Expansion of Solids
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. An object's temperature, on the Kelvin [K] scale, is proportional the object's internal kinetic energy. When heat energy (measured in Joules [J]) is transferred to the object, its constituent particles begin moving faster, thus maintaining a greater average separation and therefore expanding. Materials which contract with increasing temperature are uncommon.
If the object undergoing expansion has a predominant dimension (for example, a long metal rod), it is helpful to only observe expansion in that dimension. This is called linear thermal expansion. Each material has its own coefficient of linear thermal expansion (α). This coefficient indicates what percentage of its original length an object will expand per degree Celsius. The coefficient is found by dividing the percent change in length by the change in temperature (ΔT). Percent change in length is equal to the change in length (ΔL) divided by the original length (L0).
ΔL = L0α(ΔT) (1)
WARNING: THIS LAB USES BOILING WATER AND STEAM! PLEASE BE VERY CAREFUL WHEN HANDLING THE STEAM POT OR THE HOT METAL!
- Pasco thermal expansion apparatus
- Metal rods
- Steam generator, cap, and rubber hose
- Watch glass
- Paper towels
- Digital multimeter
- Thermistor or Digital Thermometer
- To discover how heat affects the dimensions of different metals.
- Review how to use a micrometer.
- To learn how determine temperature using a thermistor.
- To practice controlling variables in order to determine a physical property of a material.
Activity 1: Measuring the coefficient of linear thermal expansion
As steam is sent through a metal pipe, the pipe expands. This expansion is very small, and must be measured using a metric dial. See this detailed apparatus description for help using the dial. When the metal rod expands, it will push against the micrometer needle. Examine the metric dial to determine the units and precision. In order to get three significant figures in your measurement of ΔL, you will need to estimate the reading to the nearest fifth of a division.
Instead of the thermistor, we will use an Extech EasyView digital thermometer placed into the end of the metal sample to measure temperature. Here is a link to the manufacturer's user manual. Use this user manual (the section titled "Accuracy" in the Specifications table) to determine the uncertainties in your temperature measurements.
One more thing: Although the entire metal sample is expanding you are only measuring the expansion that takes place between the two clips. One clip is anchored in the mounting bracket, and the other presses against the micrometer needle. Therefore when determining L0, you are not concerned with the total length of the rod, just the effective length between the clips.
The tube from the steam pot attaches to one end of the metal rod, and a watch glass should be placed at the other end to catch the condensing steam. When the steam from the steam pot enters the rod, it will expand. You will need to watch carefully for maximum temperature and expansion.
Calculate the coefficient of linear thermal expansion. Propagate your error and display the uncertainty in your rinal result.
Locate a table of linear thermal expansion coefficients online or in your textbook and compare your experimental results to the accepted value using percent error. Be sure to cite your reference in your notebook!
Activity 2: Repeating for a different material
Allow the apparatus to cool sufficiently and repeat the experiment on one other metal sample.
Activity 3: Analysis of error
Use the following questions to develop a thorough analysis of error.
- Which of the rods had the lowest calculated percent error? Do you have any thoughts on why there seemed to be a difference in accuracy between rods?
- Measurements of three different quantities were made to determine the coefficient of linear expansion, namely the original length, the change in length, and the change in temperature. Each measurement has its own associated uncertainty, δ, which should be recorded in your data section. Which of these measurements contributes the greatest error in the final result? (Hint: Which has the greatest fractional error?) Does this make sense? Explain your reasoning.
- Is uncertainty of measurement alone enough to explain the percent error in your results? If not, identify the sources of experimental error that could explain the difference between your values and the accepted values.
- In addition to random errors, can you discuss any types of systematic error that may be present in each type of measurement?
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