# Experimental Report H7

Topics: Coefficient of thermal expansion, Young's modulus, Thermal expansion Pages: 6 (1525 words) Published: September 17, 2010
Experimental Report
Aim
The objective of the laboratory report was to determine the thermal expansion coefficient of copper and other materials by measuring the relative change in length of bars of the materials as a function of temperature.

Introduction
The average coefficient of thermal expansion α over a temperature interval ΔT is given by

ΔL / L0 = ΔT

Where L0 is the length at some initial temperature, and
ΔL is the change in length corresponding to a change in temperature ΔT.

Therefore the thermal expansion coefficient can be determined from the slope of a graph of the relative change in length Δ L/L0 versus temperature change Δ T.

Experimental Method
1. A small amount of water was placed in the copper "kettle" (there was enough water so it did not take all day for it to boil, and not too little so it would have boiled dry). The "kettle" was placed on the tripod with an asbestos mat and heated with the bunsen burner. 2. The rest of the apparatus was set up as shown below.

kettle
test material
bunsen burner

Figure 1. Apparatus showing the set up and items used for the experiment.

3. The dial gauge was observed to understand how to read it. The initial length Lo was marked on the apparatus, and the room temperature. 4. When the water boiled the temperature of the bar was noted with the thermocouple thermometer and the dial gauge reading was also noted. These are the initial conditions taken. 5. The bunsen burner was then turned off.

6. As the bar cooled, the temperature was noted as well as the dial gauge reading every ten degrees. From this the calculation of the change in length Δ L and change in temperature Δ T from the initial conditions were done. 7. A graph of Δ L/Lo versus Δ T was then plotted. The thermal expansion coefficient α was then found from the slope of the graph. 8. The stop screw was undone on the non-dial gauge end of the steam jacket, (reference to Figure 1was used, and the test rod was then carefully removed). Replacing with another test rod, steps (3) to (7) were repeated.

Results
Material | Aluminum|
Temp (◦C)| Extension (mm)| Δ L/Lo| Δ T (◦C) |
96.6| 0.50| 1.515 * 10-3| 71.6|
86.6| 0.4607| 1.264 * 10-3| 61.6|
76.6| 0.378| 1.145 * 10-3| 51.6|
66.6| 0.30| 0.909 * 10-3| 41.6|
56.6| 0.22| 0.667 * 10-3| 31.6|
46.6| 0.148| 0.449 * 10-3| 21.6|
36.6| 0.07| 0.212 * 10-3| 11.6|
29.5| 0.025| 0.076 * 10-3| 4.5|
Table 1. Results from the experiment of aluminum
Material | Copper|
Temp (◦C)| Extension (mm)| Δ L/Lo| Δ T (◦C) |
97.5| 0.36| 1.091 * 10-3| 75.2|
87.5| 0.32| 0.970 * 10-3| 65.2|
77.5| 0.27| 0.818 * 10-3| 55.2|
67.5| 0.222| 0.673 * 10-3| 45.2|
57.5| 0.177| 0.536 * 10-3| 35.2|
47.5| 0.13| 0.393 * 10-3| 25.2|
37.5| 0.092| 0.279 * 10-3| 15.2|
30.5| 0.052| 0.158 * 10-3| 8.2|
Table 2. Results from the experiment of copper

Data analysis
To find the coefficient of thermal expansion, the change in length is divided by the initial length. This is shown by the formula:
Δ L/Lo
Example from the results of Aluminum: 0.5mm / 330mm = 1.515 x 10-3 The results are shown above in Tables 1 and 2.
See appendix for graph of Thermal Expansion Δ L/Lo vs. ΔT Experimental Discussion
Problem
(1) In order to find if the expansion gaps have closed up you need to find how much the material will expand at the temperatures given. To calculate this certain data of the material is needed. The material has an expansion coefficient of 20 x 10-6 ◦C

Each beam member of the bridge is 50m long with a cross sectional area of 5m2. To find the thermal expansion of the beam is can be expressed linearly. Δ L = L0 α (t1 - t0)         (1)
where
Δ L = change in length (m)
L0 = initial length (m)
α = linear expansion coefficient (m/m ◦C)
t0 = initial temperature (◦C)
t1 = final temperature (◦C)
Δ L = 50m x (20 x 10-6 ◦C) x (60 ◦C – 20 ◦C)
Δ L =...