physics ll - Laboratory Experiment 6 ( Linear Expansion) Fall 2022.

Physics II Laboratory Experiment 6 Linear Expansion Page 1 S.A 10/12/22 INTRODUCTION Any substance that is heated experiences an increase in the kinetic energy of its atoms, which causes the atoms to vibrate and, as a result, widens the space between them. These materials expand because of the increase in distance. As a result, it can be inferred that a solid will get larger as its temperature rises; however, the rate of expansion varies depending on the nature of each substance. The equation L = L0 (1 + T) can be used to define this phenomenon, which is known as linear expansion. To test the theories that a solid is directly proportional to both its beginning length and the change in temperature, linear expansion will be investigated in this experiment, along with the dependence of a material's qualities on its expansion properties. To do this, three tests were carried out using metal rods made of aluminum, copper, and brass to determine how long each changed after being exposed to steam. A rotary motion sensor pin with a specified radius and a thermistor (temperature) sensor collected expansion data during the tests and extrapolated a graph of temperature vs. time and expansion vs. time. Each metal rod's coefficient of linear expansion was determined by extrapolating from these graphs the change in length that corresponded to the change in temperature. Aluminum was tested, and the coefficient of linear expansion we computed had an inaccuracy of 9.583 = 9.6%. The linear expansion coefficients for the brass and copper rods produced percent errors of 4.583 = 4.6% and 15.29 %, respectively. All three tests provide evidence in support of the hypotheses that the coefficient of linear expansion depends on the characteristics of each metal rod and that the change in length of the metal rod is proportional to the change in temperature, even though the percent errors for both aluminum and brass are quite high.

Physics II Laboratory Experiment 6 Linear Expansion Page 2 S.A 10/12/22 THEORY Given a solid with a length Lo at a temperature To, it is a known fact that it will expand if the temperature is increased. That is, if the length of the rod is measured again when its temperature is T > To, the new length will be L > Lo, as shown in Figure 1. For the same rod, the expansion ∆L = (L - Lo) is experimentally found to be proportional to the change in temperature ∆T = (T - To). However, for rods made of different materials, the same change in temperature ∆T results in different ∆L's. Using these experimental facts, the fractional change in length is defined as, ∆ L L 0 = α ∆T where α is called the coefficient of linear expansion and it is a property of the material that was used to make the rod. Coefficients of linear expansion for some materials are given in Table 6.1. The final length of the rod will be given by L = L 0 (1 + α∆T). EXPERIMENTAL PROCEDURE RESULT 1. ALUMINUM

Physics II Laboratory Experiment 6 Linear Expansion Page 4 S.A 10/12/22 3. COPPER DISCUSSION 1. ALUMINUM In this section of the experiment, graphs that relate the length change of the rod, temperature change, and time were produced using an expansion base, steam generator, temperature sensor, and rotating motion sensor. These graphs were used to determine the coefficient of linear expansion of aluminum. The two values ∆L and ∆T were discovered and used to calculate after the graphs had been evaluated using the intelligent capabilities on the PASCO capstone computer software. Prior to applying steam to the rod, the original rod length La was also measured. The length vs. time graph in Figure 3 has two peaks, which should be noted because they could have been a potential source of inaccuracy when calculating ∆L. The values used and calculations for a are as follows:

Physics II Laboratory Experiment 6 Linear Expansion Page 5 S.A 10/12/22 L 0 = 40.5 mm ∆L = 0.72 mm ∆T = 67.7 ֯ c α exp = 0.000263 = 2.63*10 -5 % error = | 2.63 × 10 − 5 − 2.4 × 10 − 5 | 2.4 × 10 − 5 × 100 = 9.583 ≈ 9.6% 2. BRASS L 0 = 40.5 mm ∆L = 0.56 mm ∆T = 68.9 ֯ c α exp = 0.000201 = 2.01*10 -5 % error = | 2.01 × 10 − 5 − 1.9 × 10 − 5 | 1.9 × 10 − 5 × 100 = 4.583 ≈ 4.6% 3. COPPER L 0 = 40.5 mm ∆L = 0.53 mm ∆T = 66.6 ֯ c α exp = 0.000196 = 1.96*10 -5 % error = | 1.96 × 10 − 5 − 1.7 × 10 − 5 | 1.7 × 10 − 5 × 100 = 15.29% Material L 0 [mm] ∆L [mm] ∆T [°C] α [1/°C]0 Percent Error [%] A luminum 40.5 0.72 67.7 2.63 × 10 -5 9.583 ≈ 9.6

Physics II Laboratory Experiment 6 Linear Expansion Page 7 S.A 10/12/22 Ans:

Physics II Laboratory Experiment 6 Linear Expansion Page 8 S.A 10/12/22 2. Did experimental and theoretical coefficients of thermal expansion agree? Explain Ans: Tables 1 and 2 show that the experimental and theoretical coefficients agree to a reasonable extent, but because we are working with such small values, any small modification will result in a very big percent inaccuracy. Additionally, any systematic mistakes made during the experiment could have led to discrepancies, such as prematurely ending the data collection or getting the wrong reading from the pinion that measured how far the metal rods went. 3. Did you use the value for L? Explain. Ans: No, L was not involved in this experiment because just the beginning length, the change in temperature, and the change in length were needed to determine the coefficient of linear expansion.