MAPUA INSTITUTE OF TECHNOLOGYDepartment of Physics E301: LINEAR EXPANSION DIZON, Joshua Dominic C. 2013150714 BSCE-2 Group 2 PHY12L-A4 SCORE: Analysis Conclusion Presentation TOTAL Engr. Ericson D. Dimaunahan Instructor July 30, 2015 /25 /25 /10 area expansion for two and lastly. Initially. your choice) in the expansion base. the lug should be aligned along the tube as shown the picture below. The amount of expansion not only depends on the amount of change in temperature but on the initial state of body as well. 1 Mounting of metal tube into the bracket Next. we measured the initial length of the aluminum metal tube and copper metal tube. Make sure that the stainless steel pin on the tube fits into the slot of the slotted mounting block and the bracket on the tube presses against the spring arm of the dial gauge otherwise you will get erroneous results. After that. we are also to determine the factors affecting the change in length in thermal expansion. Materials in general. To ensure maximum contact between the lug and the tube. Fig.Analysis All matters. we are to determine the coefficients of linear expansion of two different metal rods. aluminum and copper. There are three kinds of dimensional change. linear expansion for one dimensional. . Using the concept we learned. In this experiment. volume expansion for three dimensional objects. with the exception of water experience a change in its dimension in response to the change in their temperatures. expand when their temperatures increase and shrink as their temperatures decrease. we mounted the tube (aluminum or copper. We measured 702 mm initial length for the aluminum metal tube and also 700 mm for the copper metal tube. we attached the thermistor lug to the threaded hole in the middle of the tube using a thumb screw. We recorded both of the measurement as the initial length Lo . 600 Ω 25. the gauge.4167 ℃ 99. Initial Temperature At this juncture.Fig. we need to boil the water using the steam generator. .2 Attachment of the thermistor lug to the threaded hole. The resistance of the thermistor at room temperature was then determined and recorded as R rm. Metal Tube Aluminum Copper Initial Resistance Initial Temperature 102. After that. But most importantly.08785 ℃ Initial Resistance vs. This resistance will be an indicator of what is the initial temperature of the metal tube that you mounted in the expansion base. and the screws or any adjustments needed to be adjusted to make a remarkable data. We also need to adjust the gauge to zero so that the reading will be accurate.800 Ω 24. we now have the initial temperature of the metal tube. plug the leads of the ohmmeter (multi-tester) into the banana plug connector of the thermistor located in the center of the expansion base. You can determine the equivalent temperature of the Rrm by looking at the thermistor temperature vs. We need to fill the container of the steam generator ¾ its height. resistance table. we can now start to setting up the expansion base. temperature table.Fig. temperature table located in the expansion base. diagonals etc.08411 ℃ 79. This is caused by the intermolecular forces of attraction of the molecules wanting to collide because of the effect of the heat making a difference in the range of resistance. We can get the final temperature by simply looking at the resistance vs. 3 Boiling of water using the steam generator Now.260 Ω 71. copper has the higher final temperature than that of . Because of this. it only shows that the resistivity of aluminum metal is higher than that of the copper. Resistance of Thermistor in Final Temperature and Equivalent Final Temperature Aluminum Metal Tube Copper Metal Tube 14. as the resistance decreases.900 Ω 11. Any thermal expansion of a thing that has experienced thermal change will experience change in linear dimension including its edges. determine the change in temperature by getting the difference in the t hot and trm for each trial. Observe now the dial gauge and determine the increase in length ∆L and simultaneously get the resistance of the thermistor R hot. I observed that according to the table of the resistance vs. thickness. temperature in the expansion base. Find the equivalent final temperature of the tube t hot. the metal tube is expected to expand at an insignificant change in length.092 ℃ Now. Because heat is being applied or a transition of energy is applied in the system which is the metal tube. It is vital to raise one end of the expansion base during the process so that condensed water shall drain out. In the table above. the temperature increases. Attach a rubber tube from the steam generator to the end of the tube farthest from the dial gauge then turn on the stream. After that we can turn on the stream generator. set up the main of the experiment. You should interpolate when there is no direct equivalency on the data you got to the resistance vs. Expect draining water at the end of the tube. the whole experiment is now finished. the more resistance there will be. More collisions mean more resistance. As the resistivity of a material is higher. Having this proportionality between the resistance and the temperature. I can say that in terms of resistivity. the initial temperature of a material and the final temperature of a material having heat transferred to it will decrease. we can establish also the relationship between resistance. . because copper is softer than aluminum resulting the copper to have higher temperature than aluminum. I can say that as the material is longer. aluminum is better than copper which gives aluminum a lower temperature than copper (whether it is initial or final depending on the transfer of heat to the system). Here is the table indicating the change in length of aluminum and copper. In terms of conductivity. temperature and the change in length. copper conducts electricity more efficiently than aluminum. Aluminum and copper are one of the best materials in terms of resistivity. if resistance occurs as the result of collisions between charge carriers and the atoms of the wire. then there is likely to be more collisions in a longer wire. Having these speculations. but they differ in some aspects because of the unique composition between the two metals. There is a direct relationship between the amount of resistance encountered by charge and the length of wire it must traverse.79 mm We can see from the table from the above that aluminum metal tube increased more in length than that of the copper metal tube.019 mm 0.the aluminum metal tube. Change in Length Aluminum Metal tube Copper Metal Tube 1. Analyzing these unique characteristics between the two. Relating the change in length to the resistance. I can say that the resistivity of a material is directly proportional to that of the change in length of the material undergoing heat transfer. I can say further that the total length of a material affects the entire resistivity capacity of that material. From here. we can reconnect the resistivity of a material to the temperature (whether it is initial or final). And because of this. With this notion. After all. You can now compute for the experimental value for the coefficient of linear expansion using the equation: ∆ L=Lo α ∆ t . Since the laboratory room we . The table for the percentage error of the two materials: Aluminum Metal Tube Copper Metal Tube 54.80 x 10-6 / 16. as the change in temperature is increasing. this experiment must be conducted in a room temperature place. and according to our data. the coefficient of linear expansion is directly proportional to the change in length (L f – Lo) so. the coefficient of linear expansion will now decrease and it satisfy the data we have gathered. Here are the actual coefficients of linear expansion of the material used: Aluminum metal tube Copper metal tube 23. we can elucidate the relationship of the variables in and constants in the equation. the coefficient of linear expansion of the aluminum metal tube is higher than copper. But as we can see.67 x 10-5 / ℃ 2. the possible sources of error are the following: The temperature of the surrounding. the change in length is also increasing. Using this equation: ∆ L=α Lo ∆ T . According to the lab manual. the experimental coefficient of linear expansion is slightly different compared to the actual coefficient of linear expansion but they are close enough to be alike. So it means.414 % In the performance of the experiment. it satisfy this relationship.275 x 10-5 / ℃ As we can see.80 x 10-6 / ℃ ℃ And here are the experimental values for the coefficient of linear expansion we get from the series of data we have collected during the performance of the experiment: Aluminum Metal Tube Copper Metal Tube 3.05 % 35.We can now compute for the percentage error we commit between the experimental values of the coefficient of the linear expansion of the specific material. As we can see. The coefficient of linear expansion is inversely proportional to the change in temperature. if the coefficient of linear expansion is increasing. Wrong measurement of the initial length of the aluminum and copper. we were . Since we are using only meter stick. In the experiment. Remember.used has air conditioning unit. Remember. From this experiment. the metal tube will react to the temperature of the surrounding making the cooling of the metal tube faster than in a normal room temperature. Wrong reading of the resistance of the tubes both in initial and heated phase. Wrong measurement of the expansion base with built-in gauge. we learned about the one-dimensional expansion called linear expansion and we were able to determine the coefficient of linear expansion of two different metal rods. we have learned that thermal expansion is the tendency of a matter to increase in dimension or volume when the matter is being heated. a wrong reading of resistance will give us a wrong calculation for the initial and final temperature and will lead to a wrong change in temperature so it is very crucial to measure the resistivity of the tubes accurately. With the use of the equation provided and the concept we know about thermal expansion. temperatures and electrical resistance. CONCLUSION The objectives of this experiment are to determine the coefficient of linear expansion of a metal rod and to determine the factors affecting the change in length in thermal expansion. the final length of the metal tube will be given by the gauge if the hand of the gauge stopped moving which will give us the expansion. we based the measurement on how our eyes see and not what the accurate measurement is. Obtaining different values final length. wrong measurement is a source of error. there are three factors that mainly affect the change in length of a material. we can see that the coefficient of linear expansion is directly proportional to the change in length of the material. the more it will expand.able to compare the two subjects of their difference in their physical properties. At the end. the higher the coefficient. Errors in this experiment may arise because of the following reasons: wrong measurements of the length.05 % for aluminum and 35. and resistance and the most important. The expansion of any materials depends on the value of its coefficient of linear expansion. all metals have unique values of coefficients of expansion. Obviously. the coefficient of linear expansion will also increase. as the change in length tends to increase. a minor difference on the hundred thousandths value can greatly affect the percent error. there are errors that our group commits (54. the initial length of the material being observed and the change in temperature. the temperature of the surrounding. Analyzing the equation ∆ L=α Lo ∆ T . Apparently. gauge.414% for copper). we managed to obtain close experimental coefficient of linear expansion to what is the actual value since the coefficient of linear expansion is really small. Therefore. All of these can be considered as one of the factors in determining the change in length during thermal expansion. For the second and final objective. so the set of data we have gathered is not very accurate but still. aluminum has greater change of length than copper. Based on the results and data we have gathered. these are the coefficient of linear expansion. . it was too high. I therefore conclude that the coefficient of expansion of a material is directly proportional to its expansion.