Physics I: Thermal Expansion Worksheet Class: Section: Lab Group: Assignment Date: Names: answer key: Copper Steel Aluminum Length (mm) ΔL (mm) 701 701 701 .885 .500 .678 Table 1: Data and Calculations Room Resistance at Resistance Room Temp. when Heated Temperature T rm ( C˚ ) R rm (Ω) R hot (Ω) 116200 7780 22 114100 8870 22 113800 8900 22 Table 2: Results Copper Steel Aluminum Experimental Thermal Coefficient α (1/C˚) Accepted Thermal Coefficient α (1/C˚) % Error (%) 0.000018 0.000011 0.000015 0.0000176 0.0000113 0.0000215 2.3 2.6 30 Worksheet numbers data Heated Temperature T hot ( C˚ ) 90 86 86 Change in Temperature Δ T ( C˚ ) 68 64 64 ons Thermal Expansion Apparatus 012-04394C Accepted Values for Coefficient of Thermal Expansion Material a ( x10-6/∞C ) Copper 17.6 Steel 11.3 to 13.5 Aluminum 23.4 Replacement Parts The following parts can be ordered from PASCO scientific. Item Changing Tubes ➤ Caution: Tube When changing tubes be careful not to pull the wires off the thermistor. The thumbscrew must be completely removed before the thermistor can be lifted off the threaded rod. Thermistor Thumbscrew 2 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 620-050 012-04394C Thermal Expansion Apparatus Experiment: Measuring the Coefficient of Linear Expansion for Copper, Steel, and Aluminum 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 Figure 1 Measuring Tube Length Bracket on tube Stainless steel pin Dial Gauge Spring Arm Slotted bracket Figure 2 Equipment Setup (Top View) 3 Thumbscrew Thermal Expansion Apparatus 012-04394C between the lug and the tube. ➃ Place the foam insulator over the thermistor lug as shown in Figure 3. ➄ Plug the leads of your ohmmeter into the banana plug connectors labeled THERMISTOR in the center of the expansion base. Copper Tube Foam Insulator ➅ Measure and record Rrm, the resistance of the thermistor at room temperature. Record this value in the table. ➆ 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. Thermistor Lug Banana Connectors Figure 3 Thermistor Attachment 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 (Rhot) 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 TABLE 1 Data and Calculations DATA L (mm) Rrm (Ω) CALCULATIONS ∆L (mm) Rhot (Ω) Trm (C°) Thot (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, Rrm and Rhot, into temperature measurements, Trm and Thot. Record your results in the table. 4 ∆T (C°) 012-04394C Thermal Expansion Apparatus ➁ Calculate ∆T = Thot – Trm. Record the result in the table. ➂ Using the equation ∆L = αL ∆T, calculate a for copper, steel, and aluminum. αCu = __________________ αsteel = __________________ αAl = __________________ 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 = αvolV ∆T) THERMISTOR CONVERSION TABLE: Temperature versus Resistance Res. (Ω) 351,020 332,640 315,320 298,990 283,600 269,080 255,380 242,460 230,260 218,730 207,850 197,560 187,840 178,650 169,950 161,730 153,950 146,580 139,610 133,000 126,740 120,810 115,190 109,850 104,800 100,000 Temp. (°C) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Res. (Ω) 95,447 91,126 87,022 83,124 79,422 75,903 72,560 69,380 66,356 63,480 60,743 58,138 55,658 53,297 51,048 48,905 46,863 44,917 43,062 41,292 39,605 37,995 36,458 34,991 33,591 32,253 Temp. (°C) 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 5 Res. (Ω) Temp. (°C) 30,976 29,756 28,590 27,475 26,409 25,390 24,415 23,483 22,590 21,736 20,919 20,136 19,386 18,668 17,980 17,321 16,689 16,083 15,502 14,945 14,410 13,897 13,405 12,932 12,479 12,043 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 Res. (Ω) 11,625 11,223 10,837 10,467 10,110 9,767.2 9,437.7 9,120.8 8,816.0 8,522.7 8,240.6 7,969.1 7,707.7 7,456.2 7,214.0 6,980.6 6,755.9 6,539.4 6,330.8 6,129.8 5,936.1 5,749.3 5,569.3 Temp. (°C) 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Purchase answer to see full attachment