EXPERIMENT 11 LINEAR EXPANSION OF A SOLID MATERIAL

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1 EXPERIMENT 11 LINEAR EXPANSION OF A SOLID MATERIAL INTRODUCTION: Earlier this semester, we saw that the length of the pendulum effects the period. Many practical devices, such as the mercury thermometer, work on the principle of thermal expansion. It is important for engineers to take thermal expansion into account when designing structures. Bridges; for example, often have joints in the roadway to allow for thermal expansion without damage. It is found that change in length of a solid is proportional to the original length and to the change in temperature. The constant of proportionality, which is called the coefficient of linear expansion, depends on the material of which the solid is made. It is the purpose of this experiment to determine the coefficient of linear expansion of several metals. THEORY: Most solids expand when they are heated, except for those rare cases where the molecular structure simultaneously changes to a more dense form. Ice, for example, shrinks upon melting and alloy Inver gradually changes crystal form to a more compact structure upon heating. These few exceptions to the general rule extend over a range of only a few degrees. When you heat an iron rod, its molecules vibrate more violently. They shove one another away causing the rod to expand. When the rod cools again its molecules vibrate less violently and it contracts. It is interesting to note that each solid has a characteristic rate of expansion unique to that solid. The rate of expansion is determined by heating a measured length of the solid through a definite temperature change and then measuring the change in length. The coefficient of linear expansion, α, is a number which indicates the change in length per unit length per degree of temperature change. It is a characteristic property of the material and can be calculated as follows: α = L L T 0 where, T = T T H L= L L H 0 0 T H is the hot temperature at which the new length is L H, and T 0 is the initial temperature of the rod when its length is L 0. THE EXPERIMENT:

2 1. EXPERIMENTAL APPARATUS: In this experiment you will use a steam generator (boiler), heating plate, aluminium rod, brass rod, copper rod, heating jacket, laboratory fingers, thermometer, power supply, lamp, and electrical cables. Figure 1: Experimental Apparatus. 2. EXPERIMENTAL PROCEDURE: The thermal expansion of three materials will be investigated -aluminium, brass, and copper. To operate simply Insert the desired rod in to the heating jacket. Place the heating jacket onto the base so that the water in-take valve is at the end nearest to the electrical terminals. The thermometer should be facing up, and should be inserted in the stop-cock at the jacket center. The water outlet valve that is near the micrometer should be placed near a laboratory sink. The length of the rod is found by adjusting the micrometer dial until electrical contact is established (see Figure 1). To establish electrical contact between the rod and the lamp follow part (b) of Figure 1. When electrical contact is established the lamp should light up. The micrometer screw should initially not be touching the rod. If there is contact, turn the dial until a small gap exists between the rod and the screw. Fill the thermal expansion apparatus jacket with tab water and record the length of the Aluminium rod and the water bath temperature. Turn the micrometer dial counter-clockwise for two complete turns so that there s no electrical contact (the light is off). Heat-up water contained in the steam generator to a particular temperature about 35 C; and then pour it in the heating jacket through the intake hose. You should use the laboratory fingers to pour the hot water, gently, from the flask into the apparatus jacket. HANDLE WITH EXTREME CARE. DON T BURN YOURSELF!!.

3 Once the jacket is filled with the hot water, allow at least 30 seconds for the rod temperature to reach equilibrium with the water temperature, and turn the micrometer dial until the screw just makes contact with the rod, then record the micrometer s reading for the final length, L H. Repeat this procedure (i.e. heating water, pouring it in the heating jacket, and measuring new length of the rod) for four different hot water temperatures (about 50, 60, 70, and 85 ). Record all the data in data Table 1. For the Copper, and brass rods it is only necessary to measure L obtained from the tab water bath and at another hot water temperature. Record this data in data Table 2. ANALYSIS OF RESULTS: For the aluminium rod (data table 1): Construct a graph of L versus T. Calculate the slope and compare the value obtained for α with the given theoretical value. Discuss your graph. From Table 2: Compare results. Summarise all of your results and calculate percent errors for all α s. TABLE: Linear Expansion Constants for Common Materials: Solid Aluminium Brass Copper Glass Glass (Pyrex) Invar (nickel/iron alloy) Iron Platinum Quartz Steel Tungsten α (Per C) QUESTIONS: What would happen to the coefficient of thermal expansion if the rod is not made of a pure metal? For an Aluminium rod that is twice as long as the one used in our experiment, estimate the expected linear expansion of this rod at the same highest temperature used in our experiment.

4 PHY 1401 LABORATORY REPORT EXPERIMENT 11 LINEAR EXPANSION OF A SOLID MATERIAL NAME:. DATE:. SECTION:. THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION 1. EXPERIMENTAL PURPOSE: State the purpose of the experiment.( 5 points ) 2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points ) Briefly outline the apparatus General procedures adopted.

5 3. DATA and ANALYSIS: TABLE 1: (25 points) T 0 T H T L 0 L H L GRAPH: (30 points) Slope of Graph and α Al calculation: (10 points) Discussion of Graph: (5 points) Percent errors: (10 points) 4. CONCLUSIONS: (5 points)

6 5. QUESTION (5 points)