1.3 Measurement

Key ConceptsWhy is scientificnotation useful?

What units doscientists use for theirmeasurements?

How does the precisionof measurements affectthe precision of scientificcalculations?

Vocabulary◆ scientific notation◆ length◆ mass◆ volume◆ density◆ conversion factor◆ precision◆ significant figures◆ accuracy◆ thermometer

How old are you? How tall are you? The answers to these questionsare measurements. Measurements are important in both science andeveryday life. Hardly a day passes without the need for you to measureamounts of money or the passage of time. It would be difficult to imag-ine doing science without any measurements.

Using Scientific NotationHow many stars do you see in Figure 11? There are too manyto count. Scientists often work with very large or very smallnumbers. For example, the speed of light is about 300,000,000meters per second. On the other hand, an average snail hasbeen clocked at a speed of only 0.00086 meter per second.

Instead of having to write out all the zeroes in these num-bers, you can use a shortcut called scientific notation.Scientific notation is a way of expressing a value as the prod-uct of a number between 1 and 10 and a power of 10. Forexample, the number 300,000,000 written in scientific nota-tion is 3.0 � 108. The exponent, 8, tells you that the decimalpoint is really 8 places to the right of the 3.

For numbers less than 1 that are written in scientific nota-tion, the exponent is negative. For example, the number0.00086 written in scientific notation is 8.6 � 10�4. The neg-ative exponent tells you how many decimals places there areto the left of the 8.6. Scientific notation makes very largeor very small numbers easier to work with.

Measurement

Why is scientific notation useful?

a. ?

b. ?

Reading StrategyPreviewing Make a table like the one below.Before you read the section, rewrite the greenand blue topic headings as questions. As youread, write answers to the questions.

14 Chapter 1

Figure 11 Scientists estimate thatthere are more than 200 billionstars in the Milky Way galaxy.Applying Concepts What is thisnumber in scientific notation?

14 Chapter 1

FOCUS

Objectives1.3.1 Perform calculations involving

scientific notation andconversion factors.

1.3.2 Identify the metric and SIunits used in science andconvert between commonmetric prefixes.

1.3.3 Compare and contrastaccuracy and precision.

1.3.4 Relate the Celsius, Kelvin, andFahrenheit temperature scales.

Build VocabularyLINCS Use LINCS to help students learnand review section vocabulary, includingscientific notation: List parts that theyknow (Scientific means “related toscience,” and notation means “a systemof symbols.”); Imagine a picture(Students might visualize a series ofsymbols written in a table.); Note asound-alike word (Notation is similar tonote.); Connect the terms in a sentence(The scientist used scientific notation tocommunicate her results.);Self-test (quiz themselves).

Reading StrategyPossible answers may include:a. What is SI? SI is a set of metricmeasuring units used by scientists.b. What are base units? Base units arethe fundamental units of SI. There areseven SI base units, including the meter,the kilogram, the kelvin, and the second.

INSTRUCT

Using ScientificNotationUse VisualsFigure 11 Ask, Would it be easy tocount the number of stars shown inthe photo? (No) Why might usingscientific notation be appropriatewhen counting the number of stars?(The number of stars could be very large.)Visual, Logical

L1

2

L2

L2

Reading Focus

1

Section 1.3

Print• Laboratory Manual, Investigations 1A

and 1B• Reading and Study Workbook With

Math Support, Section 1.3 andMath Skill: Using Scientific Notation

• Math Skills and Problem SolvingWorkbook, Section 1.3

•Transparencies, Section 1.3

Technology• Interactive Textbook, Section 1.3• Presentation Pro CD-ROM, Section 1.3• Go Online,

Planet Diary, Universal measurements;PHSchool.com, Data sharing

Section Resources

Using Scientific NotationA rectangular parking lot has a length of 1.1 � 103 meters and awidth of 2.4 � 103 meters. What is the area of the parking lot?

Read and UnderstandWhat information are you given?

Length (l) � 1.1 � 103 m

Width (w) � 2.4 � 103 m

Plan and SolveWhat unknown are you trying to calculate?

Area (A) � ?

What formula contains the given quantities andthe unknown?

A = l � w

Replace each variable with its known value.

A � l � w � (1.1 � 103 m)(2.4 � 103 m) � (1.1 � 2.4) (103 � 3)(m � m) � 2.6 � 106 m2

Look Back and CheckIs your answer reasonable?

Yes, the number calculated is the product of the numbersgiven, and the units (m2) indicate area.

1. Perform the followingcalculations. Express youranswers in scientific notation.

a. (7.6 � 10�4 m) �(1.5 � 107 m)

b. 0.00053 � 29

2. Calculate how far light travels in 8.64 � 104 seconds. (Hint:The speed of light is about 3.0 � 108 m/s.)

Science Skills 15

When multiplying numbers written in scientific notation, youmultiply the numbers that appear before the multiplication signs andadd the exponents. For example, to calculate how far light travels in500 seconds, you multiply the speed of light by the number of seconds.

(3.0 � 108 m/s) � (5.0 � 102 s) � 15 � 1010 m � 1.5 � 1011 m

This distance is about how far the sun is from Earth.When dividing numbers written in scientific notation, you divide

the numbers that appear before the exponential terms and subtract theexponents. For example, to calculate how long it takes for light fromthe sun to reach Earth, you would perform a division.

� � 1011 � 8 s � 0.50 � 103 s � 5.0 � 102 s1.53.0

1.5 � 1011 m3.0 � 108 m/s

For: Links on universalmeasurements

Visit: PHSchool.com

Web Code: ccc-0013

Solutions1. a. (7.6 � 10�4 m) (1.5 � 107 m) �(7.6 � 1.5) (10�4 + 7) (m � m) �11 � 103 m2 � 1.1 � 104 m2

1. b. 0.00053/29 �

(5.3 � 10�4)/(2.9 � 101) �

(5.3/2.9) � 10(�4 � 1) � 1.8 � 10�5

2. (3.0 � 108 m/s) (8.64 � 104 s) �(3.0 � 8.64) (108 + 4) m �26 � 1012 � 2.6 � 1013 m(Note: This is how far light travels in one day.)Logical

For Extra HelpReinforce the concepts of addingexponents when numbers in scientificnotation are multiplied and subtractingexponents when numbers in scientificnotation are divided. Logical

Direct students to the Math Skills inthe Skills and Reference Handbookat the end of the student text foradditional help.

Additional Problems1. Perform the following calculations: a. 1.5 � 103 m � 1.0 � 105 m(1.5 � 108 m2)b. 4.5 � 103/0.9 (5.0 � 103)Logical, Portfolio

L1

L1

L2

Science Skills 15

Customize for Inclusion Students

Visually Impaired To help visually impaired students understandthe concepts of length, mass, and volume,give students common objects. Ask students to

describe the objects in regard to their lengths,masses, and volumes. Help students to under-stand the definitions of these terms during the exercise.

Answer to . . .

Figure 11 2 � 1011

Find links to additional activitiesand have students monitor phenomena that affect Earth and its residents.

16 Chapter 1

SI Units of MeasurementFor a measurement to make sense, it requires both a number and aunit. For example, if you told one of your friends that you had fin-ished a homework assignment “in five,” what would your friendthink? Would it be five minutes or five hours? Maybe it was a longassignment, and you actually meant five days. Or maybe you meantthat you wrote five pages.You should always express measurementsin numbers and units so that their meaning is clear. In Figure 12,students are measuring temperature in degrees Celsius.

Many of the units you are familiar with, such as inches, feet,and degrees Fahrenheit, are not units that are used in science.

Scientists use a set of measuring units called SI, or theInternational System of Units. The abbreviation stands for theFrench name Système International d’Unités. SI is a revised ver-sion of the metric system, which was originally developed inFrance in 1791. By adhering to one system of units, scientists canreadily interpret one another’s measurements.

Base Units and Derived Units SI is built upon seven metricunits, known as base units, which are listed in Figure 13. In SI, the baseunit for length, or the straight-line distance between two points, is themeter (m). The base unit for mass, or the quantity of matter in anobject or sample, is the kilogram (kg).

Additional SI units, called derived units, are made from combina-tions of base units. Figure 14 lists some common derived units. Forexample, volume is the amount of space taken up by an object. Thevolume of a rectangular box equals its length times its width times itsheight. Each of these dimensions can be measured in meters, so youcan derive the SI unit for volume by multiplying meters by meters bymeters, which gives you cubic meters (m3).

Figure 12 A measurementconsists of a number and a unit.One of the units used to measuretemperature is the degree Celsius.

Quantity

Length

Mass

Temperature

Time

Amount of substance

Electric current

Luminous intensity

Unit

meter

kilogram

kelvin

second

mole

ampere

candela

Symbol

m

kg

K

s

mol

A

cd

SI Base Units

Quantity

Area

Volume

Density

Pressure

Energy

Frequency

Electric charge

Unit

square meter

cubic meter

kilograms per cubic meter

pascal (kg/m•s2)

joule (kg•m2/s2)

hertz (1/s)

coulomb (A•s)

Symbol

m2

m3

kg/m3

Pa

J

Hz

C

Derived Units

Figure 13 Seven metric base units make up thefoundation of SI.

Figure 14 Specific combinations of SI base units yieldderived units.

16 Chapter 1

SI Units ofMeasurement

Some students may incorrectly thinkthat scientists use the metric systembecause it is more accurate than othermeasurement systems. Point out tostudents that the units of the measure-ment system have little to do withaccuracy. Help students overcome thismisconception by measuring one object with several different centimeter-and inch-rulers. Have students recordthe measurements. List the metricmeasurements in one column on theboard and the English measurements in another column. Point out that all the measurements in the metric columnare similar to one another and that the measurements in the English columnare also similar to one another. Visual

L2

Section 1.3 Section 1.3 (continued)

The Meter The meter was originally definedby the French Academy of Science in 1791. At that time, a meter was intended to be oneten-millionth part of the quadrant of Earth.This length was transferred to a platinum barwith polished ends. The bar could bemeasured at a specific temperature to definethe length of a meter. Later measurements ofEarth showed that the length of the bar wasnot one ten-millionth of the quadrant.

However, the meter’s length was not changed.It was redefined to be the length on the bar. In 1960, the length of a meter was moreprecisely defined by the number of wave-lengths of light, of a very precise color,emitted by krypton-86. This method wasdifficult to perform and was quickly replacedwith the current method. Currently, a meter is defined as the distance light travels in avacuum in second.1

299,792,458

Facts and Figures

HSPS_1eTE_C01.qxd 6/20/03 1:06 PM Page 16

Science Skills 17

Another quantity that requires a derived unit is density. Density isthe ratio of an object’s mass to its volume.

Density �

To derive the SI unit for density, you can divide the base unit for massby the derived unit for volume. Dividing kilograms by cubic metersyields the SI unit for density, kilograms per cubic meter (kg/m3).

Metric Prefixes The metric unit for a given quantity is not alwaysa convenient one to use. For example, the time it takes for a computerhard drive to read or write data—also known as the seek time—is inthe range of thousandths of a second. A typical seek time might be0.009 second. This can be written in a more compact way by using ametric prefix. A metric prefix indicates how many times a unit shouldbe multiplied or divided by 10. Figure 15 shows some common metricprefixes. Using the prefix milli- (m), you can write 0.009 second as 9 milliseconds, or 9 ms.

9 ms � s � 0.009 s

Note that dividing by 1000 is the same as multiplying by 0.001.Metric prefixes can also make a unit larger. For example, a distance

of 12,000 meters can also be written as 12 kilometers.

12 km � 12 � 1000 m � 12,000 m

Metric prefixes turn up in non-metric units as well. If you work withcomputers, you probably know that a gigabyte of data refers to1,000,000,000 bytes. A megapixel is 1,000,000 pixels.

91000

What is the SI derived unit for density?

MassVolume

Prefix

giga-

mega-

kilo-

deci-

centi-

milli-

micro-

nano-

Symbol

G

M

k

d

c

m

n

Meaning

billion (109)

million (106)

thousand (103)

tenth (10�1)

hundredth (10�2)

thousandth (10�3)

millionth (10�6)

billionth (10�9)

Multiply Unit by

1,000,000,000

1,000,000

1000

0.1

0.01

0.001

0.000001

0.000000001

SI Prefixes

µ

Figure 15 Metric prefixes allowfor more convenient ways toexpress SI base and derived units.

Figure 16 A bar of gold hasmore mass per unit volume than afeather. Inferring Which takesup more space—one kilogram ofgold or one kilogram of feathers?

Build Science SkillsInferring Have students look at Figure15. Ask, What factor are the metricprefixes based on? (10) How does thatmake it convenient for convertingbetween units? (The numbers stay thesame but the decimal point moves.)Logical, Visual

Build Math SkillsConversion Factors Give students theconversion factors 1 in � 2.54 cm and 1 ft � 30.48 cm. Divide students intopairs, and have each pair measure thelengths of at least three different objectsof various sizes, such as a pencil, a desk-top, and the floor of a room. Direct thepairs to calculate the measurements ofeach object in inches, feet, centimeters,meters, and kilometers. (Answers will varydepending upon the objects measured.) Askstudents which conversion factors theyused to make their calculations.Kinesthetic, Logical

Direct students to the Math Skills inthe Skills and Reference Handbookat the end of the student text foradditional help.

L1

L2

Science Skills 17

Answer to . . .

Figure 16 Because feathers are lessdense than gold, one kilogram offeathers takes up more space than onekilogram of gold.

The SI derived unit fordensity is the kilogram

per cubic meter (kg/m3).

18 Chapter 1

The easiest way to convert from one unit of measurement toanother is to use conversion factors. A conversion factor is a ratioof equivalent measurements that is used to convert a quantityexpressed in one unit to another unit. Suppose you want to con-vert the height of Mount Everest, 8848 meters, into kilometers.Based on the prefix kilo-, you know that 1 kilometer is 1000meters. This ratio gives you two possible conversion factors.

Since you are converting from meters to kilometers, the numbershould get smaller. Multiplying by the conversion factor on theleft yields a smaller number.

8848 m � � 8.848 km

Notice that the meter units cancel, leaving you with kilometers (thelarger unit).

To convert 8.848 kilometers back into meters, multiply by the con-version factor on the right. Since you are converting from kilometersto meters, the number should get larger.

8.848 km � � 8848 m

In this case, the kilometer units cancel, leaving you with meters.

1000 m1 km

1 km1000 m

1000 m1 km

1 km1000 m

Comparing Precision

Materials3 plastic bottles of different sizes, beaker,graduated cylinder

Procedure1. Draw a data table with three rows and three

columns. Label the columns Estimate, Beaker,and Graduated Cylinder.

2. Record your estimate of the volume of a plasticbottle in your data table. Then, fill the bottlewith water and pour the water into the beaker.Read and record the volume of the water.

3. Pour the water from the beaker into thegraduated cylinder. Read and record thevolume of water.

4. Repeat Steps 2 and 3 with two otherplastic bottles.

Analyze and Conclude1. Analyzing Data Review your volume

measurements for one of the bottles. Howmany significant figures does the volumemeasured with the beaker have? How manysignificant figures does the volume measuredwith the graduated cylinder have?

2. Comparing and Contrasting Whichprovided a more precise measurement—the beaker or the graduated cylinder?

3. Inferring How could you determine theaccuracy of your measurements?

Figure 17 Nutrition labels oftenhave some measurements listed ingrams and milligrams. Calculating How many gramsare in 160 milligrams?

18 Chapter 1

Conversion Factor

Purpose Students observe howconversion factors work.

Materials 12-in. object, 3-in. object,metric ruler

Procedure Give students theconversion factor 1 in. � 2.54 in.Measure the 12-in. object and report itslength in centimeters. Tell the studentsthe length in inches of the 3-in. object.Ask them to use the conversion factorto calculate its length in centimeters.(7.6 cm) Measure the object and reportthe length in centimeters.

Expected Outcome Students see howconversion factors convert between unitsof different measure. Visual, Logical

Comparing PrecisionObjectiveAfter completing this lab, students willbe able to• describe and distinguish accuracy and

precision.• compare the precision of measuring

devices.

Skills Focus Measuring, Comparing

Prep Time 10 minutes

Class Time 15 minutes

Safety Caution students to handleglassware carefully.

Teaching Tips• Provide 3 different plastic bottles with

labels removed, and a beaker andgraduated cylinder large enough tocontain the volume of each bottle.

• If necessary, use paper cups instead ofplastic bottles.

Expected Outcome The graduatedcylinder will provide a more precisemeasurement than the beaker.

L2

L2

Section 1.3 (continued)

Analyze and Conclude1. Answers will vary, depending on the sizeof the beaker and graduated cylinder.Typically, the graduated cylindermeasurement will have more significantfigures than the beaker measurement.2. The graduated cylinder3. By comparing them to measurementsmade with a container known to beaccurate Visual, Logical

Science Skills 19

Limits of MeasurementSuppose you wanted to measure how much time it takes for you to eatyour breakfast. Figure 18 shows two clocks you could use—an analogclock and a digital clock. The analog clock displays time to the nearestminute. The digital clock displays time to the nearest second (or onesixtieth of a minute). Which clock would you choose?

Precision The digital clock offers more precision. Precision is agauge of how exact a measurement is. According to the analog clock,it might take you 5 minutes to eat your breakfast. Using the digitalclock, however, you might measure 5 minutes and 15 seconds, or 5.25 minutes. The second measurement has more significant figures.Significant figures are all the digits that are known in a measurement,plus the last digit that is estimated. The time recorded as 5.25 minuteshas three significant figures. The time recorded as 5 minutes has onesignificant figure. The fewer the significant figures, the less precise themeasurement is.

When you make calculations with measurements, theuncertainty of the separate measurements must be correctlyreflected in the final result. The precision of a calculatedanswer is limited by the least precise measurement used inthe calculation. So if the least precise measurement in yourcalculation has two significant figures, then your calculatedanswer can have at most two significant figures.

Suppose you measure the mass of a piece of iron to be34.73 grams on an electronic balance. You then measure thevolume to be 4.42 cubic centimeters. What is the density ofthe iron?

Density � � 7.857466 g/cm3

Your answer should have only three significant figures becausethe least precise measurement, the volume, has three signifi-cant figures. Rounding your answer to three significant figuresgives you a density of 7.86 grams per cubic centimeter.

Accuracy Another important quality in a measurementis its accuracy. Accuracy is the closeness of a measurement tothe actual value of what is being measured. For example, sup-pose the digital clock in Figure 18 is running 15 minutesslow. Although the clock would remain precise to the near-est second, the time displayed would not be accurate.

What is accuracy?

34.73 g4.42 cm3

Figure 18 A more precise time can be readfrom the digital clock than can be read fromthe analog clock. The digital clock is precise tothe nearest second, while the analog clock isprecise to the nearest minute.

Limits ofMeasurementBuild Reading LiteracyUse Prior Knowledge Refer to page 2D in this chapter, which providesthe guidelines for using prior knowledge.

Have students make a three-column chart with columns headed Term, PriorKnowledge, and New Knowledge. Tellstudents to write accuracy and precision inthe first column and then fill in the PriorKnowledge column. Discuss students’responses and determine whether theyhave misconceptions about these terms. Ifso, begin to address those misconceptionsdirectly in discussion. After students finishreading, have them complete the thirdcolumn, correcting or revising their priorknowledge as needed.Verbal

Use VisualsFigure 18 Have students look at thefigure and read the caption. Ask, Howprecisely does this digital clock measuretime? (It measures time to the second.) Ask,How precisely does the analog clockmeasure time? (It is divided into five-minute intervals, so time to the nearestminute can be estimated.) What wouldmake the analog clock more precise?(The clock would be more precise if it hadtick marks for minutes, and a second hand.)Visual

L1

L1

Science Skills 19

Measuring Time Precisely As scientificknowledge increases, so does the accuracy andprecision of time measurements. In theseventeenth century, Robert Hooke developed amechanically powered clock. It was based onGalileo’s 1583 observation that each swing of apendulum takes the same amount of time. Earlypendulum clocks were much more accurateand precise than hourglasses, which may havebeen precise to within an hour or two.

Quartz clocks, developed in 1929, are moreprecise. They generally lose only one five-hundredths of a second per year. Atomic clocksmeasure time using the frequencies at whichatoms absorb or emit light. They are the mostprecise clocks today. Today’s cesium atomicclocks are projected to neither lose nor gain asecond in 1,000,000 years. Even more precisetime measurements are based on pulsars, radiopulsations from collapsed stars.

Facts and Figures

Answer to . . .

Figure 17 The measurement 160 milligrams is equivalent to 0.160 gram.

Accuracy is the closenessof a measurement to the

actual value of what is being measured.

20 Chapter 1

Section 1.3 Assessment

Reviewing Concepts1. Why do scientists use scientific notation?

2. What system of units do scientists usefor measurements?

3. How does the precision of measurementsaffect the precision of scientific calculations?

4. List the SI units for mass, length,and temperature.

Critical Thinking5. Applying Concepts A bulb thermometer

gives an indoor temperature reading of 21°C.A digital thermometer in the same room givesa reading of 20.7°C. Which device ismore precise? Explain.

6. Calculating Convert �11°F into degreesCelsius, and then into kelvins.

Measuring TemperatureA thermometer is an instrument that measurestemperature, or how hot an object is. The How ItWorks box on page 21 describes how a bulb ther-mometer measures temperature.

The two temperature scales that you are prob-ably most familiar with are the Fahrenheit scaleand the Celsius scale. On the Fahrenheit scale,

water freezes at 32°F and boils at 212°F at sea level. On the Celsius (orcentigrade) scale, water freezes at 0°C and boils at 100°C. A degreeCelsius is almost twice as large as a degree Fahrenheit. There is also adifference of 32 degrees between the zero point of the Celsius scale andthe zero point of the Fahrenheit scale. You can convert from one scaleto the other by using one of the following formulas.

°C � (°F � 32.0°) °F � (°C) � 32.0°

The SI base unit for temperature is the kelvin (K). A temperatureof 0 K, or 0 kelvin, refers to the lowest possible temperature that canbe reached. In degrees Celsius, this temperature is �273.15°C. To con-vert between kelvins and degrees Celsius, use the following formula.

K � °C � 273

Figure 19 compares some common temperatures expressed in degreesCelsius, degrees Fahrenheit, and kelvins.

95

59

7. Write the following measurements inscientific notation. Then convert eachmeasurement into SI base units.

a. 0.0000000000372 g

b. 45,000,000,000 km

8. The liquid in a bulb thermometer falls1.1 cm. Calculate the liquid’s changein volume if the inner radius of thetube is 6.5 � 10�3 cm.

Celsius (�C)

Water boils

Human body

Average room

Water freezes

100

37

20

0

Common TemperaturesFahrenheit (�F)

212

98.6

68

32

Kelvin (K)

373

310

293

273

Figure 19 Temperature can beexpressed in degrees Fahrenheit,degrees Celsius, or kelvins.

20 Chapter 1

MeasuringTemperatureUse VisualsFigure 19 Have students look at thefigure. Ask, Is any one of the threescales more accurate than the others?(No, they all can be used to measuretemperature accurately.) Why do youthink scientists use degrees Celsiusfor measuring temperature? (Somestudents may note that the rangebetween the freezing and boiling pointsis 100 degrees and that like other SI unitsof measure, it can easily be divided intohundredths. Other students may saythat it is just an agreed-upon standard.)Visual, Logical

ASSESSEvaluateUnderstandingAsk students to write three conversionproblems (with solutions) based onthe prefixes used in the metric system.Have students take turns analyzing andsolving the problems in class. Note thateven incorrectly worded problems areuseful, as students can be asked toidentify and correct the errors.

ReteachUse Figure 15 to help students under-stand how prefixes modify units ofmeasurement. Give students examplessuch as kilogram, milliliter, andmicrosecond and ask students to nameunits that are larger and smaller.

Solutions7. a. 3.72 � 10�11 g;3.72 � 10�11 g � ( ) �3.72 � 10�14 kgb. 4.5 � 1010 km;4.5 � 1010 km � ( ) �4.5 � 1013 m8. V = (�r2 � l ) �

(3.14) (6.5 � 10�3 cm)2 (1.1 cm) �

(3.14) (6.5 � 6.5) (10�3 �3) (1.1)(cm � cm � cm) � 145.9 � 10�6 cm3 �

1.5 � 10�4 cm3

If your class subscribesto the Interactive Textbook, use it toreview key concepts in Section 1.3.

1000 m1 km

1 kg1000g

L1

L2

3

L1

Section 1.3 (continued)

4. Kilogram (kg), meter (m), kelvin (K)5. The digital thermometer (which yields ameasurement with three significant figures)is more precise than the bulb thermometer(which yields a measurement of only twosignificant figures).6. �11�F � �24�C � 249 K

Section 1.3 Assessment

1. Scientific notation is useful because it makesvery large or very small numbers easier towork with.2. Scientists use a set of measuring unitscalled SI.3. The precision of a calculated answer islimited by the least precise measurement usedin the calculation.

Change boxb/g to white

ThermometerA bulb thermometer consists of a sealed, narrow glass tube,called a capillary tube. It has a glass bulb at one end and isfilled with colored alcohol or mercury. The thermometerworks on the principle that the volume of a liquid changeswhen the temperature changes. Whenwarmed, the liquid in the bulb takesup more space and moves up thecapillary tube. Interpreting Diagrams Why is athermometer with a narrow tubeeasier to read than a thermo-meter with a wide tube?

Measuring temperatureThermometers are usefulscientific instruments. They can be used to measure the statictemperature of a material, or to record the change in temperature of a substancebeing heated, as shown above.

Wide or narrow? The volume of a tube is calculatedusing the formula V = πr2l, where r is the radius and l is the length. For a given volume, if the radius ofa tube is decreased (as in a capillarytube), the length of the liquidcolumn increases. Any change involume is then easier to see.

Scale The scale indicates thetemperature according to howfar up or down the capillarytube the liquid has moved.

Capillary tube

Colored liquid Theliquid moves up and

down the capillarytube as the tem-

perature changes.

Fahrenheit scale

Celsius (centigrade)temperature scale

Liquid risesless in a

wide tubefor the sametemperature

change.

Expanded,easy-to-read scale

Compressedscale Liquid rises

more in anarrow tubefor the sametemperaturechange.

Bulb The bulbcontains the

reservoir of liquid.

Science Skills 21

ThermometerLiquid thermometers work because theliquid expands and contracts. Point outto students that all liquids do not expandat the same rate. Students may also befamiliar with spiral metal thermometersfound in outdoor thermometers, cookingthermometers, and thermostats. Thespirals are strips made of two differentmetals. As the temperature changes, the two metals expand or contractdifferently. This expansion or contractionmoves a pointer needle that points at thetemperature.

Interpreting Diagrams The scalemarkings on a narrow-tubethermometer are further apart (andhence easier to read) than thecorresponding markings on a wide-tubethermometer. It is also easier to record a temperature change on a thermo-meter with a narrow tube because for agiven change in the thermometerliquid’s volume, the narrow thermo-meter will show a greater change in theheight of the liquid.Logical

For EnrichmentTell students that in the early 1600s,Galileo created a thermometer based ondensity. Interested students can find outmore about Galileo’s thermometer andcreate a brief report and illustration.Portfolio

L3

L2

Science Skills 21