Coefficient of Linear Expansion
The objective is to measure the coefficients of linear expansion for a few selected substances.
Thermal expansion apparatus, a few different metal rods, strain gauge, thermometer, water heater, rubber seals, and calculator
Objects generally expand due to increase in their temperatures. There are few exceptions. For example, water expands at freezing causing ice to be less dense than water and float. Conversely, when ice is heated up, its volume shrinks. This is true for water up to 4˚C. Following is a brief explanation of the thermal expansion of solids, specially for linear expansion that applies to wires and thin rods.
Thermal Expansion of Solids:
Coefficient of Linear Expansion (α ):
The coefficient of linear expansion, α, is defined as the change in length per unit length per unit change in temperature. Mathematically,
1) Fill the water heater to about 2/3 and turn it on to bring water to boil.
2) Measure the initial length, Lo of the expansion rod by a meter stick to the best possible estimate and record the result in (mm).
3) Place the linear expansion apparatus on the table and insert an expansion rod into it with one end in contact with the fixed end.
4) Mount a strain gauge at the other end of the rod such that it is barely in contact with it.
5) Place a thermometer in the appropriate hole on the apparatus (through an appropriate rubber bushing) to where its bottom is in contact with the rod.
6) By turning the outer rim of the strain gauge, it can be adjusted to zero. It is difficult to have the free end of the rod to barely touch the strain gauge, and at the same time have the gauge adjusted to zero. To solve this problem push the gauge slightly toward the free end of the rod to where it does not reads zero. It really doesn’t matter what it reads, as long as it is slightly passed zero, it assures you of being in contact with the rod and it will do the job. Watch the gauge for possible changes in length of the rod due to possible temperature changes. When the gauge is not changing, record its initial reading Ri as well as the initial temperature, Ti.
7) When water starts boiling and producing a good amount of steam, connect the boiler to the apparatus via its rubber hose. As soon as steam reaches the rod, you will see its expansion by observing the gauge. However, as steam reaches the apparatus, it condensates. If there is a good flow of steam into the apparatus, we may think that, at condensation, the temperature of the system is equal to the condensation temperature of water (nearly 99 ˚C, in the Lab). The rod may not exactly be at that temperature, because its ends lose heat to the ambient. The rod temperature read by the thermometer (placed in the apparatus), may be used as the final temperature, if equilibrium is reached. Equilibrium is reached when at a good flow of steam, the thermometer reading is constant and the gauge is not showing any further expansion. Record the final temperature, Tf , and the final gauge reading, Rf .
8) Calculate Δ L and Δ T from equations: ΔL = Rf – Ri and ΔT = Tf – Ti.
9) Calculate the measured value of α , by using the formula:
10) Calculate a %error for this coefficient by comparing it with its accepted value that you obtain from your text or a physics handbook.
11) Repeat the experiment for other materials that are made available in the Lab.
Three typical values for α are:
αCu = 17x10-6 °C , αFe = 11.7x10-6 °C , and αAl = 24x10-6 °C.
Comparison of the results:
Provide the %error formula used and the calculated amounts.
State your conclusions of the experiment.
Provide a discussion if necessary.