer reading to the actual temperature after any correction is applied. Conditions that can affect a thermometer's accuracy include variations in capillary diameter and external pressure variations on the bulb.

2.5.6 Shortand Long-Term Temperature Variations

Thermometers do not maintain their accuracy over time. Depending on how they are used, they are subject to short-term or permanent changes in measurement. The problem stems from the fact that the density of glass and the volume of the bulb change as temperature changes. If a thermometer is brought to a high temperature and allowed to cool very fast, its density may not return to the original density. Under these conditions the glass may "set" to a new density while cooling and may thereafter be too viscous to return to the originally manufactured density. By selecting special types of glass, thermometer designs, and manufacturing techniques, manufacturers limit the amount of temperature-caused errors as much as possible.*

Generally, using a thermometer only within the scale range for which it was designed should limit changes. Overheating a thermometer (not designed to be used for high temperatures) above 260°C should be avoided. When change occurs, it typically results in a low reading that is often called an ice-point depression. During temperature-caused changes, the bulb increases in size as the temper-

*Because partial-immersion thermometers are designed for a specific test, uniformity of procedure is more important than overall accuracy.

trrhere is likely to be changes in the stem volume as well, but the amount of those changes is likely to be negligible.

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Measurement

Table 2.32 Tolerance (±) and Accuracy for Mercury Thermometers"

Temperature

range in

degrees

0 up to 150°

Oupto 150°

0 up to 100°

Oupto 100

Above 100

up to 300

Oupto 100

Above 100

up to 200

0 up to 300

Above 300

up to 500

0 up to 300

Above 300

up to 500

Total Immersion

Partial Immersion

Graduatio intervalin degrees

+ °C

Accuracyin degrees

Graduation intervalin degrees

±°C

Accuracyin degrees

 

 

 

 

Thermometers graduated under 150°C

 

 

1.0 or 0.5

0.5

0.1 to 0.2

1.0 or 0.5

1.0

0.1 to 0.3

0.2

0.4

0.02 to 0.05

1.0 or 0.5

1.0

0.1 to 0.5

0.1

0.3

0.01 to 0.03

 

 

 

Thermometers graduated under 300°C

 

 

1.0 or 0.5

0.5

0.1 to 0.2

1.0

1.0

0.1 to 0.3

1.0 or 0.5

1.0

0.2 to 0.3

1.0

1.5

0.5 to 1.0

0.2

0.4

0.02 to 0.05

 

 

 

0.2

0.5

0.05 to 0.1

 

 

 

Thermometers graduated above 300°C

 

 

2.0

2.0

0.2 to 0.5

2.0 or 1.0

2.5

0.5 to 1.0

2.0

4.0

0.5 to 1.0

2.0 or 1.0

5.0

1.0 to 2.0

1.0 or 0.5

2.0

0.1 to 0.5

 

 

 

1.0 or 0.5

4.0

0.2 to 0.5

 

 

 

"From Tables 5 and 7 from Liquid-in-Glass Thermometry, NBS Monograph #150by Jacquelyn A. Wise. Printed by the U.S. Government Printing Office. Reprinted courtesy of the national Institute of Standards and Technology, Technology Adminstration, U.S. Department of Commerce. Not copyrightable in the United States.

ature increases, but it does not contract to its original size as the temperature returns to normal. Thereafter, once recalibrated at the ice point, the thermometer temperature will always read less than the real temperature.

These changes may be either temporary or permanent, often depending on whether the thermometer was cooled slowly through the higher-temperature regions, or simply removed and haphazardly laid on a table. Depending on a thermometer's glass quality, the hysteresis* effect can cause from 0.01 to 0.001 "of a degree per 10 degrees difference between the temperature being measured and the higher temperature to which the thermometer has recently been exposed."15

Hysteresis is when a material is stretched or distorted to a new position or shape and does not return to its original position or shape.

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