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144

Measurement

Table 2.28 Tolerance by Class ofWeights (continued)

 

Class 4a

 

 

Class Sb

 

 

Class 6C

 

 

Tolerance (g)

 

Tolerance (g)

 

Tolerance (g)

Weight (kg)

Individual

Group

Weight (kg)

Individual

Group

Weight (kg)

Individual

Group

(mg)

 

 

(mg)

 

 

 

 

 

500

0.16

 

500

0.38

 

 

 

 

300

0.14

0.65

300

0.30

1.40

 

 

 

200

0.12

200

0.26

 

 

 

 

 

 

 

 

100

0.10

 

100

0.20

 

 

 

 

50

0.085

 

50

0.16

 

 

 

 

30

0.075

0.363

30

0.14

0.65

 

 

 

20

0.070

20

0.12

 

 

 

 

 

 

 

 

10

0.060

 

10

0.10

 

 

 

 

5

0.055

 

5

0.080

 

 

 

 

3

0.052

0.255

3

0.070

0.325

 

 

 

2

0.050

2

0.060

 

 

 

 

 

 

 

 

1

0.050

 

1

0.050

 

 

 

 

"From the ASTM document E 617, Table X5.1, Class 4 Metric, reprinted with permission. *From the ASTM document E 617, Table X6.1, Class 5 Metric, reprinted with permission. Trom the ASTM document E 617, Table X7.1, Class 6 Metric, reprinted with permission.

2.5Temperature

2.5.1TheNature of Temperature Measurement

Most of the measurements discussed in this chapter deal with physical properties, such as length, volume, or weight. Measurement of these properties canbe made directly. Temperature is different because it is anenergy property, and energy cannot be measured directly. However, we can quantify the effect that one body's energy (in this case heat) has on thephysical properties of another body, and we can measure that physical effect.

Unfortunately, heat energy does not have the same percentage of effect onall materials in the same way. For example, heat makes most materials expand, but few materials, if any, expand thesame amount for an equal amount of heat. Thus, the size increase for onematerial (for a given amount of heat change) is unlikely

Temperature 2.5

145

to equal the size increase for another material (with the same amount of heat change).

On the other hand, it is possible to obtain the same temperature from two different materials if they are calibrated the same. This operation is done as follows: take two different materials and heat them to a specific (and repeatable) temperature. Place a mark on some reference material that has not expanded (or contracted). Then heat the materials to another specific and repeatable temperature and place a new mark as before. Now, if equal divisions are made between those two points, the specific temperature readings along the calibrated region should be the same even if the actual changes in lengths of the materials are different.

An interesting aspect about temperature measurement is that calibration is consistent across different types of physical phenomena. Thus, once you have calibrated two or more established points for specific temperatures, the various physical phenomena of expansion, resistance, emf, and other variable physical properties of temperature will give the same temperature reading.

Table 2.29 The International Practical

Temperature Scale of 1968 for K and °Ca

Material and Condition

K

°C

of Fixing Point*

 

 

Hydrogen, solid-liquid-gas equilibrium

13.81

-259.34

Hydrogen, liquid gas equilibrium at 33,330.6

17.042

-256.108

Pa (25/76 standard atmosphere)

 

 

Hydrogen, liquid-gas equilibrium

20.28

-252.87

Neon, liquid-gas equilibrium

27.102

-246.048

Oxygen, solid-liquid-gas equilibrium

54.361

-218.789

Argon, solid-liquid-gas equilibrium

83.798

-189.352

Oxygen, liquid-gas equilibrium

90.188

-182.962

Water, solid-liquid-gas, equilibrium

273.16

0.01

Water, liquid-gas equilibrium

373.15

100.00

Tin, solid-liquid equilibrium

505.1181

231.9681

Zinc, solid-liquid equilibrium

692.73

419.58

Silver, solid-liquid equilibrium

1235.08

961.93

Gold, solid-liquid equilibrium

1337.58

1064.43

"From the ASTM document E 77, Section 3.2.2, reprinted with permission.

^Except for the triple points and one equilibrium hydrogen point (17.042 K), the assigned values of temperature are for equilibrium states at a pressure:

p0 = 1 Standard atmosphere (101,325 Pa)

'Although not all of these temperature measurement techniques provide a uniform linear measurement, the variations are known and can be calibrated and accounted for.

146

Measurement

Table 2.30 Secondary Reference Points of the IPTS-68 in °Ca

Temperature of

°C

Equilibrium between solid carbon dioxide and its vapor

-78.476

Freezing mercury

-38.862

Freezing water

0

Triple point of phenoxy benzene (diphenyl ether)

26.87

Triple point of benzoic acid

122.37

Freezing indium

156.634

Freezing cadmium

321.108

Freezing lead

327.502

Boiling mercury

356.66

Freezing aluminum

660.46

aFrom the ASTM document E 77, Section 3.2.3, reprinted with permission.

The establishing, or fixing, of points for temperature scales is done so that anyone, anywhere can replicate a specific temperature to create or verify a thermometer. The specific temperature points become (in effect) the International Prototypes for heat. The General Conference of Weights and Measures accepted the new International Practical Temperature Scale of 1968 (IPTS 1968) with 13 fixed points (see Table 2.29). The new (IPTS 1968) scale was a revision from the IPTS 1948 (which had been amended in 1960).

There are two reasons for having many points with which to fix a temperature scale. One is that, as mentioned before, few materials affected by heat change length equally or linearly. Having many points allows scales to be calibrated in short ranges, where nonlinearity is less likely to have a pronounced effect. The second is that few, if any, thermometers can read all temperatures. Most thermometers are calibrated to read a small range of temperatures. Many "fixing" points allows for a robust system of calibration. Unfortunately, most of these points require expensive equipment, and even then they are not easy to obtain and/or verify.

However, in addition to these primary reference points, a secondary series of reference points was established by the IPTS-68 (see Table 2.30). These secondary points can more easily be used (than the primary temperature points) for testing temperature equipment such as liquid-in-glass thermometers. They are useful because they require less equipment and are therefore easier to obtain. Remember that these points are secondary standards and should not be considered primary standards.

Note that Table 2.29 refers to the temperature "K" or the temperature "°C." Both of these measurement scales are temperature measurement units. There is another scale, also known as "K," which is the unit of measurement for the Kelvin thermodynamic scale. Because heat is a thermodynamic property, temperature

Temperature 2.5

147

measurements should be capable of easy referral to the Kelvin temperature "K," more properly known as the Thermodynamic Kelvin Temperature Scale (TKTS). One degree K is exactly equal to the thermodynamic unit of K, and likewise is exactly equal to one degree C. Otherwise, any specific temperature in one scale can easily be converted to another by the relation

K = °C + 273.15

Values given in Kelvin temperature (TKTS) are designated as "T." Values given in degrees centigrade (°C) are designated as "t." When either T or t is used to express temperature from the International Practical Temperature Scale, it should be designated as T68 or t68*For example, if you were to refer to the freezing point of mercury, you would write -38.862%g.

2.5.2 The Physics of Temperature-Taking

When we measure the temperature of a body, we are depending on the heat of the body to be transferred to (or from) our measuring device. Once the heat has been taken to (or from) our measuring device, any physical changes in that device are interpreted as a temperature change. The process where we analyze the effects caused by a property to determine the amount of that property is known as inferred measurement. For temperature we have a variety of physical properties from which to infer the amount of energy (heat) that a given object has.

Measurement of temperature (or any energy property) has one major difference from measurement of physical materials: It is not cumulative. To measure the length of a room, you can lay several meter sticks end to end. The sum of the number of meter sticks will be the length of the room. Temperature, however, is not cumulative. If you have a liquid that is hotter than the range of temperatures measurable on one thermometer, you cannot use a second thermometer to obtain the remaining temperature.

Because the temperature ranges and conditions of a system can vary, a variety of materials have been incorporated into different types of thermometers. The following is a list of common thermometer types and the property measured in each to obtain a heat measurement.

1. Liquid-in-glass thermometer. Volume of liquid increases as heat increases.

2.Gas or vapor at constant volume. Pressure of gas increases as heat increases.

3.Dilatometer (or bimetal coil). As heat rises, the length of one metal expands more than the length of the other metal.

The subscripted "68" is used to indicate that these temperatures conform to the IPTS-68 guidelines.

148

 

 

Measurement

Table 2.31 Ranges of Common Temperature Measuring Devices0

Measuring Device (method)

Approximate Ranges

Mercury in glass thermometer

-38°C

to

400°C

Alcohol in glass thermometer

-80°C

to

100°C

Constant volume gas thermometer

4K

to

1850 K

Bimetallic thermometer

-40°C

to

500°C

Thermocouple

-250°C

to

1600°C

Resistance thermometer

0.8K

to

1600°C

Optical pyrometer

600°C

to

up

Total radiation pyrometer

100°C

to

up

Speed of sound

no limits

 

 

Thermodynamic

no limits

 

 

aFrom Robert L. Weber, Heat and TemperatureMeasurement, Prentice-Hall © 1950,Englewood Cliffs, NJ, p. 7, with permission.

4.Platinum wire. Electrical resistance of the wire increases as heat increases.

5.Thermocouple. Thermal emf* goes up as heat increases.

Table 2.31 displays some common temperature ranges of a variety of thermometers.

In addition to desired temperature ranges, variables affecting the selection of a thermometer may include:

1. The material to be studied. Is it acidic, alkaline, oxidizing, flame, plasma, hydrocarbon solvent, or conducting? One environment may affect one type of thermometer, but have no effect on a different type of thermometer.

2.The amount of material to be studied. The smaller the sample, the more you need to be concerned about the heat capacity of the thermometer. More specifically, a large thermometer with a large heat capacity can change the temperature of a small sample, whereas a small thermometer with a small heat capacity will read the temperature of a small sample without changing the temperature.

3.The environment. Is is cramped, dusty, wet, hot, cold? Some thermometers require very controlled environmental conditions to properly operate.

4.The cost. Platinum resistance thermometers are incredibly accurate over

*"emf' stands for electromotive force, which is further discussed in Subsection 2.5.11.

Temperature 2.5

149

a wide temperature range. Unless you need the accuracy they can provide, you might be wasting your money.

5. The amount of support equipment required. A thermocouple is not very expensive, but the controller can be. Similarly, constant volume gas thermometers can be very bulky and cumbersome.

The reason for the variety of thermometers is that no one type is economical, practical, accurate, or capable of measuring all temperatures in all conditions. Selecting the right thermometer is a matter of analyzing your needs for a given job and identifying what thermometer best satisfies those needs.

As stated before, temperature (or heat) is a form of energy. Heat always travels from hot to colder bodies until thermal equilibrium is achieved. Thus, ice in a drink does not cool the drink. Rather, the heat in the drink is transferred to the cold ice, causing the ice to warm and melt. What remains is a "colder" drink because heat energy was lost melting the ice.

The significance of this "ice story" leads us to an important principle of temperature measurement: The act of taking an object's temperature changes the object's temperature because we depend on some amount of heat being given off or absorbed by the object to affect our measuring device. If the object being studied is very large in comparison to the temperature measuring device, this effect is negligible. If the material being studied is in a dynamic system (with heat constantly being introduced), the effect is irrelevant. However, if a small, static amount of material is being studied, the thermometer may have a significant effect. You need to select a temperature recording device that will have the least amount of effect on the sample's temperature. Optimally, you want the heat capacity of the temperature measuring device to be so much smaller than the heat capacity of the material being studied that it provides an insignificant change.

Temperature (heat) is transferred from one body (or region) to another by three thermal processes, conduction, convection, and radiation-adsorption, or some combination of the three.

1.Conduction is the transfer of heat from one body to another by molecules (or atoms) in direct contact with other molecules (or atoms). This mechanism explains how a coffee cup is heated by hot coffee.

2.Convection is the physical motion of material. Examples of this process would include hot air (or water) rising and cold air (or water) sinking. Rigid materials cannot have convection.

3.Radiation and absorption are the results of heat energy being transformed into radiant energy (the energy, for example, that gives us a suntan).

One excellent example of an energy-efficient vessel is the Dewar. The Dewar effectively limits heat transfer by limiting all three heat transport mechanisms. Because its glass is a poor conductor of heat, the liquids on the inside of the Dewar do not readily conduct their heat to the outside surfaces. The vacuum in the

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