Physics Lab conclusion

Thermal Expansion Apparatus 012-04394C

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Accepted Values for Coefficient of Thermal Expansion

Material a ( x10-6/∞C )

Copper 17.6

Steel 11.3 to 13.5

Aluminum 23.4

Changing Tubes

➤ Caution: When changing tubes be careful not to pull the wires off the thermistor. The thumb- screw must be com- pletely removed before the thermistor can be lifted off the threaded rod.

Replacement Parts

The following parts can be ordered from PASCO scientific.

Item PASCO Part #

mod. Thermistor (100 kΩ) 150-03140

Al Tube Assy 003-04413

Cu Tube Assy 003-04412

Steel Tube Assy 003-04414

Foam Insulator 648-03100

Dial Gauge 620-050

Thermistor

Tube

Thumbscrew

012-04394C Thermal Expansion Apparatus

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Introduction

Most materials expand somewhat when heated through a temperature range that does not produce a change in phase. The added heat increases the average amplitude of vibration of the atoms in the material which increases the average separation between the atoms.

Suppose an object of length L undergoes a temperature change of magnitude ∆T. If ∆T is reasonably small, the change in length, ∆L, is generally proportional to L and ∆T. Stated mathematically:

∆L = αL ∆T;

where α is called the coefficient of linear expansion for the material.

For materials that are not isotropic, such as an asymmetric crystal for example, a can have a different value depending on the axis along which the expansion is measured. a can also vary somewhat with temperature so that the degree of expansion depends not only on the magnitude of the temperature change, but on the absolute temperature as well.

In this experiment, you will measure α for copper, aluminum, and steel. These metals are isotropic so that a need only be measured along one dimension. Also, within the limits of this experiment, a does not vary with temperature.

Procedure

➀ Measure L, the length of the copper tube at room temperature. Measure from the inner edge of the stainless steel pin on one end, to the inner edge of the angle bracket at the other end (see Figure 1). Record your results in Table 1.

➁ Mount the copper tube in the expansion base as shown in Figure 2. The stainless steel pin on the tube fits into the slot on the slotted mounting block and the bracket on the tube presses against the spring arm of the dial gauge.

➤ NOTE: Slide or push the tube to one side of the slide support. Drive the thumbscrew against the pin until the tube can no longer be moved. Use this as your reference point.

➂ Use one of the provided thumbscrews to attach the thermistor lug to the threaded hole in the middle of the copper tube. The lug should be aligned with the axis of the tube, as shown in Figure 2, so there is maximum contact

L

Bracket on tube

Dial Gauge Spring Arm

Stainless steel pin

Figure 2 Equipment Setup (Top View)

Slotted bracket Thumbscrew

Figure 1 Measuring Tube Length

Experiment: Measuring the Coefficient of Linear Expansion for Copper, Steel, and Aluminum

Thermal Expansion Apparatus 012-04394C

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between the lug and the tube.

Place the foam insulator over the thermistor lug as shown in Figure 3.

➄ Plug the leads of your ohmmeter into the banana plug connec- tors labeled THERMISTOR in the center of the expansion base.

Measure and record R rm

, the resistance of the thermistor at room temperature. Record this value in the table.

Use tubing to attach your steam generator to the end of the copper tube. Attach it to the end farthest from the dial gauge.

➇ Use a book or a block of wood to raise the end of the expansion base at which steam enters the tube—a few centimeters is sufficient. This will allow any water that condenses in the tube to drain out. Place a container under the other end of the tube to catch the draining water.

➈ Turn the outer casing of the dial gauge to align the zero point on the scale with the long indicator needle. As the tube expands, the indicator needle will move in a counterclockwise direction.

➉ Turn on the steam generator. As steam begins to flow, watch the dial gauge and the ohmmeter. When the thermistor resistance stabilizes, record the resistance (R

hot ) in Table 1. Also record

the expansion of the tube length (∆L) as indicated by the displacement of the indicator on the dial gauge. (Each increment on the dial gauge is equivalent to 0.01 mm of tube expansion.) Note that ∆L is the difference betwen the dial gauge readings.

➤ Repeat the experiment for the steel and aluminum tubes.

Data and Calculations

DATA CALCULATIONS

L (mm) Rrm (Ω) ∆L (mm) Rhot (Ω) Trm (C°) Thot (C°) ∆T (C°)

Copper

Steel

Aluminum

➀ Use the Conversion Table at the end of this manual, or the one on the top of the expansion base, to convert your thermistor resistance measurements, R

rm and R

hot , into temperature

measurements, T rm

and T hot

. Record your results in the table.

Figure 3 Thermistor Attachment

Thermistor Lug

Copper Tube

Banana Connectors

Foam Insulator

TABLE 1 Data and Calculations

➃

➅

➆

012-04394C Thermal Expansion Apparatus

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Res. Temp. (Ω) (°C)

Res. Temp. (Ω) (°C)

Res. Temp. (Ω) (°C)

Res. Temp. (Ω) (°C)

351,020 0 332,640 1 315,320 2 298,990 3 283,600 4 269,080 5 255,380 6 242,460 7 230,260 8 218,730 9 207,850 10 197,560 11 187,840 12 178,650 13 169,950 14 161,730 15 153,950 16 146,580 17 139,610 18 133,000 19 126,740 20 120,810 21 115,190 22 109,850 23 104,800 24 100,000 25

95,447 26 91,126 27 87,022 28 83,124 29 79,422 30 75,903 31 72,560 32 69,380 33 66,356 34 63,480 35 60,743 36 58,138 37 55,658 38 53,297 39 51,048 40 48,905 41 46,863 42 44,917 43 43,062 44 41,292 45 39,605 46 37,995 47 36,458 48 34,991 49 33,591 50 32,253 51

30,976 52 29,756 53 28,590 54 27,475 55 26,409 56 25,390 57 24,415 58 23,483 59 22,590 60 21,736 61 20,919 62 20,136 63 19,386 64 18,668 65 17,980 66 17,321 67 16,689 68 16,083 69 15,502 70 14,945 71 14,410 72 13,897 73 13,405 74 12,932 75 12,479 76 12,043 77

11,625 78 11,223 79 10,837 80 10,467 81 10,110 82 9,767.2 83 9,437.7 84 9,120.8 85 8,816.0 86 8,522.7 87 8,240.6 88 7,969.1 89 7,707.7 90 7,456.2 91 7,214.0 92 6,980.6 93 6,755.9 94 6,539.4 95 6,330.8 96 6,129.8 97 5,936.1 98 5,749.3 99 5,569.3 100

THERMISTOR CONVERSION TABLE: Temperature versus Resistance

➁ Calculate ∆T = T hot

– T rm

. Record the result in the table.

➂ Using the equation ∆L = αL ∆T, calculate a for copper, steel, and aluminum.

α Cu

= __________________

α steel

= __________________

α Al

= __________________

Questions

➀ Look up the accepted values for the linear expansion coefficient for copper, steel, and aluminum. Compare these values with your experimental values. What is the percentage difference in each case? Is your experimental error consistently high or low?

➁ On the basis of your answers in question 1, speculate on the possible sources of error in your experiment. How might you improve the accuracy of the experiment?

➂ From your result, can you calculate the coefficients of volume expansion for copper, aluminum, and steel? (i.e. ∆V = α

vol V ∆T)