Thermal Expansion

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Thermal Expansion

Purpose

The purpose of the experiment was to learn how different materials change their lengths exposed to temperatures.

Introduction

Most materials do expand after being exposed to very high temperatures and then contract when there is a decrease in temperature. Therefore, various materials having the same length do not necessarily contract and expand equally due to changes in temperature; some of the materials contract and expand more compared to others based on their nature because of the amplitude average of vibration for the atoms within the materials increases after heating the material. It results in to increase in the average separation between the atoms. For instance, if one tries opening glass jar using a lid metal, it will definitely be easily open. The reason being metals expand more when compared to glass and after they have been exposed to very high temperatures. The increasing length of a material is known as linear expansion stated mathematically as .  Change in temperature is calculated by . The capability of a material is the coefficient of thermal expansion denoted as (). Given in units of .

Calculations;

 

Some materials are isotropic, which means they are going to expand in only one direction, so they need to be measure in one direction. In this experiment, I’m going to measure the coefficient of thermal expansion for Aluminum, copper, and brass as the temperature changes. Then, I’m going to compare my experimental values with the accepted values reported by the manufacturer of the metal rods to check the accuracy and precision of my results to finally find the percent error between my values and the theoretical values. My purpose is to prove that different materials with the same length expand different amounts under heat exposure.

Lab’s objectives

The lab objectives included measuring the coefficient of thermal expansion for Aluminum, copper, and brass as the temperature changes.

Lab activities

1. In this experiment, the first thing I did was to take the rubber lid off from the Steam Generator to fill the tank with room-temperature water using the glass cup.
2. After filling the tank approximately 3/4 full of water, I placed the rubber lid back over the top to close it.
3. There were two long plastic tubes attached to the rubber stopped; one of them was blocked with a tubing clamp while the other was free. I placed the closed tube inside the sink, and the free tube was placed inside a separate flask near to the right of the apparatus.
4. I set the dial of the Steam Generator from LOW to HIGH and turned it ON to allow it to boil the water inside the tank.
5. While the Steam Generator was heating the water, I measured the lengths of each of the three rods (Aluminum, Copper, and Brass) with a meter stick. I measured from the inner edge of the larger circular disk to the smaller disk’s inner edge.
6. I converted the values of the measurements from centimeter (cm) to meter (m) before recording the values in the data table.
7. Then, I mounted the aluminum tube in the Thermal Expansion apparatus with the larger disk to my left and the smaller disk to my right.
8. I tightened up the thumb-screw in the right end of the apparatus frame to lock the tube; I centered the foam insulator over the thermistor lug and connected the phone plug into the phone jack of the temperature sensor.
9. Next, I turned the digital indicator ON and pressed the Zero button to set the initial digital reading to zero.
10. I connected the Pasco Thermal Sensor to the computer, opened the T4a experiment software, and clicked the record button to record the temperature of the aluminum rod.
11. Using heat resistant gloves, I  took the free plastic tubing from inside the separate flask and stuck it on the right side of the aluminum rod to allow the steam to flow through the tube.
12. As the aluminum rod heated, the value of the temperature in the computer was increasing, and the digital indicator was reflecting the length that the metal tube was expanding.
13. Once the final temperature stabilized (stopped changing) and the value displayed in the digital indicator kept the same, I stopped the data collection and recorded the values of the Initial Temperature, Final Temperature, and Change in Length for the aluminum rod.
14. Using the protective gloves again, I removed the plastic tubing from the right side of the metal rod and put it back inside the auxiliary glass. I disconnected the phone plug, untightened the thumb-screw, and removed the aluminum rod from the Thermal Expansion apparatus.
15. I repeated the steps 7 through 14 with the other two metal rods. First, I did it with the copper rod and then, with the brass rod. I collected all the values in the data table.
16. After finishing collecting the data of the three metal rods, I turned the Steam Generator OFF.
17. I calculated the temperature change for all three metal rods using the values of the beginning and ending temperatures.
18. Then, I calculated the coefficient of thermal expansion for each of the three metals and compared my calculated values with the theoretical values registered in Table 1.
19. Using my experimental values and the theoretical values, I calculated the percentage of error for each metal.
20. Finally, I answered the four questions to check my understanding of this experiment.

 

Data analysis

Raw Data

 

 

Table 1. Accepted values for the coefficient of thermal expansion, α.

Material	α ()	Composition (%)
Aluminum (6061-T6)	23.6	Al (95.8-98.6), Mg (0.80-1.2), Fe (<0.70), Si (0.40-0.80)
Brass (C270)	20.3	Brass (63-68.5), Zn (31.3-37), Pb (0.1), Fe (0.07)
Copper (C122)	17.0	Cu (99.9), P (0.02 nominal)

 

 

 

Table 2. Collected values from the experiment.

 

Tube Material	Initial Length (m)	Initial Temperature (o)	Final Temperature (o)	Change of length (m)	Thermal Expansion Coefficient	Percent Error
Aluminum	0.751	21.875	97.383	0.00139		3.81%
Brass	0.751	21.859	98.367	0.00113		2.96%
Copper	0.751	22.016	98.180	0.00100		2.95%

 

Processed data

the first calculation I did was to convert the values for the Initial Length of each rod from a centimeter (cm ) to meter (m ), and I did by dividing the initial value by 100 because:

1m = 100cm

 

I did the same calculation to convert the values of the other two rods.

 

 

Then, using the values of the Initial Temperature () and the Final Temperature (), I calculated the Change in Temperature () using the following equation:

 

 

 

I used the same equation to find the Change in Temperature () of the other two rods.

 

 

Next, I converted the values of the Change of Length () from millimeter (mm ) to meter (m ) by dividing the values by 1000 because:

1m = 1000mm

 

I did the same calculation to convert the values of the other two rods from millimeter to meter.

 

 

 

Then, I proceeded to calculate the Experimental Coefficient of Thermal Expansion (α) using the following equation:

 

 

 

 

I used the same equation to find the Experimental Coefficient of Thermal Expansion of the other two rods.

 

 

I calculated Percent Error using the equation below;

 

 

 

 

%

I repeated the same calculation to find the percent error of the other two metal rods.

%

%

 

 

Questions:

After completing the experiment and all the calculations, I was able to answer the questions to check my understanding. The questions are the followings:

Question one

The material with the largest coefficient of thermal expansion is Aluminum.

Question two

Civil engineers leave gaps between segments to allow the materials to expand under heat exposure and to recoil under low temperatures. Those gaps prevent the bridge or the concrete wall from breaking off.

Conclusion

This experiment’s main purpose was to show how different materials with the same initial length are affected differently when exposed to temperature changes, in this case, to an increase in the temperature. The materials used were three metal rods: one made of Aluminum, other made of copper, and the last one made of brass. I heated each of the three different rods and calculated their thermal expansion coefficient to then proceed to compare those values with the theoretical values and find the percent error between them.

In this experiment, I was able to demonstrate that different materials expand at different rates when heated. I was also able to learn how high temperatures affect the magnitudes of those metals by calculating their thermal expansion coefficient. After finishing this experiment, I can say that I accomplished my goal because I obtained very precise values for the coefficient of thermal expansion of each of the three metal rods with very low values of percent error. The percent error between the experimental coefficient of expansion and the theoretical coefficient of thermal expansion for each metal rod was: 3.81 % for the aluminum rod, 2.95 % for the copper rod, and 2.96% for the brass rod.

Even though my percent error was quite low for each material, I can assume that there were some systematic errors because all experiment has limitations. One possible source of error is the fact that none of the rods were heated at the same temperature because I stopped the data collection as soon as the values of the change of length stopped changing. In other words, not waiting enough time to allow the rods to get heated the time necessary to expand at their maximum could lead me to obtain erroneous values. However, I’m very pleased with my results because I demonstrated that the coefficient of thermal expansion for Aluminum, copper, and brass is not the same even though they were heated at similar temperatures.  To conclude, different materials with the same initial length expand by different amounts as the temperature increases due to the nature of the material that is being heated.