Physics 110 Lab 2 Thermal Expansion THERMAL EXPANSION - PRELAB Please answer the following questions: 1. By how much would a 1.00 m long aluminum rod increase in length if its temperature were raised by 80.0 C? 2. By how much would a 1.00 m long copper rod shrink if its temperature were lowered by 80.0 C? 1Physics 110 Lab 2 Thermal Expansion LAB 2 - Thermal Expansion SUMMARY: In this experiment, you will measure the coefficient of linear expansion for copper, aluminum, and steel. These metals are isotropic so that the coefficient need only be measured along one dimension. Also, within the limits of this experiment, the coefficient does not vary with temperature. APPARATUS: Pasco Thermal Expansion Apparatus, 2 multimeters, 2 temperature probes, hot plate, steam generator, tubing, meter stick, beaker, block THEORY: 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 AT. If AT is reasonably small, the change in length AL, is generally proportional to _ and A T. Stated mathematically: AL = LaAT; where a is called the coefficient of linear expansion for the material. a has units of 1/C. 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. The accepted values of the coefficients of linear expansion for copper, aluminum and steel are 17.6 x 10 1/K, 23.4 x 10 1/K and 11.3 to 13.5 x 10 1/K respectively. PROCEDURE: 1. Measure and record L, the length of the copper tube at room temperature. Measure from the inner edge of the stainless pin on one end, to the inner edge of the angle bracket at the other end (See Figure 1). Figure 1 Measuring Tube Length 2Physics 110 Lab 2 Thermal Expansion 2. 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 on the dial gauge. Bracket on tube Stainless steel pin Dial Gauge Spring Arm Slotted bracket Thumbscrew Figure 2 Equipment Setup (Top View) 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. 3. Use tubing to attach your steam generator to the end of the copper tube. Attach it to the end farthest from the dial gauge. 4. Use the block of wood to raise the end of the expansion base at which steam enters the tube. This will allow any water that condenses in the tube to drain out. Place the small beaker under the other end of the tube to catch the draining water. 5. Thread two digital thermometers into the tube to measure the temperature at the near and far ends of the tube. 6. 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. 7. Turn on the steam generator. As steam begins to flow, watch the dial gauge very carefully. Record the maximum tube length AL 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.) 8. Calculate and record the average temperature of the two digital thermometers. 9. Repeat the experiment for the steel and aluminum tubes. 10. Repeat the experiment two more times. 3Physics 110 Lab 2 Thermal Expansion DATAAND CALCULATIONS: 1. Calculate AT. 2. Calculate the coefficients of thermal expansion for copper, steel, and aluminum for each trial. 3. Calculate the average coefficients of thermal expansion for copper, steel, and aluminum. The average you determined represents a single best value, derived from all your measurements. The minimum and maximum values give an indication of how much the measurement can vary from trial to trial; that is, they indicate the precision of your measurement. One way of stating the precision is to take half the difference between the minimum and maximum values and use the result as the uncertainty of the measurement. Express your final experimental result as the average value, + the uncertainty. QUESTIONS: 1. Calculate the relative errors for the coefficients of thermal expansion for copper, steel, and aluminum. 2. What is the percentage fractional discrepancy in each case? 3. Does the experiment have systematic error? 4. Discuss at least three sources of experimental (not human) error in this experiment. 5. How might you improve the accuracy of the experiment? 6. From your result, calculate the coefficients of volume expansion for copper, aluminum, and steel. 4