Linear Expansion Coefficient

https://www.youtube.com/watch?v=m7tTUW1XHbQ

The part to watch is about 10 minutes long.

Theoretical considerations. It is found that most solids expand when heated. The change in length, DL, of the solid is found to be directly proportional to the original length of the solid, L_o, and to the change in temperature, DT, of the solid. Stated mathematically,

DL L_oDT

Letting be the proportionality constant, then

DL = aL_oDT

where a is called the coefficient of linear expansion. It is a constant for a given solid depending upon the material composition of the solid. Solving for we see that is the fractional change in length of the solid per unit temperature change. The temperature change is measured in Celsius degrees, and L_o is the length of the solid at 0^oC. However, little error will be introduced into this experiment if L_o is taken as the length of the solid at room temperature.

The change in length of the solid is very small, therefore, a micrometer is used in this experiment to measure the change in length, DL. When the metal rod expands in length, the dial indicator will register the change in length.

Materials

Power Macintosh or Windows PC Universal Lab Interface	Vernier Temperature Probe
Logger Pro	Steam generator
Expansion Chamber and Rods

Procedure:

1. Measure the length of the rod at room temperature and record this value in your data table.

2. Place the rod in the cylinder using corks at each end. Adjust the thumbscrew at one end until the dial on the indicator at the other end just starts to move. Set the face of the dial indicator to read zero. Warning: Do not jam the rod into the dial indicator, irreparable damage to the indicator will occur. The dial indicator scale is divided into .01millimeters.

3. Carefully place a Vernier thermometer through the rubber stopper in the center of the cylinder. Connect the Temperature Probe to the Universal Lab Interface. Prepare the computer for data collection by opening an appropriate temperature-collecting program from the Physics with Computers experiment files of Logger Pro. Once the temperature reading has stabilized, record the value in your data table.

4. Fill thesteam generator so it is about 2/3 full. Attach the boiler tube to the upper inlet of the apparatus and heat the water. Be careful not to disturb the apparatus.

5. Heat the water and allow steam to pass through the cylinder. Place a beaker at the other outlet of the cylinder to catch condensation.

6. Allow the rod to come to thermal equilibrium (until the dial has stopped moving). Record the thermometer reading and the dial reading. Print a copy of the temperature graph for proof of the temperature reached.

7. Repeat the experiment using a second and third rod of different materials.

Data Table:

Material	L0 m	L m	Ti C	Tf C	T C
Aluminum	0.60	1.09 x 10-3	24.1	100.1
Brass	0.70	1.01 x 10-3	23.0	99.7
Unknown	0.55	6.98 x 10-4	25.2	100

Data Analysis Table

Material	Experimental	Accepted /oC	Error %
Aluminum		24.0 x 10-6
Brass		19.0 x 10-6
Identify the metal

Questions.

1. Explain how the metal was identified.
2. Give two reasons why it is important to pay attention to thermal expansion and contraction

in real-life situations.