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DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY In-Lab Assignment: Thermal Expansion of Solids PHY 1104, Section 203 Date: 2/25/21 Name: Kristina Hicks ● Make sure that you read the Introduction to the lab and complete the Pre-lab Quiz on Asulearn before starting the lab activities. ● Note: You need to make a copy of this document and save to your own google drive using “ File>Make a Copy ” in order to have editing permission. Do not email asking for permission to edit this document. Use the question forum if you have questions on the Quiz or the lab. Someone else may have the answer or the same question! ● After completing the lab, make sure that you download your document as a pdf and contribute to the Post-lab Discussion forum ! This lab will be conducted on-line and each student will submit an individual lab report . You are allowed to work on the lab content with another student, but you MUST SUBMIT YOUR OWN UNIQUE images, data, calculations, graphs, explanations, conclusions, etc. Copying items on Lab Assignments constitutes an academic integrity code violation and will be brought before the Oﬃce of Student Conduct. I worked on this lab with: All images, data, calculations, graphs, explanations, conclusions in this lab assignment are my own and are not copied from another student or a previous semester. Type your name below to accept the honor statement. Kristina Hicks Purpose Investigate how the dimensions of solid materials change with temperature by taking measurements and plotting results. By the end of this lab students will: ● Use a spec sheet to determine the precision of a digital thermometer in order to determine the uncertainty in temperature that may be less than what the digital display indicates. ● Read a change in length from a micrometer dial. ● Plot change in length as temperature changes to determine the coefficient of thermal expansion of a copper tube. Necessary Equipment Vernier Graphical Analysis App : There is a help document on Graphical Analysis if you need help downloaded and using it. PHY 1104: Thermal Expansion of Solids, Page | 1

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY Introduction: Thermal Expansion of Solids The materials that we touch and come into contact with every day are made of atoms and molecules that are bonded together and separated by very small distances. These bonds act like springs such that they keep materials together and that they can stretch. In general, when these materials are cold, the bonds between atoms and molecules have the lowest energy level, IE they contain the smallest amount of every. When materials are warmed, the atoms and molecules are given energy and this has the effect of stretching these bonds or increasing the distance between the particles. We can measure this thermally induced expansion, called thermal expansion, and define it to be the tendency of matter to change in size in response to a change in temperature. We know from the study of thermodynamics that an object's temperature using the Kelvin [K] scale is proportional to the object's internal kinetic energy. When energy in the form of heat, which is measured in Joules [J], is transferred to an object, its constituent particles maintain a greater average separation. Since all the distances between particles increases, the material’s volume will expand. While not impossible, materials which contract with increasing temperature are uncommon. Water, over a very narrow range of temperatures, is such a material. Linear Thermal Expansion Consider an object that is being thermally excited. We will look at just one dimension of the material: for example, if we have a long metal rod we will look at its length. The specifics of exactly how the material changes shape with temperature depends on many material properties and many physical laws, such as those of quantum mechanics. Luckily, many materials behave in a very reproducible and linear way over a rather wide range of temperatures around room temperature. Specifically, many materials will expand linearly with the change in temperature. Thus, if we double the temperature change, we double the change in length. This relationship is called linear thermal expansion . Since materials differ greatly in terms of chemical and physical construct, each material has its own coeﬃcient of linear thermal expansion coeﬃcient α . This coeﬃcient indicates the fractional change of its original length per change in temperature °C. The coeﬃcient is found by dividing the percent change in length by the change in temperature , Thus the change in Δ𝑇 = (𝑇 ? − 𝑇 𝑖 ) length ΔL of an object will be equal to the linear thermal expansion coeﬃcient α times original length L o times change in temperature ΔT: (1) ∆𝐿 = 𝐿 ? α ∆𝑇 ( ) where ΔT is the change in temperature or T f – T i . We can rewrite equation 1 as: (2) ∆𝐿 = 𝐿 ? α(𝑇 ? − 𝑇 𝑖 ) This week, you will set up an experiment to measure how the length of an object changes with temperature. If this relationship is linear, the linear thermal expansion coeﬃcient α can be determined and compared to an accepted value, such as that given by table 13-1 in your textbook. PHY 1104: Thermal Expansion of Solids, Page | 2

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY If steam is sent through a metal pipe which is at room temperature, the pipe will expand as the pipe warms up. The amount of expansion is not large and must be measured using a precise micrometer. For such an experiment, the pipe and other components will be hot and we have provided an assembly similar to that shown in Figure 1 to allow for the measurement of small distances effectively and safely. Using the assembly shown in Figure 1, we will start with a metal rod at room temperature (around 20 ℃ ). After measuring the initial temperature and length, we will fill the rod with steam. After the rod is the same temperature as the steam (around 100 ℃ ), we will measure the final temperature and change in length of the rod. From the measured values of initial length, change in length, and the initial and final temperature of a metal rod, we can experimentally determine the coeﬃcient of linear expansion for the rod. PHY 1104: Thermal Expansion of Solids, Page | 3

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY The Micrometer Metric Dial Examine the micrometer metric dial in figure 2, a similar metric dial is attached to the apparatus we will use in this experiment to measure the change in distance of two different types of metal rods as they expand and contract due to temperature changes. The micrometer metric dial is used to measure very small changes in distance. The least count, or distance between the smallest tick marks, of the big needle is 0.01 mm. There are 100 increments in a full circle of the needle. The small needle counts the number of times the large needle has made a complete circle; we will not use this needle since the dial will not make a full rotation in today’s experiment. There is a set screw on the side of the dial that will allow one to zero the markers to the needle, then retighten. You can estimate the needle position to the nearest half of a division, which will give you an estimated error of 0.005 mm. For example, consider the micrometer dial in the picture. This micrometer is reading 0.628 mm +/- 0.005 mm = 0.000628 m +/- 0.0000005 m If you are uncertain about how to use this device, there are many articles and videos on the web, use the search term “How to read a metric dial indicator”. We will not be using the smaller dial at all (this measures mm), just the large outer dial which measures hundredths of a mm and has a least count of 0.001 mm. The Digital Thermometer To measure temperature, we will use an Extech EasyView digital thermometer (or a similar device) placed into the end of the metal sample to measure temperature. The digital thermometer is an example of digital reading where the device is less accurate than the display implies. PHY 1104: Thermal Expansion of Solids, Page | 4

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY An excerpt of the user manual is shown in figure 3. Examine the section that describes the accuracy of the digital thermometer. This accuracy describes the confidence or uncertainty of the reading in a particular temperature range. Notice that the accuracy of the measurement is a percentage of the temperature itself plus an additional amount of error. The steps you must take to determine the measurement uncertainty are a little bit different than for other digital devices that are more accurate than the display shows. For the thermometer the accuracy depends on what temperature you are measuring, and is reported as a percentage of the measurement with an additional uncertainty. Steps to take to find uncertainty in a digital thermometer Determine the uncertainty in your measurement (with units): 1. Consider the temperature range that you will be using to find the correct uncertainty formula in the manual. 2. Take your measurement. 3. Calculate the uncertainty for that measurement using the correct formula for the range you are in. Express your measurement with uncertainty in the correct format: 4. Round your uncertainty to one DIGIT. Keep in mind that you will be rounding the value up, except in extreme cases. 5. Determine the place (tens, ones, tenths, hundreds) where the uncertainty digit is. Round your measurement to that place, making sure that both the measurement and uncertainty have the same units. You are rounding your measurement to the least significant digit, since any digit in a place less than the least significant one is INSIGNIFICANT. 6. Report your measurement and uncertainty with the same number of decimal places and units. PHY 1104: Thermal Expansion of Solids, Page | 5

DEPARTMENT OF PHYSICS AND ASTRONOMY APPALACHIAN STATE UNIVERSITY ???? ?𝑖?ℎ ??𝑖?? ± ???????𝑖??? ?𝑖?ℎ ??𝑖?? It is easier to describe in an example of the temperature of steam: 1. Steam should fall in the range of -93°C to 1000°C which means the device has an accuracy of +/- (0.3% reading + 1°C) 2. Take the measurement: 96.7°C 3. Calculate the uncertainty in the measurement: +/- (0.003*96.7°C + 1°C) = 1.29°C 4. Round the error up and to 1 digit : 2°C The error should be rounded to one digit, which is in the ones place. It should also be rounded up, not down, so the calculated uncertainty of 1.29°C rounds to 2°C. 5. Round your measurement to the ones place to re port: 97°C +/- 2°C PHY 1104: Thermal Expansion of Solids, Page | 6

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